**Calibration Approaches**

**Chapter 2**

**Provisional chapter**

**Analytical Calibrations: Schemes, Manuals, and**

**Analytical Calibrations: Schemes, Manuals, and** 

DOI: 10.5772/intechopen.72580

Chemical measurement processes (CMPs) must be performed in a setup of controlled statistical conditions. Thus, validation of such a measurement process and assessment of its ability to accurately measure the analyte is important. Analytical calibration is the most crucial step in any analytical procedure targeting the estimation of analyte concentration. As a key component of any validation procedure, calibration must be properly conducted. To achieve that, firm knowledge with the realms of the calibration process must exist. Several jurisdictions help to build up this acquaintance, including the terminology and definitions, the international guidelines and how they differ, schemes and manuals to be used to build a calibration model, metrological considerations, and assessment procedures. Careful thinking prior to any of the previous calibration aspects is necessary and helps to improve the product of the calibration process. Throughout this chapter, aspects of the calibration assembly will be thoroughly discussed. Different types of calibration will be revealed with a focus on analytical calibration for a CMP. Steps for a successful calibration will be described. The reader will be able to use information given throughout

**Keywords:** analytical calibration, terminology, regulatory agencies, multi-, one- and

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Millions of analytical investigations are instigated every day. Despite the massive progress and advancements implemented to the developed techniques and instrumentations, calibration stays as the most critical stage in every analytical practice leading to the estimation of the

**Metrological Deliberations**

**Metrological Deliberations**

http://dx.doi.org/10.5772/intechopen.72580

Additional information is available at the end of the chapter

this chapter as a guide for an effective calibration process.

two-standard calibrations, calibration methodologies

Additional information is available at the end of the chapter

Marwa S. El-Azazy

**Abstract**

**1. Introduction**

target analyte.

Marwa S. El-Azazy

### **Chapter 2**

**Provisional chapter**

### **Analytical Calibrations: Schemes, Manuals, and Metrological Deliberations Metrological Deliberations**

**Analytical Calibrations: Schemes, Manuals, and** 

DOI: 10.5772/intechopen.72580

Marwa S. El-Azazy Marwa S. El-Azazy Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72580

#### **Abstract**

Chemical measurement processes (CMPs) must be performed in a setup of controlled statistical conditions. Thus, validation of such a measurement process and assessment of its ability to accurately measure the analyte is important. Analytical calibration is the most crucial step in any analytical procedure targeting the estimation of analyte concentration. As a key component of any validation procedure, calibration must be properly conducted. To achieve that, firm knowledge with the realms of the calibration process must exist. Several jurisdictions help to build up this acquaintance, including the terminology and definitions, the international guidelines and how they differ, schemes and manuals to be used to build a calibration model, metrological considerations, and assessment procedures. Careful thinking prior to any of the previous calibration aspects is necessary and helps to improve the product of the calibration process. Throughout this chapter, aspects of the calibration assembly will be thoroughly discussed. Different types of calibration will be revealed with a focus on analytical calibration for a CMP. Steps for a successful calibration will be described. The reader will be able to use information given throughout this chapter as a guide for an effective calibration process.

**Keywords:** analytical calibration, terminology, regulatory agencies, multi-, one- and two-standard calibrations, calibration methodologies

### **1. Introduction**

Millions of analytical investigations are instigated every day. Despite the massive progress and advancements implemented to the developed techniques and instrumentations, calibration stays as the most critical stage in every analytical practice leading to the estimation of the target analyte.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

An analytical measurement process is a setup with a demarcated configuration that has been carried to be statistically controlled under the designated experimental conditions. To substantiate the efficacy of analytical processes and subsequently the applicability in routine analysis, the ability of such a method to "quantify" must be assessed. Thus, and to fetch such a status of statistical management, key elements including *validation*, and hence its metrological frontier, *calibration*, must be clearly comprehended [1].

**2. Calibration in analytical sciences: fundamentals**

alone in the above definition is perceived as being calibration.*"*

**Figure 1.** Schematic representation of the different approaches for calibration.

types of processes, etc.

Several definitions exist in literature for calibration. In addition to the previously mentioned definition given by the VIM [2, 3], IUPAC definition of calibration can be viewed as a "general" description where it is given as "an operation that relates an output quantity to an input quantity" [9]. Unfortunately, these definitions instead of giving a clear-cut understanding of the term and the corresponding process have created a kind of confusion where it is common to find the wrong term being given to the wrong process or similar names given to different

Analytical Calibrations: Schemes, Manuals, and Metrological Deliberations

http://dx.doi.org/10.5772/intechopen.72580

19

However, it is noteworthy to mention that the additional "notes" given by the JCGM [3] on the definition of calibration would clarify this misunderstanding where: "A calibration may be expressed by a statement, calibration function, calibration diagram, calibration curve, or calibration table. In some cases, it may consist of an additive or multiplicative correction of the indication with associated measurement uncertainty" and "Calibration should not be confused with adjustment of a measuring system, often mistakenly called 'self-calibration', nor with verification of calibration.*"* Furthermore, and according to JCGM, "Often, the first step

Yet, and as per these definitions, it is important to distinguish between the different types of calibration and whether it is designed for a qualitative or a quantitative purpose. As a relation between an input quantity and another output quantity, quantitative calibration can be performed *directly* (where the measurement and the reference values are being compared

In the latest definition released by the Joint Committee for Guides in Metrology (JCGM) in their 3rd edition of the "International Vocabulary of Metrology, VIM", calibration is: "operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication*"* [2, 3]. Validation, in the same edition, was defined as "verification, where the specified requirements are adequate for an intended use.*"*

Though *validation* as an idiom is already well-known, the protocols of its application are not clear for many of the analytical chemists. No need to say that validation of an already developed analytical process must be performed following a clearly written protocol and through a series of laboratory experiments. Moreover, different regulatory bodies (e.g., IUPAC, ICHQ2R1) do have different nomenclature for such a term (as well as its components) and hence dissimilar manuals, an issue that in turn leads to different performance and approval criterions [4, 5].

As a component of the validation process, calibration is also a subject of controversy in terms of vocabularies, the perception of the calibration procedure starting with method development to fitting of results obtained, implementation of the appropriate linearity testing, and hence the assessment of goodness-of-fit and deviation from linearity.

It is very important to recognize that though the existence of intrinsic discrepancies between chemical (CMPs) and physical (PMPs) measurement processes in terms of uncertainty associated with the results and the availability of reference materials; both are still treated with the same metrological approach. Yet, an imperative difference between both processes must be carefully considered which is *calibration* [6–8].

The purpose of this treatise is to shed light on the "appropriate" definition of calibration as a process that encompasses metrological/statistical as well as procedural evaluation of the analytical measurement. The different types of calibration will be revealed. Analytical calibration, across the different guidelines and with respect to definitions and terminologies, schemes, metrologies, and methodologies will be discussed.

Though in some sections of this piece complicated terminologies would be used, a reader of this chapter, even if not from the scientific community, would be able to understand information given with the help of definitions revealed in almost every section.

### **2. Calibration in analytical sciences: fundamentals**

An analytical measurement process is a setup with a demarcated configuration that has been carried to be statistically controlled under the designated experimental conditions. To substantiate the efficacy of analytical processes and subsequently the applicability in routine analysis, the ability of such a method to "quantify" must be assessed. Thus, and to fetch such a status of statistical management, key elements including *validation*, and hence its metrologi-

In the latest definition released by the Joint Committee for Guides in Metrology (JCGM) in their 3rd edition of the "International Vocabulary of Metrology, VIM", calibration is: "operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication*"* [2, 3]. Validation, in the same edition, was defined as "verification, where the specified

Though *validation* as an idiom is already well-known, the protocols of its application are not clear for many of the analytical chemists. No need to say that validation of an already developed analytical process must be performed following a clearly written protocol and through a series of laboratory experiments. Moreover, different regulatory bodies (e.g., IUPAC, ICHQ2R1) do have different nomenclature for such a term (as well as its components) and hence dissimilar manuals, an issue that in turn leads to different performance and approval

As a component of the validation process, calibration is also a subject of controversy in terms of vocabularies, the perception of the calibration procedure starting with method development to fitting of results obtained, implementation of the appropriate linearity testing, and

It is very important to recognize that though the existence of intrinsic discrepancies between chemical (CMPs) and physical (PMPs) measurement processes in terms of uncertainty associated with the results and the availability of reference materials; both are still treated with the same metrological approach. Yet, an imperative difference between both processes must be

The purpose of this treatise is to shed light on the "appropriate" definition of calibration as a process that encompasses metrological/statistical as well as procedural evaluation of the analytical measurement. The different types of calibration will be revealed. Analytical calibration, across the different guidelines and with respect to definitions and terminologies, schemes,

Though in some sections of this piece complicated terminologies would be used, a reader of this chapter, even if not from the scientific community, would be able to understand informa-

hence the assessment of goodness-of-fit and deviation from linearity.

tion given with the help of definitions revealed in almost every section.

cal frontier, *calibration*, must be clearly comprehended [1].

18 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

requirements are adequate for an intended use.*"*

carefully considered which is *calibration* [6–8].

metrologies, and methodologies will be discussed.

criterions [4, 5].

Several definitions exist in literature for calibration. In addition to the previously mentioned definition given by the VIM [2, 3], IUPAC definition of calibration can be viewed as a "general" description where it is given as "an operation that relates an output quantity to an input quantity" [9]. Unfortunately, these definitions instead of giving a clear-cut understanding of the term and the corresponding process have created a kind of confusion where it is common to find the wrong term being given to the wrong process or similar names given to different types of processes, etc.

However, it is noteworthy to mention that the additional "notes" given by the JCGM [3] on the definition of calibration would clarify this misunderstanding where: "A calibration may be expressed by a statement, calibration function, calibration diagram, calibration curve, or calibration table. In some cases, it may consist of an additive or multiplicative correction of the indication with associated measurement uncertainty" and "Calibration should not be confused with adjustment of a measuring system, often mistakenly called 'self-calibration', nor with verification of calibration.*"* Furthermore, and according to JCGM, "Often, the first step alone in the above definition is perceived as being calibration.*"*

Yet, and as per these definitions, it is important to distinguish between the different types of calibration and whether it is designed for a qualitative or a quantitative purpose. As a relation between an input quantity and another output quantity, quantitative calibration can be performed *directly* (where the measurement and the reference values are being compared

**Figure 1.** Schematic representation of the different approaches for calibration.

employing the same units) or *indirectly* (where the measured response is being decoded into the corresponding quantity to be determined, i.e., *analytical calibration*). Both *direct* and *indirect* calibrations can target the equipment as well as the process itself [10]. More details on these subdivisions will be given under the relevant section.

• How to select the concentrations that will be measured?

• How many times the analysis should be repeated (replications)?

• How the calibration mode will be set? (details will be discussed later)

The elements of *calibration hierarchy* according to JCGM [3] *are one or more measurement standards and measuring systems operated according to the measurement procedure*. Typically, a minimum of 5–6 calibration standards is used for this purpose. Yet, the number of standards used might vary according to the performed analytical process as well as the guidelines proposed by the supervisory body followed. The calibration standard might be *matrix-free* if the purpose is to calibrate solvents, for example, or *matrix-matched* (*MMC*) if it is expected that the presence of matrix would affect the response signal and hence the calibration outcomes. In

Analytical Calibrations: Schemes, Manuals, and Metrological Deliberations

http://dx.doi.org/10.5772/intechopen.72580

21

Careful distribution of the selected concentration levels over the working range is necessary for appropriate calibration. In this concern, discrimination between narrow and wide calibration ranges is essential. Attention should be paid for the case where a wide concentration range is calibrated where keeping the selected levels at very wide distances, a common approach in literature, might deteriorate the detecting system of the instrument, an issue that produces erroneous readings. The best approach is to keep the data points consistently dispersed across the selected range. Moreover, selected concentrations should be independently

Selection of the concentration range to be covered should be based on the expected content of the real samples taking in consideration the matrix and the intended application of the proposed procedure [14]. According to ICH guidelines, for example, if the calibration is performed on an active ingredient or a final product, the range is usually 80–120% of the analyte concentration [4]. In case of using MMC, the blank sample (zero concentration, solvent)

The appropriate protocol for a measurement will be the one that simulates the actual circumstances. In this itinerary, it is recommended that calibration samples are to be unevenly analyzed instead of being measured in an increasing concentration sequence. Moreover, insertion of calibration standards randomly in between the unknown samples within the measurement

Every experiment is associated with an error! Diminishing the random error (measurement uncertainty) and hence improving the precision is usually one of the goals when analytical calibration is performed. Replicate analysis is usually the approach. The number of recommended replicates differs according to the implemented guideline. While EMA, FDA, and AOAC indorse five replicates, ICH recommends three replicates or six replicates at a single concentration level compared by replication for 2–3 times at 6–10 concentrations evenly spaced across the linear range by Eurachem [4, 5, 14–17]. However, and due to economic

• How the measurement procedure would be like?

this case, a blank sample (analyte free) should be used.

prepared (no serial dilutions) to avoid augmentation of error.

considerations, triplicate analysis is the common approach.

should be considered.

stream is commended.

Calibration then can be tackled using different standpoints depending on its implication. In other words, is the calibration targeting the system of measurement and its quality so it is *metrological calibration* or it is an *analytical calibration* that merely describes the relation between the analyte and the corresponding response? Distinction of direct from indirect calibration and then process and instrument can be performed using the metrological maneuver. Another approach to see the calibration process would be in terms of methodologies and schemes followed to achieve such a status. **Figure 1** shows a schematic representation of the calibration process with the different approaches commonly found in literature. The following subsections will be dealing mainly with analytical calibration of a chemical measurement processes in terms of *steps and guidelines, schemes, manuals and methodologies,* and *metrological considerations*.

### **3. Analytical calibration**

#### **3.1. Steps and guidelines**

As previously mentioned, the term *analytical calibration* is used when the calibration process cannot be performed *directly.* In general, the objective of doing calibration is to establish an experiential liaison between the instrument response signal "*y*-variable" and the reaction factors "*x*-variable." The purpose of establishing such a liaison is to be able to assess the influence of these variables on the response and hence quantify the analyte.

Surveying the literature shows that different validation strategies proposed by the different regulatory institutions usually involve quite different guidelines for analytical calibration. In addition to the differences in terminologies used to define analytical calibration and hence associated terms, other major differences can be found as follows.

#### *3.1.1. Proposing a strategy for a calibration study*

*Planning* is the preliminary step in conducting the calibration study. The conventional scheme for performing calibration is to prepare a set of standards (plus a blank) followed by quantifying the response signal for such a set [11–13]. Common several "How" questions usually evolve as the analyst is getting ready to conduct this study:


employing the same units) or *indirectly* (where the measured response is being decoded into the corresponding quantity to be determined, i.e., *analytical calibration*). Both *direct* and *indirect* calibrations can target the equipment as well as the process itself [10]. More details on these

Calibration then can be tackled using different standpoints depending on its implication. In other words, is the calibration targeting the system of measurement and its quality so it is *metrological calibration* or it is an *analytical calibration* that merely describes the relation between the analyte and the corresponding response? Distinction of direct from indirect calibration and then process and instrument can be performed using the metrological maneuver. Another approach to see the calibration process would be in terms of methodologies and schemes followed to achieve such a status. **Figure 1** shows a schematic representation of the calibration process with the different approaches commonly found in literature. The following subsections will be dealing mainly with analytical calibration of a chemical measurement processes in terms of *steps and guidelines, schemes, manuals and methodologies,* and *metrological* 

As previously mentioned, the term *analytical calibration* is used when the calibration process cannot be performed *directly.* In general, the objective of doing calibration is to establish an experiential liaison between the instrument response signal "*y*-variable" and the reaction factors "*x*-variable." The purpose of establishing such a liaison is to be able to assess the influence

Surveying the literature shows that different validation strategies proposed by the different regulatory institutions usually involve quite different guidelines for analytical calibration. In addition to the differences in terminologies used to define analytical calibration and hence

*Planning* is the preliminary step in conducting the calibration study. The conventional scheme for performing calibration is to prepare a set of standards (plus a blank) followed by quantifying the response signal for such a set [11–13]. Common several "How" questions usually

• How the selected number of standards will be patterned and disseminated on the studied

• How the target of calibration will affect the composition of calibration standards?

of these variables on the response and hence quantify the analyte.

associated terms, other major differences can be found as follows.

evolve as the analyst is getting ready to conduct this study:

*3.1.1. Proposing a strategy for a calibration study*

• How many standards will be used?

concentration range?

subdivisions will be given under the relevant section.

20 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

*considerations*.

**3. Analytical calibration**

**3.1. Steps and guidelines**


The elements of *calibration hierarchy* according to JCGM [3] *are one or more measurement standards and measuring systems operated according to the measurement procedure*. Typically, a minimum of 5–6 calibration standards is used for this purpose. Yet, the number of standards used might vary according to the performed analytical process as well as the guidelines proposed by the supervisory body followed. The calibration standard might be *matrix-free* if the purpose is to calibrate solvents, for example, or *matrix-matched* (*MMC*) if it is expected that the presence of matrix would affect the response signal and hence the calibration outcomes. In this case, a blank sample (analyte free) should be used.

Careful distribution of the selected concentration levels over the working range is necessary for appropriate calibration. In this concern, discrimination between narrow and wide calibration ranges is essential. Attention should be paid for the case where a wide concentration range is calibrated where keeping the selected levels at very wide distances, a common approach in literature, might deteriorate the detecting system of the instrument, an issue that produces erroneous readings. The best approach is to keep the data points consistently dispersed across the selected range. Moreover, selected concentrations should be independently prepared (no serial dilutions) to avoid augmentation of error.

Selection of the concentration range to be covered should be based on the expected content of the real samples taking in consideration the matrix and the intended application of the proposed procedure [14]. According to ICH guidelines, for example, if the calibration is performed on an active ingredient or a final product, the range is usually 80–120% of the analyte concentration [4]. In case of using MMC, the blank sample (zero concentration, solvent) should be considered.

The appropriate protocol for a measurement will be the one that simulates the actual circumstances. In this itinerary, it is recommended that calibration samples are to be unevenly analyzed instead of being measured in an increasing concentration sequence. Moreover, insertion of calibration standards randomly in between the unknown samples within the measurement stream is commended.

Every experiment is associated with an error! Diminishing the random error (measurement uncertainty) and hence improving the precision is usually one of the goals when analytical calibration is performed. Replicate analysis is usually the approach. The number of recommended replicates differs according to the implemented guideline. While EMA, FDA, and AOAC indorse five replicates, ICH recommends three replicates or six replicates at a single concentration level compared by replication for 2–3 times at 6–10 concentrations evenly spaced across the linear range by Eurachem [4, 5, 14–17]. However, and due to economic considerations, triplicate analysis is the common approach.

Some guidelines impose more regulations than those previously mentioned. For example, FDA for bioanalytical method validation [18] necessitates that at least four concentrations (lower limit of quantification LLOQ, low, medium, and high) measured in six runs in duplicate/run.

(*linear*) *least squares* (*OLS*) and *weighted least squares (WLS)* [21, 22]. As the name implies, OLS is the least-squares regression approach used when errors have a constant variance across the working range, *homoscedasticity*. That is of course in addition to the general assumptions of the OLS; errors are not correlated, conditional mean of errors is zero, and regressors are not linearly dependent (no multicollinearity). In contrary, WLS should be only used when vari-

Analytical Calibrations: Schemes, Manuals, and Metrological Deliberations

http://dx.doi.org/10.5772/intechopen.72580

As an example of how to construct a calibration graph, spectrophotometric determination of tioconazole (antifungal, electron donor) using chloranilic acid (electron acceptor) via charge transfer reaction, and other calculated parameters needed to establish the regression relationship between [drug] and absorbance are shown in **Table 1**. Equations used to calculate essential regression parameters, *r (correlation coefficient)* and hence the *coefficient of determination* (*R*<sup>2</sup>

*slope (a)* and *intercept* (*b*), are shown in **Figure 2**, which is the calibration graph plotted from

Evaluation of a linear relationship between concentration and response is usually performed by assessing the regression statistics, calibration graphs, and residual plots of the proposed model. Inspection of linearity is usually made *visually* by observing the calibration plot. Again, different guidelines do use different terminologies to describe the linearity and range, FDA for example uses the term calibration (standard) curve, compared to ICH guidelines which clearly defines linearity and Eurachem which uses the term working range [4, 14, 16, 18].

 **–** *x*̄**)2** *y<sup>i</sup>*

 0.073 −180 32400 −0.4537 0.205844 81.666 0.175 −140 19600 −0.3517 0.123693 49.238 0.276 −100 10000 −0.2507 0.06285 25.07 0.372 −60 3600 −0.1547 0.023932 9.282 0.473 −20 400 −0.0537 0.002884 1.074 0.582 20 400 0.0553 0.003058 1.106 0.677 60 3600 0.1503 0.02259 9.018 0.781 100 10000 0.2543 0.064668 25.43 0.878 140 19600 0.3513 0.123412 49.182 0.98 180 32400 0.4533 0.205481 81.594

2200 5.267 0 132000 0 0.838412 332.66

 **–** *ŷ* **(***y<sup>i</sup>*

 **–** *ŷ***)2 (***x<sup>i</sup>*

 **–** *x*̄**)(***y<sup>i</sup>*  **–** *ŷ***)** )*,* 

23

ances are different, *heteroscedasticity,* and the working range is wide.

 **–** *x*̄ **(***x<sup>i</sup>*

data shown in **Table 1**.

*x<sup>i</sup> y<sup>i</sup> x<sup>i</sup>*

Ʃ =

*x*̄ = 220 *ŷ* = 0.5267

**Table 1.** Parameters needed for the calibration graph (**Figure 1**).

*3.1.2.2. Assessment of performance: model metrics*

#### *3.1.2. Assembling and modeling of experimental data*

Following the fulfillment of the previous checklist of "How questions*,"* the subsequent movement will be to corroborate the liaison between the measured concentration and the equipment response. This liaison is usually established via *regression analysis* and hence *calibration graphs (commonly described as curves)*. According to JCGM [3], *calibration curve* is *"*expression of the relation between indication and corresponding measured quantity value", and *"*a calibration curve expresses a one-to-one relation that does not supply a measurement result as it bears no information about the measurement uncertainty.*"*

#### *3.1.2.1. Construction of calibration curve*

The calibration curve is generally constructed by plotting the response values (*y-*axis, *dependent variable*) against the known standard concentration values (on *x-*axis, *independent variable*, *predictor)* either manually or by operating popular software like Excel®, for example. Performing regression analysis and drawing a regression line require a cautious decision on a bundle of three main components: *model*, *mode, and fitting technique.*

Typically, the number of predictors and so the type of response variable differ between various measurements. Accordingly, the regression pattern would be different. A common regression model is the *linear regression* where a *best-fit* straight line is drawn between *x* and *y* variables. Other types of regressions include *logistic, polynomial, stepwise (forward selection and backward removal), and ridge* regression.

In the simple linear regression, one independent variable is involved compared to more than one in case of multiple linear regression. The best-fit line is usually obtained employing the method of least squares (the most popular technique). This regression line is usually presented by the equation: *y = ax + b,* where *a* and *b* are the slope and the intercept, respectively. In this method, the line is calculated by minimizing the sum of squares of the residuals for each data point.

Regression analysis based on *principle component analysis* (*PCA*) is known as *principle component regression* (*PCR*), in which the response is regressed against a set of variables and using the PCA to find the regression coefficients. Other regression methods such as *partial leastsquares (PLS)* establish a linear regression model by protruding *x* and *y* variables to a new space. This technique is mainly used when the number of data points is less than the number of variables [19, 20].

The last step after deciding upon the method and the model used is the selection of fitting technique. Adopting the case of a linear regression model being generated using the method of least squares, two approaches are commonly followed to find the best-fit line: *ordinary*

(*linear*) *least squares* (*OLS*) and *weighted least squares (WLS)* [21, 22]. As the name implies, OLS is the least-squares regression approach used when errors have a constant variance across the working range, *homoscedasticity*. That is of course in addition to the general assumptions of the OLS; errors are not correlated, conditional mean of errors is zero, and regressors are not linearly dependent (no multicollinearity). In contrary, WLS should be only used when variances are different, *heteroscedasticity,* and the working range is wide.

As an example of how to construct a calibration graph, spectrophotometric determination of tioconazole (antifungal, electron donor) using chloranilic acid (electron acceptor) via charge transfer reaction, and other calculated parameters needed to establish the regression relationship between [drug] and absorbance are shown in **Table 1**. Equations used to calculate essential regression parameters, *r (correlation coefficient)* and hence the *coefficient of determination* (*R*<sup>2</sup> )*, slope (a)* and *intercept* (*b*), are shown in **Figure 2**, which is the calibration graph plotted from data shown in **Table 1**.

#### *3.1.2.2. Assessment of performance: model metrics*

Some guidelines impose more regulations than those previously mentioned. For example, FDA for bioanalytical method validation [18] necessitates that at least four concentrations (lower limit of quantification LLOQ, low, medium, and high) measured in six runs in

Following the fulfillment of the previous checklist of "How questions*,"* the subsequent movement will be to corroborate the liaison between the measured concentration and the equipment response. This liaison is usually established via *regression analysis* and hence *calibration graphs (commonly described as curves)*. According to JCGM [3], *calibration curve* is *"*expression of the relation between indication and corresponding measured quantity value", and *"*a calibration curve expresses a one-to-one relation that does not supply a measurement result as it

The calibration curve is generally constructed by plotting the response values (*y-*axis, *dependent variable*) against the known standard concentration values (on *x-*axis, *independent variable*, *predictor)* either manually or by operating popular software like Excel®, for example. Performing regression analysis and drawing a regression line require a cautious decision on

Typically, the number of predictors and so the type of response variable differ between various measurements. Accordingly, the regression pattern would be different. A common regression model is the *linear regression* where a *best-fit* straight line is drawn between *x* and *y* variables. Other types of regressions include *logistic, polynomial, stepwise (forward selection and* 

In the simple linear regression, one independent variable is involved compared to more than one in case of multiple linear regression. The best-fit line is usually obtained employing the method of least squares (the most popular technique). This regression line is usually presented by the equation: *y = ax + b,* where *a* and *b* are the slope and the intercept, respectively. In this method, the line is calculated by minimizing the sum of squares of the residuals for

Regression analysis based on *principle component analysis* (*PCA*) is known as *principle component regression* (*PCR*), in which the response is regressed against a set of variables and using the PCA to find the regression coefficients. Other regression methods such as *partial leastsquares (PLS)* establish a linear regression model by protruding *x* and *y* variables to a new space. This technique is mainly used when the number of data points is less than the number

The last step after deciding upon the method and the model used is the selection of fitting technique. Adopting the case of a linear regression model being generated using the method of least squares, two approaches are commonly followed to find the best-fit line: *ordinary*

duplicate/run.

*3.1.2. Assembling and modeling of experimental data*

*3.1.2.1. Construction of calibration curve*

*backward removal), and ridge* regression.

each data point.

of variables [19, 20].

bears no information about the measurement uncertainty.*"*

22 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

a bundle of three main components: *model*, *mode, and fitting technique.*

Evaluation of a linear relationship between concentration and response is usually performed by assessing the regression statistics, calibration graphs, and residual plots of the proposed model. Inspection of linearity is usually made *visually* by observing the calibration plot. Again, different guidelines do use different terminologies to describe the linearity and range, FDA for example uses the term calibration (standard) curve, compared to ICH guidelines which clearly defines linearity and Eurachem which uses the term working range [4, 14, 16, 18].


**Table 1.** Parameters needed for the calibration graph (**Figure 1**).

of quantitation (LOQ) and ends where there is an obvious deviation from linearity. Working range is usually wider compared to the linear range. Thus, the latter can be defined as the range where there is a direct proportionality between concentration and response [14, 23, 24]. Though not being a component of the validation process, sensitivity is mentioned in variety of guidelines with the purpose of method evaluation. As a parameter, sensitivity can be easily estimated from the linear calibration graph as the function gradient. As per FDA guidelines [16], sensitivity is defined as "the lowest analyte concentration that can be measured with acceptable accuracy and precision (i.e., LLOQ).*"* In this itinerary, parameters such as *limit of* 

Once the status of "linearity" is established, statistical analysis is needed. Model metrics such as the correlation coefficient, slope of the regression line, and the intercept should be included (**Figure 2**). A comparison between the linearity assessment practices as per the different guidelines will be revealed in the following subsections. **Table 2** shows a comparison

**Assessment approach Recommended by Pros Cons Ref.**

Helpful together with the visual inspection in detecting linearity

Not a powerful tool in confirming linearity and needs a former experience with the different residual patterns

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Subjective and cannot be used alone to indicate linearity

Greatly dependent on the method precision, and usually several replicates are needed

model

increases

Needs more samples compared to regular fitting tests and needs an estimation of the nonlinear

Sometimes deceptive and is monotonously getting higher as the number of variables

Depends on the measurement tool and different from one equipment to another

Not decisive [9]

[14, 25–27]

[16, 18]

[25, 27]

[9]

[4, 14, 25–27]

[26]

*detection* (*LoD*) and *limit of quantitation* (*LoQ*) need to be distinguished [23].

– Easy and useful in clear-

IUPAC *Fcalculated* value can be easily calculated

similar

software

NATA Easy to understand and calculate

Lack-of-Fit (LOF) IUPAC, INAB Easy to be implemented

Mandel's fitting test IUPAC Easy to calculate and

ICH, Eurachem, IUPAC, INAB, NATA

**Table 2.** A comparison between different linearity assessment approaches.

cut situations

in many software spreadsheets

is mainly used when variances of two calibration functions are

Widely used and implemented in almost all

*Graphical inspection*

Visual inspection (nongraphical)

*Statistical analysis* Analysis of variance

*Numerical evaluation* Coefficients of correlation (*r*) and determination (*R*<sup>2</sup>

Residual standard deviation (RESSD)

)

(ANOVA)

Residuals plot IUPAC, NATA,

INAB

**Figure 2.** Calibration graph plotted from data presented in **Table 1**.

**Figure 3** shows three commonly used terms to describe the range: *analytical (dynamic range)*, *working (calibration) range*, and *linear range.*

The analytical or the dynamic range is the range in which the equipment is showing a response to the tested concentration, and this response is changing as the concentration varies. This relationship might be linear or nonlinear. The calibration range, in which the liaison between response and analyte concentration has an adequate uncertainty, usually starts with the limit

**Figure 3.** A demonstration of different ranges: analytical, working, and linear ranges.

of quantitation (LOQ) and ends where there is an obvious deviation from linearity. Working range is usually wider compared to the linear range. Thus, the latter can be defined as the range where there is a direct proportionality between concentration and response [14, 23, 24].

Though not being a component of the validation process, sensitivity is mentioned in variety of guidelines with the purpose of method evaluation. As a parameter, sensitivity can be easily estimated from the linear calibration graph as the function gradient. As per FDA guidelines [16], sensitivity is defined as "the lowest analyte concentration that can be measured with acceptable accuracy and precision (i.e., LLOQ).*"* In this itinerary, parameters such as *limit of detection* (*LoD*) and *limit of quantitation* (*LoQ*) need to be distinguished [23].

Once the status of "linearity" is established, statistical analysis is needed. Model metrics such as the correlation coefficient, slope of the regression line, and the intercept should be included (**Figure 2**). A comparison between the linearity assessment practices as per the different guidelines will be revealed in the following subsections. **Table 2** shows a comparison


**Table 2.** A comparison between different linearity assessment approaches.

**Figure 3** shows three commonly used terms to describe the range: *analytical (dynamic range)*,

The analytical or the dynamic range is the range in which the equipment is showing a response to the tested concentration, and this response is changing as the concentration varies. This relationship might be linear or nonlinear. The calibration range, in which the liaison between response and analyte concentration has an adequate uncertainty, usually starts with the limit

*working (calibration) range*, and *linear range.*

**Figure 2.** Calibration graph plotted from data presented in **Table 1**.

24 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

**Figure 3.** A demonstration of different ranges: analytical, working, and linear ranges.

between the nongraphical, graphical, statistical, and numerical evaluation approaches for linearity evaluation. Contrast is shown in terms of the pros and cons of each approach as well as the recommending guideline(s).

• *Correlation coefficient (r)* and *coefficient of determination (R<sup>2</sup>*

close to 1 is an indication for linearity [31].

standard, which is *reference materials (RM).*

procedures*"*, it will be known as certified RM, CRM [3].

replicates and the measurement levels (please see Section 3.1.1).

**3.2. Schemes**

used standards.

*3.2.1. Multi-standard calibration*

*3.2.2. Two-standard calibration*

commonly used to express the GOF of a model. In general, *R*<sup>2</sup>

compared to *r,* where the former measures the proportion of variance of the dependent variable being diminished by prediction of the independent variable, while the latter is just a measure for the correlation between the two variables. In general, a value of *r/R*<sup>2</sup>

Analytical Calibrations: Schemes, Manuals, and Metrological Deliberations

• *Residual standard deviation (RESSD)*: the smaller the value of RESSD, the better the obtained fit. RESSD measures the digression of data away from a fitted regression line.

As previously mentioned under steps and guidelines for a successful calibration, the first step is to decide on how many standards will be used for calibration? Usually, the most common approach is the use of more than one standard "multi-standard calibration." It is noteworthy to mention that the term standard can be described as *"*realization of the definition of a given quantity, with stated quantity value and associated measurement uncertainty, used as a reference*"* and in *NOTE 1A* "realization of the definition of a given quantity can be provided by a measuring system, a material measure, or a reference material*"* and in *NOTE 9 "*The term 'measurement standard' is sometimes used to denote other metrological tools, e.g., 'software measurement standard'" [3]. Another term is usually used then to describe the measurement

As per JCGM [3], RM is *"*material, sufficiently homogeneous and stable with reference to specified properties, which has been established to be fit for its intended use in measurement or in examination of nominal properties.*"* The composition of RM would vary depending on the application. For example, substance RM has an individual pure component in solvent of use, compared to matrix RM, which consists of analytes prepared in a matched matrix. When RM is "accompanied by documentation issued by an authoritative body and providing one or more specified property values with associated uncertainties and traceabilities, using valid

Several schemes are usually available to perform calibration depending on the number of

This is the most popular approach for calibration where a minimum of three standards is usually used. Different guidelines do have different specifications in this concern and in terms of

This approach is usually used for investigations performed at a narrow concentration range and after the linearity of the employed function has been confirmed, probably as a continued calibration. It can be also used when the applied procedure has a background. As a condition,

the analyte concentration needs to be within the range covered by the two standards.

*)*: these two parameters are

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27

	- *Analysis of variance* (*ANOVA*): this test depends on calculation of combined variances (*S*<sup>2</sup> ) between or within a group of data replicates assembled together in a certain way. This test is only recommended by IUPAC [9]. As a significance test, *Fcalculated* is compared with *Ftabulated.* The calculated *F-*values is found using the following formula: *Fcalculated* = (*S*y/x/*S*<sup>y</sup> )2 , *S*y/x is the standard error for residuals and *S*<sup>y</sup> is the pure error.
	- *Lack-of-fit (LOF) test:* this test is a part of IUPAC validation guidelines [25, 27]. The calculated *F-*value is a ratio of mean sum of squares of random error (*MSSerror*) as a measure for divergence of points from the regression line being caused by the haphazard distribution of the points following replicate measurements to the mean sum of squares due to the lack-of-fit (*MSSLOF*) as a measure for deviation of points caused by incongruity of the calibration paradigm. A comparison between the calculated and the tabulated value is then performed. Another approach to perform LOF test is to find the probability, *p-*value. Having a *p-*value higher than 0.05 means that the lack of fit is not significant [29, 30].
	- *Mandel's fitting test*: this test is used to compare between two models (one is linear and the other is nonlinear) in terms of linearity when the variances are similar. The first step is to calculate the residual standard deviation for both models [9]. Again, if *Fcalculated* is greater than *Ftabulated*, the linear model cannot be accepted.

#### **3.2. Schemes**

between the nongraphical, graphical, statistical, and numerical evaluation approaches for linearity evaluation. Contrast is shown in terms of the pros and cons of each approach as well as

**i.** *Graphical inspection:* this approach is recommended by most of validation guidelines. The preliminary step is to construct a plot between concentration and response on the *x* and *y* axes, respectively. The second step involves examining the plot visually. Majority of guidelines support using the plot of residuals as a tool to inspect linearity. Residuals can be defined as the difference between an observed value for a dependent measurement (*y*) and the estimated value of this measurement. As an approach, plot of residuals is a plot where calculated residuals are shown on the *y*-axis and the independent variable is shown on the *x*-axis. Linearity is confirmed when points are randomly scattered around the horizontal *x*-axis. Some data are not suitable candidates for plotting residuals; e.g.,

**ii.** *Nongraphical approach*: visual inspection of data without plotting the graph or using statis-

**iii.** *Statistical assessment:* statistical evaluation of data is a vital tool to confirm linearity when visual and residual plots cannot confirm a status of linearity. Generally, tests of significance are the methods used to infer whether stated claims about a sample of data extracted from a certain population are in favor or against the stipulated evidence. In other words, the significance tests are testing whether the *null hypothesis* (*H*0) is being verified or not. Examples for significance tests include the student *t-*test and the *F-*test. Significance

• *Analysis of variance* (*ANOVA*): this test depends on calculation of combined variances

• *Lack-of-fit (LOF) test:* this test is a part of IUPAC validation guidelines [25, 27]. The calculated *F-*value is a ratio of mean sum of squares of random error (*MSSerror*) as a measure for divergence of points from the regression line being caused by the haphazard distribution of the points following replicate measurements to the mean sum of squares due to the lack-of-fit (*MSSLOF*) as a measure for deviation of points caused by incongruity of the calibration paradigm. A comparison between the calculated and the tabulated value is then performed. Another approach to perform LOF test is to find the probability, *p-*value. Having a *p-*value higher than 0.05 means that the lack of fit is not significant [29, 30]. • *Mandel's fitting test*: this test is used to compare between two models (one is linear and the other is nonlinear) in terms of linearity when the variances are similar. The first step is to calculate the residual standard deviation for both models [9]. Again, if *Fcalculated* is

**iv.** *Numerical assessment*: numerical fitting parameters are used as a measure of goodness-offit (GOF) in regression analysis. The following parameters are commonly used:

) between or within a group of data replicates assembled together in a certain way. This test is only recommended by IUPAC [9]. As a significance test, *Fcalculated* is compared with *Ftabulated.* The calculated *F-*values is found using the following formula: *Fcalculated* =

is the pure error.

tical tools cannot be used as a linearity assessment tool by itself [16–18].

tests reported in literature to test linearity can be summarized as follows:

, *S*y/x is the standard error for residuals and *S*<sup>y</sup>

greater than *Ftabulated*, the linear model cannot be accepted.

the recommending guideline(s).

(*S*<sup>2</sup>

(*S*y/x/*S*<sup>y</sup> )2

heteroscedastic data and outliers [14, 25–28].

26 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

As previously mentioned under steps and guidelines for a successful calibration, the first step is to decide on how many standards will be used for calibration? Usually, the most common approach is the use of more than one standard "multi-standard calibration." It is noteworthy to mention that the term standard can be described as *"*realization of the definition of a given quantity, with stated quantity value and associated measurement uncertainty, used as a reference*"* and in *NOTE 1A* "realization of the definition of a given quantity can be provided by a measuring system, a material measure, or a reference material*"* and in *NOTE 9 "*The term 'measurement standard' is sometimes used to denote other metrological tools, e.g., 'software measurement standard'" [3]. Another term is usually used then to describe the measurement standard, which is *reference materials (RM).*

As per JCGM [3], RM is *"*material, sufficiently homogeneous and stable with reference to specified properties, which has been established to be fit for its intended use in measurement or in examination of nominal properties.*"* The composition of RM would vary depending on the application. For example, substance RM has an individual pure component in solvent of use, compared to matrix RM, which consists of analytes prepared in a matched matrix. When RM is "accompanied by documentation issued by an authoritative body and providing one or more specified property values with associated uncertainties and traceabilities, using valid procedures*"*, it will be known as certified RM, CRM [3].

Several schemes are usually available to perform calibration depending on the number of used standards.

#### *3.2.1. Multi-standard calibration*

This is the most popular approach for calibration where a minimum of three standards is usually used. Different guidelines do have different specifications in this concern and in terms of replicates and the measurement levels (please see Section 3.1.1).

#### *3.2.2. Two-standard calibration*

This approach is usually used for investigations performed at a narrow concentration range and after the linearity of the employed function has been confirmed, probably as a continued calibration. It can be also used when the applied procedure has a background. As a condition, the analyte concentration needs to be within the range covered by the two standards.

The real [analyte] can be calculated using the formula: [anal] = [std1 or 2] + k (yunknown – ystd 1or2), where the brackets express concentrations, k is the reciprocal of slope (sensitivity), and y is the response for the unknown and the standard, respectively [11, 12, 32]. Examples for this calibration are the pH meter and temperature sensor calibrations. A special scheme of a twopoint calibration is known as bracketing calibration. In this approach, the [anal] is bracketed between the two standards assuming that a linear arithmetical interpolation can be proposed based on the knowledge of [std1 and 2]. The uncertainty associated with this approach is thus small if compared to the overall uncertainty [33, 34].

*3.3.2. Matrix-matched calibration (MMC)*

*3.3.3. Standard addition calibration (AC)*

matrix effect [11, 35].

within the linearity limits.

*3.3.4. Internal standard calibration (IC)*

**3.4. Metrological considerations**

*3.4.1. Uncertainty*

[11, 36].

In contrast to the EC, MMC is used when the matrix has an impact on the response to the analyte. Both matrix RMs or substance RMs (together with an analyte-free matrix) can be employed for this approach. Attention should be paid that the matrix should be carefully matched. Again, the presence of analytes other than the target in the matrix could produce a

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In this approach, known amounts of the analyte are added to aliquots of the test solution. Measurement is then performed by extrapolation of the calibration line to the zero response (no analyte). This approach can explain only certain types of the matrix effect; however; it cannot account for the effect of instrumental drift. Before the implementation of this method, the linearity of the calibration line should be confirmed over the whole concentration range. Moreover, the added concentration should be at least five times as high as the [anal] but

The actual [anal] is calculated using the equation: [anal] = CF ((*yunknown*/*yspiked* – *yunknown*)), where *yspiked* and *yunknown* are the responses for the spiked and the unknown sample, respectively

This approach is used to correct for both matrix effect and the drift over time. This technique is not the opposite to the previously mentioned EC; however, they can be used together. The matrix RM or as commonly known, internal standard (IS), which is structurally analogous to the analyte, is added for both unknown samples as well as the standards. The IS is selected in such a way that it can be distinguishably measured from the analyte. Moreover, there should be no interference between the IS and the analyte from one hand, and between the IS and the matrix of the unknown from the other hand. In addition to saving time and effort, the presence of the IS serves to compensate for sample loss during the preparation process [11]. The only limitation of this procedure is the availability of the ideal IS that can satisfy the previous

The product of the calibration scheme is usually portrayed as a mathematical model after performing the appropriate regression. Assessment of the proposed model depends on estimation of the experimental error which in turn affects linearity. Moreover, an important feature of the validation process which can be viewed as a direct calibration is the recovery studies. The concentration in the coming subsections will be on the metrological features of calibration

As previously mentioned, the product of calibration is an experiential formula that relates the instrumental response to the analyte concentration. Thus, in other words, the actual value of

conditions and emulate the matrix effect and the instrumental drift.

in terms of error associated with the measurement and the recovery studies.

#### *3.2.3. Single-standard calibration*

As a direct calibration technique, this approach is applicable only when the calibration function linearity is established (especially in the region covering the [anal] and between the selected [std] and the origin) and if the graph intercept is zero [11, 12]. In this case, [anal] can be calculated using the calibration factor CF (which is the ratio between [std] and the average analytical response for the standard), where the unknown [anal] = CF\*yunknown. This simple calibration is generally used to test the drift from the response.

Multi-standard application then seems to be the most feasible and accurate scheme for calibration. However, this is not the case when, for example, the detector response varies with the time. In this case, the one-standard calibration is advantageous assuming that the unknown signal is within ±10–50% of the standard signal depending on whether the maximum analyte concentration limit has been surpassed or not [11, 12]. Depending on the analyte, availability of the standard, nature of the process, presence of concomitant analytes/interferences, and matrix effect, the procedure of calibration significantly varies and any of the previously reported schemes can be chosen.

#### **3.3. Methodologies and manuals**

While external and internal calibrations are the major themes, standard addition method (AC) and matrix-matched calibration (MMC) are also employed when required. Therefore, different methodologies for calibration can be proposed depending on how the RM will be applied within the course of calibration process. Through this section, emphasis will be basically on the CMPs, and the common methodologies usually followed to calibrate such a process.

#### *3.3.1. External calibration (EC)*

This approach is commonly known as *"*solvent/ standard calibration." As the name implies, EC is performed externally applied, i.e., the known standard solution, which is a substance RM prepared in the working solvent, is prepared and then analyzed distinctly from target samples. This approach can be applied using any of the previously mentioned schemes for calibration. The analysis protocol involves comparing the response for the unknown sample to the response for the target in the standard solution. One of the drawbacks of this methodology is the postulation that the impact of the difference between the matrices (standard and sample) can be ignored, an issue that leads to incorporation and propagation of a matrix systematic error. Nonetheless, this approach can be used when there is a minor or no contribution from the matrix effect and the instrumental drift can be ignored [11].

### *3.3.2. Matrix-matched calibration (MMC)*

The real [analyte] can be calculated using the formula: [anal] = [std1 or 2] + k (yunknown – ystd 1or2), where the brackets express concentrations, k is the reciprocal of slope (sensitivity), and y is the response for the unknown and the standard, respectively [11, 12, 32]. Examples for this calibration are the pH meter and temperature sensor calibrations. A special scheme of a twopoint calibration is known as bracketing calibration. In this approach, the [anal] is bracketed between the two standards assuming that a linear arithmetical interpolation can be proposed based on the knowledge of [std1 and 2]. The uncertainty associated with this approach is thus

As a direct calibration technique, this approach is applicable only when the calibration function linearity is established (especially in the region covering the [anal] and between the selected [std] and the origin) and if the graph intercept is zero [11, 12]. In this case, [anal] can be calculated using the calibration factor CF (which is the ratio between [std] and the average analytical response for the standard), where the unknown [anal] = CF\*yunknown. This simple

Multi-standard application then seems to be the most feasible and accurate scheme for calibration. However, this is not the case when, for example, the detector response varies with the time. In this case, the one-standard calibration is advantageous assuming that the unknown signal is within ±10–50% of the standard signal depending on whether the maximum analyte concentration limit has been surpassed or not [11, 12]. Depending on the analyte, availability of the standard, nature of the process, presence of concomitant analytes/interferences, and matrix effect, the procedure of calibration significantly varies and any of the previously

While external and internal calibrations are the major themes, standard addition method (AC) and matrix-matched calibration (MMC) are also employed when required. Therefore, different methodologies for calibration can be proposed depending on how the RM will be applied within the course of calibration process. Through this section, emphasis will be basically on the CMPs, and the common methodologies usually followed to calibrate such a process.

This approach is commonly known as *"*solvent/ standard calibration." As the name implies, EC is performed externally applied, i.e., the known standard solution, which is a substance RM prepared in the working solvent, is prepared and then analyzed distinctly from target samples. This approach can be applied using any of the previously mentioned schemes for calibration. The analysis protocol involves comparing the response for the unknown sample to the response for the target in the standard solution. One of the drawbacks of this methodology is the postulation that the impact of the difference between the matrices (standard and sample) can be ignored, an issue that leads to incorporation and propagation of a matrix systematic error. Nonetheless, this approach can be used when there is a minor or no contri-

bution from the matrix effect and the instrumental drift can be ignored [11].

small if compared to the overall uncertainty [33, 34].

28 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

calibration is generally used to test the drift from the response.

*3.2.3. Single-standard calibration*

reported schemes can be chosen.

**3.3. Methodologies and manuals**

*3.3.1. External calibration (EC)*

In contrast to the EC, MMC is used when the matrix has an impact on the response to the analyte. Both matrix RMs or substance RMs (together with an analyte-free matrix) can be employed for this approach. Attention should be paid that the matrix should be carefully matched. Again, the presence of analytes other than the target in the matrix could produce a matrix effect [11, 35].

#### *3.3.3. Standard addition calibration (AC)*

In this approach, known amounts of the analyte are added to aliquots of the test solution. Measurement is then performed by extrapolation of the calibration line to the zero response (no analyte). This approach can explain only certain types of the matrix effect; however; it cannot account for the effect of instrumental drift. Before the implementation of this method, the linearity of the calibration line should be confirmed over the whole concentration range. Moreover, the added concentration should be at least five times as high as the [anal] but within the linearity limits.

The actual [anal] is calculated using the equation: [anal] = CF ((*yunknown*/*yspiked* – *yunknown*)), where *yspiked* and *yunknown* are the responses for the spiked and the unknown sample, respectively [11, 36].

#### *3.3.4. Internal standard calibration (IC)*

This approach is used to correct for both matrix effect and the drift over time. This technique is not the opposite to the previously mentioned EC; however, they can be used together. The matrix RM or as commonly known, internal standard (IS), which is structurally analogous to the analyte, is added for both unknown samples as well as the standards. The IS is selected in such a way that it can be distinguishably measured from the analyte. Moreover, there should be no interference between the IS and the analyte from one hand, and between the IS and the matrix of the unknown from the other hand. In addition to saving time and effort, the presence of the IS serves to compensate for sample loss during the preparation process [11]. The only limitation of this procedure is the availability of the ideal IS that can satisfy the previous conditions and emulate the matrix effect and the instrumental drift.

#### **3.4. Metrological considerations**

The product of the calibration scheme is usually portrayed as a mathematical model after performing the appropriate regression. Assessment of the proposed model depends on estimation of the experimental error which in turn affects linearity. Moreover, an important feature of the validation process which can be viewed as a direct calibration is the recovery studies. The concentration in the coming subsections will be on the metrological features of calibration in terms of error associated with the measurement and the recovery studies.

#### *3.4.1. Uncertainty*

As previously mentioned, the product of calibration is an experiential formula that relates the instrumental response to the analyte concentration. Thus, in other words, the actual value of a measurement is equated with the experimental value. As a result, the uncertainty associated with the measurement needs to be determined. Principally talking about the systematic error of a measurement, and according to JCGM [3], it can be defined as "component of measurement error that in replicate measurements remains constant or varies in a predictable manner." NOTE 1 "A reference quantity value for a systematic measurement error is a true quantity value, or a measured quantity value of a measurement standard of negligible measurement uncertainty, or a conventional quantity value." As per NOTE 2 "Systematic measurement error, and its causes, can be known or unknown. A correction can be applied to compensate for a known systematic measurement error" and NOTE 3 "Systematic measurement error equals measurement error minus random measurement error."

For a linear calibration function generated from a multi-standard calibration approach using any of the methodologies of EC or IC, the linear regression line can be described by the equation: *y = ax + b.* This straight-line equation can be used to find an unknown concentration assuming that the response for this concentration is known. As the location of the regression line varies with the uncertainties associated with the regression parameters, *a* and *b*, the predicted concentration of the unknown would also be associated to uncertainty [37]. Metrologically, uncertainty of calibration is estimated using the following formula:

$$\text{(momentum)} \text{ (momentum) of ammonia} \text{ (or } \text{maximum is common to form)}$$

$$\mu \text{(x\_o)} = \frac{S\_{y\_{\bar{y}}}}{b} \sqrt{\frac{(x\_o - \bar{x})^2}{\sum\_{i=1}^{n} (x\_o - \bar{x})} + \frac{1}{m} + \frac{1}{n}} \tag{1}$$

**4. Conclusion**

**Author details**

Marwa S. El-Azazy

University, Doha, Qatar

mistry. 1995;**67**:1699-1723

rance. 1999;**4**:477-478

Quality Assurance. 2012;**17**:231-232

**References**

Address all correspondence to: marwasaid@qu.edu.qa

Department of Chemistry and Earth Sciences, College of Arts and Sciences, Qatar

[1] Currie LA. Nomenclature in evaluation of analytical methods including detection and quantification capabilities (IUPAC Recommendations 1995). Pure and Applied Che-

[2] Bièvre PD. The 2012 International Vocabulary of Metrology: "VIM". Accreditation and

[3] "BIPM—International Vocabulary of Metrology (VIM)," International Vocabulary of Metrology (VIM). Basic and General Concepts and Associated Terms, 3rd ed. Joint Committee

[4] ICH Harmonized Tripartite Guideline. Validation of analytical procedures: Text and methodology, Q2(R1), Current Step 4th version, Parent guidelines on Methodology

[5] Association of Official Analytical Chemists (AOAC). Official Methods of Analysis. Vol. 1.

[6] Muijlwijk R. Is metrology in chemistry really special? Accreditation and Quality Assu-

for Guides in Metrology (JCGM), 200: 2012 (JCGM 200:2008 with minor corrections)

Dated November 6, 1996, Incorporated in November 2005

15th ed. Arlington, VA: AOAC; 1990. p. 673

Thousands of analyses and so validations are being performed every day. Calibration is a fundamental module of any analytical validation procedure. Different regulatory bodies propose different idioms and hence procedures for putting calibration in effect. Existence of a welldefined terminology for calibration and therefore a harmonized procedure would significantly improve the outcome of the analytical measurement. Appropriate selection of the calibration scheme and the subsequent methodology are the key factors for the success of analytical calibration. This chapter has outlined the process of analytical calibration in terms of appropriate designation (and considering the different releases by different documentary agencies), schemes (multi-, one-, and two-standard calibrations), and the operating manuals. Moreover, the metrological aspects of the calibration process have been revealed throughout the discussion with a focus on the recovery and uncertainties associated with analytical measurement.

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where *u*(x0 ) is the uncertainty associated with the unknown measurement, *Sy/x* is the residual standard deviation, *m* is the number of replicates, *n* is the number of calibration points, *x*̄ is the mean of *x* data points. It is noteworthy to mention that uncertainty associated with a measurement would be also sourced from the random error.

The *accuracy* and *trueness* are the terms used by majority of guidelines [1–5, 15–18]. However, there is a metrological difference between both terms. The term accuracy expresses how close an individual measurement to the real value of this measurement; however, trueness measures how close the mean of large number of values to the true value [3]. Thus, method trueness is measured as *absolute bias* or *relative bias*, which is expressed as % error and % relative error (%RE), respectively. Random error, however, affects the precision, which is calculated from the formula of standard deviation and in turn it affects the method accuracy [38]. Thus, uncertainty is affected by both bias as well as standard deviation.

#### *3.4.2. Recovery*

Generally, recovery investigations performed within the course of validation and following the calibration process can be treated as direct calibration of the proposed methods. Simply, the recovery is equal to = [found]/[actual]. It is important to declare that recovery outcome would differ per data point investigated and that the recovery value obtained at a certain value cannot be extrapolated to find the recovery at another data point.

For a linear function, the relation between recovered and actual analyte can be given as: [actual] = *a* [found]+ *b,* where *a* and *b* are the slope and the intercept, or the proportional and the additive errors, respectively [39].

### **4. Conclusion**

a measurement is equated with the experimental value. As a result, the uncertainty associated with the measurement needs to be determined. Principally talking about the systematic error of a measurement, and according to JCGM [3], it can be defined as "component of measurement error that in replicate measurements remains constant or varies in a predictable manner." NOTE 1 "A reference quantity value for a systematic measurement error is a true quantity value, or a measured quantity value of a measurement standard of negligible measurement uncertainty, or a conventional quantity value." As per NOTE 2 "Systematic measurement error, and its causes, can be known or unknown. A correction can be applied to compensate for a known systematic measurement error" and NOTE 3 "Systematic measure-

For a linear calibration function generated from a multi-standard calibration approach using any of the methodologies of EC or IC, the linear regression line can be described by the equation: *y = ax + b.* This straight-line equation can be used to find an unknown concentration assuming that the response for this concentration is known. As the location of the regression line varies with the uncertainties associated with the regression parameters, *a* and *b*, the predicted concentration of the unknown would also be associated to uncertainty [37].

> \_\_\_\_\_\_\_\_\_\_\_\_\_\_ (*<sup>x</sup>*<sup>0</sup> <sup>−</sup> *<sup>x</sup>*¯) 2 \_\_\_\_\_\_\_\_\_ ∑*<sup>i</sup>*=1

*<sup>m</sup>* <sup>+</sup> \_\_1

*<sup>n</sup>* (1)

*<sup>n</sup>* (*x*<sup>0</sup> <sup>−</sup> *<sup>x</sup>*¯) <sup>+</sup> \_\_1

) is the uncertainty associated with the unknown measurement, *Sy/x* is the residual

standard deviation, *m* is the number of replicates, *n* is the number of calibration points, *x*̄ is the mean of *x* data points. It is noteworthy to mention that uncertainty associated with a measure-

The *accuracy* and *trueness* are the terms used by majority of guidelines [1–5, 15–18]. However, there is a metrological difference between both terms. The term accuracy expresses how close an individual measurement to the real value of this measurement; however, trueness measures how close the mean of large number of values to the true value [3]. Thus, method trueness is measured as *absolute bias* or *relative bias*, which is expressed as % error and % relative error (%RE), respectively. Random error, however, affects the precision, which is calculated from the formula of standard deviation and in turn it affects the method accuracy [38]. Thus,

Generally, recovery investigations performed within the course of validation and following the calibration process can be treated as direct calibration of the proposed methods. Simply, the recovery is equal to = [found]/[actual]. It is important to declare that recovery outcome would differ per data point investigated and that the recovery value obtained at a certain

For a linear function, the relation between recovered and actual analyte can be given as: [actual] = *a* [found]+ *b,* where *a* and *b* are the slope and the intercept, or the proportional and

ment error equals measurement error minus random measurement error."

30 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Metrologically, uncertainty of calibration is estimated using the following formula:

\_\_\_*<sup>y</sup>*/*<sup>x</sup> b* √

*<sup>u</sup>*(*x*0) <sup>=</sup> *<sup>S</sup>*

ment would be also sourced from the random error.

uncertainty is affected by both bias as well as standard deviation.

value cannot be extrapolated to find the recovery at another data point.

where *u*(x0

*3.4.2. Recovery*

the additive errors, respectively [39].

Thousands of analyses and so validations are being performed every day. Calibration is a fundamental module of any analytical validation procedure. Different regulatory bodies propose different idioms and hence procedures for putting calibration in effect. Existence of a welldefined terminology for calibration and therefore a harmonized procedure would significantly improve the outcome of the analytical measurement. Appropriate selection of the calibration scheme and the subsequent methodology are the key factors for the success of analytical calibration. This chapter has outlined the process of analytical calibration in terms of appropriate designation (and considering the different releases by different documentary agencies), schemes (multi-, one-, and two-standard calibrations), and the operating manuals. Moreover, the metrological aspects of the calibration process have been revealed throughout the discussion with a focus on the recovery and uncertainties associated with analytical measurement.

### **Author details**

Marwa S. El-Azazy

Address all correspondence to: marwasaid@qu.edu.qa

Department of Chemistry and Earth Sciences, College of Arts and Sciences, Qatar University, Doha, Qatar

### **References**


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**Chapter 3**

Provisional chapter

**Multivariate Calibration for the Development of**

DOI: 10.5772/intechopen.72598

Vibrational spectroscopy, namely near infrared (NIR) and Raman spectroscopy, is based on the interaction between the electromagnetic radiation and matter. The technique is sensitive to chemical and physical properties and delivers a wide range of information about the analyzed sample, but in order to extract the information, multivariate calibration of the spectral data is required. The main goal of this work will be to present in detail the available multivariate calibration strategy for development of NIR and Raman

Keywords: multivariate calibration, vibrational spectroscopy, NIR spectroscopy, Raman

The development and implementation of vibrational spectroscopic methods such as near infrared (NIR) or Raman spectroscopy has increased significantly as the use of computer technology and chemometric methods has become more available. Considering the pharmaceutical domain, these methods have been extensively applied to quantify active pharmaceutical ingredients, excipients, or physical properties either as offline method for intermediate/final product characterization [1] or as real-time-monitoring methods implemented within blending [2],

The high-throughput analysis associated with vibrational spectroscopy favored its application to gain better process understanding, sustaining the pharmaceutical product development from a Quality by Design and Process Analytical Technology point of view [8], thus enhancing the opportunity to develop well-understood, well-controlled, and continuously optimized manufacturing processes and products [5]. The nondestructive nature of vibrational spectroscopic

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

granulation [3], extrusion [4], tableting [5], coating [6], or freeze-drying processes [7].

spectroscopic methods, which was successfully applied in pharmaceutics.

Multivariate Calibration for the Development

**Vibrational Spectroscopic Methods**

of Vibrational Spectroscopic Methods

Ioan Tomuta, Alina Porfire, Tibor Casian and

Ioan Tomuta, Alina Porfire, Tibor Casian and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72598

spectroscopy, design of experiments

Alexandru Gavan

Alexandru Gavan

Abstract

1. Introduction


#### **Multivariate Calibration for the Development of Vibrational Spectroscopic Methods** Multivariate Calibration for the Development of Vibrational Spectroscopic Methods

DOI: 10.5772/intechopen.72598

Ioan Tomuta, Alina Porfire, Tibor Casian and Alexandru Gavan Ioan Tomuta, Alina Porfire, Tibor Casian and Alexandru Gavan

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72598

#### Abstract

[35] Steger HF. Uses of matrix reference materials. In: Fagelj A, Parkany M, editors. The Use of Matrix Reference Materials in Environmental Analytical Processes. Cambridge: The

[36] AMC technical briefs. In: Thompson M, editor. Analytical Methods Committee AMCTB

[37] Kadis R. Evaluation of the measurement uncertainty: Some common mistakes with a focus on the uncertainty from linear calibration. Journal of Chromatography A. 2017;

[38] Kruve A, Rebane R, Kipper K, Oldekop M-L, Evard H, Herodes K, Ravio P, Leito I. Tutorial review on validation of liquid chromatography–mass spectrometry methods:

[39] Harmonised Guidelines for the Use of Recovery Information in Analytical Measurement,

No 37 March 2009, Standard additions: Myth and reality, pp. 1-2

IUPAC Technical Report. Pure and Applied Chemistry. 1999;**1**:337

Royal Society of Chemistry; 1999. p. 128

34 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Part II. Analytica Chimica Acta. 2015;**870**:8-28

**1499**:226-229

Vibrational spectroscopy, namely near infrared (NIR) and Raman spectroscopy, is based on the interaction between the electromagnetic radiation and matter. The technique is sensitive to chemical and physical properties and delivers a wide range of information about the analyzed sample, but in order to extract the information, multivariate calibration of the spectral data is required. The main goal of this work will be to present in detail the available multivariate calibration strategy for development of NIR and Raman spectroscopic methods, which was successfully applied in pharmaceutics.

Keywords: multivariate calibration, vibrational spectroscopy, NIR spectroscopy, Raman spectroscopy, design of experiments

#### 1. Introduction

The development and implementation of vibrational spectroscopic methods such as near infrared (NIR) or Raman spectroscopy has increased significantly as the use of computer technology and chemometric methods has become more available. Considering the pharmaceutical domain, these methods have been extensively applied to quantify active pharmaceutical ingredients, excipients, or physical properties either as offline method for intermediate/final product characterization [1] or as real-time-monitoring methods implemented within blending [2], granulation [3], extrusion [4], tableting [5], coating [6], or freeze-drying processes [7].

The high-throughput analysis associated with vibrational spectroscopy favored its application to gain better process understanding, sustaining the pharmaceutical product development from a Quality by Design and Process Analytical Technology point of view [8], thus enhancing the opportunity to develop well-understood, well-controlled, and continuously optimized manufacturing processes and products [5]. The nondestructive nature of vibrational spectroscopic

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

methods is of great importance in the quality evaluation of production batches, as they allow the testing of a high number of samples or the entire process, depending on the type of method. Using classical methods, such as chromatography the quality of a 1–3 million tablet batch is certified on 20–30 tablets, and many functional excipients that directly influence product performance are not quantified. These limitations are exceeded by implementing process analytical instruments, such as NIR or Raman [9].

In the calibration set development phase, the analyst has to incorporate the expected variability of future prediction sets, to ensure the representativeness of the samples. This expected variability is given first by the quality attributes that are to be predicted, for example, the concentration ranges of important formulation constituents. Frequently, this is not enough for a robust model, and other type of variability has to be included in the calibration process, such as process-induced variability or environmental variability. Production samples contain process-induced variability; however, constructing a calibration set solely on production samples is not appropriate as the factor ranges do not cover the required interval. A first option would be to prepare pilot-plant samples reproducing full-scale conditions. As the number of responses increases, the calibration set becomes larger and quickly becomes unfeasible due to the high costs of production. The second option would be to prepare laboratory samples in which the concentration ranges of desired components are varied simultaneously within

Multivariate Calibration for the Development of Vibrational Spectroscopic Methods

http://dx.doi.org/10.5772/intechopen.72598

37

The calibration set development strategy applied for the development of quantitative spectroscopic methods depends on the sample complexity (the number of responses and the number of interfering factors included in the calibration) and on the type of method that is developed, here considering off-line or real-time-monitoring methods. In the following section, a description of calibration opportunities will be provided starting from the simplest cases and heading

The most simple calibration situations include a low number of responses, one or two, here considering a chemical and a physical property of a sample. In this case, the calibration set development strategy simply resumes to the preparation of a sample with different levels of the investigated property. Mbinze et al. developed quantitative NIR and Raman methods for the assay of antimalarial oral drops and prepared a calibration set by diluting a stock solution of quinine to obtain three concentration levels. For each level, three series with three replicates were prepared resulting in a calibration set with 27 samples [14]. Tomuta et al. used NIR to characterize meloxicam tablets by evaluating content uniformity, tablet hardness, disintegration, and friability. For content uniformity assay, the calibration set included active ingredient concentration range (five levels), days (three), and batches (three) as a source of variation, whereas in the case of physical properties assay the middle formulation was compressed on seven levels of compression force, ranging from 5 to 42 kN. Compressing the powder mixture with different forces yielded tablets with different hardness, disintegration, and friability. Different settings of a one-process factor were enough to induce variability in physical properties of the samples [15]. In a similar study, Tomuta et al. developed NIR method for physicochemical characterization of low active content indapamide tablets (2%, w/w) [1]. Virtanen et al. evaluated the crushing strength of theophylline tablets through Raman spectroscopy by considering both a process factor and a formulation factor to generate variability in tablet surface roughness. In this case, the tablets were prepared considering two particle sizes of theophylline, as raw material for the granulation phase, followed by mixing with lubricants

and by compressing each granulate on five different compression forces [16].

appropriate ranges to avoid correlations [13].

2.1. Different levels of the investigated property

toward more complex situations.

Near infrared spectra are generated by molecular vibrations that imply a change of the dipole moment (dCH, dNH, dOH, dSH) and are further complicated by overtones and combination bands that reduce the specificity of spectra. In case of Raman spectroscopy, the spectra are generated by inelastic scattering, caused by chemical groups that undergo a change in polarizability when excited with an incident light beam. These differences in molecular contribution to the generation of spectral data make the two methods complementary [10].

NIR and Raman spectra are considered a source of multivariate data, as they contain information related to physical and chemical properties of the analyzed sample. Thus, the application of chemometric methods for extracting predictive spectral variability and reducing orthogonal sources of variation is indispensable [11]. The sensitivity to both physical and chemical properties of the sample can be considered an advantage, if the analyst wants to predict several quality attributes of a drug product, such as content uniformity and crystalline structure. However, if only active content characterization is desired and polymorphism is not considered to be a critical attribute, but it is present, the calibration phase still has to include both aspects to ensure the accuracy of prediction for active content. The main disadvantage of vibrational spectroscopic methods relates to the need of an extensive calibration set that needs to include chemical, physical, instrumental, and environmental variability that is expected in future prediction sets and analysis conditions.

Vibrational spectroscopy is well suited to the means of multivariate calibration, as each observation is characterized by analytical signal/absorbance recorded at multiple wavelengths. Using multiple predictor variables instead of one wavelength overcomes some univariate calibration problems related to selectivity, precision, and diagnosis, resulting in a more robust calibration model [12].

### 2. Calibration set development strategies

The milestone in the development of a vibrational spectroscopic method is the chemometric model that is able to accurately predict the sample properties considered in calibration phase. Before building a model, there are several key steps that need to be considered, as they directly influence its quality and predictive performance. The first step would be the specification of responses along with variation ranges, followed by the selection of instrumental method and configuration, building a representative calibration set, recording of spectral data, data preprocessing, and developing the multivariate regression model that is further tested using external prediction sets. Each step plays an important role; however, a well-built calibration set is the best starting point to a well-performing model, as it is the source of spectral data that is used for further processing and model development.

In the calibration set development phase, the analyst has to incorporate the expected variability of future prediction sets, to ensure the representativeness of the samples. This expected variability is given first by the quality attributes that are to be predicted, for example, the concentration ranges of important formulation constituents. Frequently, this is not enough for a robust model, and other type of variability has to be included in the calibration process, such as process-induced variability or environmental variability. Production samples contain process-induced variability; however, constructing a calibration set solely on production samples is not appropriate as the factor ranges do not cover the required interval. A first option would be to prepare pilot-plant samples reproducing full-scale conditions. As the number of responses increases, the calibration set becomes larger and quickly becomes unfeasible due to the high costs of production. The second option would be to prepare laboratory samples in which the concentration ranges of desired components are varied simultaneously within appropriate ranges to avoid correlations [13].

The calibration set development strategy applied for the development of quantitative spectroscopic methods depends on the sample complexity (the number of responses and the number of interfering factors included in the calibration) and on the type of method that is developed, here considering off-line or real-time-monitoring methods. In the following section, a description of calibration opportunities will be provided starting from the simplest cases and heading toward more complex situations.

#### 2.1. Different levels of the investigated property

methods is of great importance in the quality evaluation of production batches, as they allow the testing of a high number of samples or the entire process, depending on the type of method. Using classical methods, such as chromatography the quality of a 1–3 million tablet batch is certified on 20–30 tablets, and many functional excipients that directly influence product performance are not quantified. These limitations are exceeded by implementing process

Near infrared spectra are generated by molecular vibrations that imply a change of the dipole moment (dCH, dNH, dOH, dSH) and are further complicated by overtones and combination bands that reduce the specificity of spectra. In case of Raman spectroscopy, the spectra are generated by inelastic scattering, caused by chemical groups that undergo a change in polarizability when excited with an incident light beam. These differences in molecular contribution

NIR and Raman spectra are considered a source of multivariate data, as they contain information related to physical and chemical properties of the analyzed sample. Thus, the application of chemometric methods for extracting predictive spectral variability and reducing orthogonal sources of variation is indispensable [11]. The sensitivity to both physical and chemical properties of the sample can be considered an advantage, if the analyst wants to predict several quality attributes of a drug product, such as content uniformity and crystalline structure. However, if only active content characterization is desired and polymorphism is not considered to be a critical attribute, but it is present, the calibration phase still has to include both aspects to ensure the accuracy of prediction for active content. The main disadvantage of vibrational spectroscopic methods relates to the need of an extensive calibration set that needs to include chemical, physical, instrumental, and environmental variability that is expected in

Vibrational spectroscopy is well suited to the means of multivariate calibration, as each observation is characterized by analytical signal/absorbance recorded at multiple wavelengths. Using multiple predictor variables instead of one wavelength overcomes some univariate calibration problems related to selectivity, precision, and diagnosis, resulting in a more robust calibration model [12].

The milestone in the development of a vibrational spectroscopic method is the chemometric model that is able to accurately predict the sample properties considered in calibration phase. Before building a model, there are several key steps that need to be considered, as they directly influence its quality and predictive performance. The first step would be the specification of responses along with variation ranges, followed by the selection of instrumental method and configuration, building a representative calibration set, recording of spectral data, data preprocessing, and developing the multivariate regression model that is further tested using external prediction sets. Each step plays an important role; however, a well-built calibration set is the best starting point to a well-performing model, as it is the source of spectral data that

to the generation of spectral data make the two methods complementary [10].

analytical instruments, such as NIR or Raman [9].

36 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

future prediction sets and analysis conditions.

2. Calibration set development strategies

is used for further processing and model development.

The most simple calibration situations include a low number of responses, one or two, here considering a chemical and a physical property of a sample. In this case, the calibration set development strategy simply resumes to the preparation of a sample with different levels of the investigated property. Mbinze et al. developed quantitative NIR and Raman methods for the assay of antimalarial oral drops and prepared a calibration set by diluting a stock solution of quinine to obtain three concentration levels. For each level, three series with three replicates were prepared resulting in a calibration set with 27 samples [14]. Tomuta et al. used NIR to characterize meloxicam tablets by evaluating content uniformity, tablet hardness, disintegration, and friability. For content uniformity assay, the calibration set included active ingredient concentration range (five levels), days (three), and batches (three) as a source of variation, whereas in the case of physical properties assay the middle formulation was compressed on seven levels of compression force, ranging from 5 to 42 kN. Compressing the powder mixture with different forces yielded tablets with different hardness, disintegration, and friability. Different settings of a one-process factor were enough to induce variability in physical properties of the samples [15]. In a similar study, Tomuta et al. developed NIR method for physicochemical characterization of low active content indapamide tablets (2%, w/w) [1]. Virtanen et al. evaluated the crushing strength of theophylline tablets through Raman spectroscopy by considering both a process factor and a formulation factor to generate variability in tablet surface roughness. In this case, the tablets were prepared considering two particle sizes of theophylline, as raw material for the granulation phase, followed by mixing with lubricants and by compressing each granulate on five different compression forces [16].

The impact of polymorphism is a well-recognized phenomenon in the pharmaceutical industry, as the differences in crystalline structure of the same active ingredient generate different physical properties that get reflected in the quality of the final medicinal product. Croker et al. developed NIR and Raman methods to quantify FII and FIII of nootropic drug-piracetam from binary mixtures using a calibration set of 15 formulations with FII ranging from 0 to 100% [17].

spectrum represents the difference between the laboratory sample spectrum and the intermediate/final product spectra of an identical composition prepared on a different scale. The variability given by the process spectra can be further increased by multiplying the data with

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In situations where solid-state transformations occur within the manufacturing process, it is frequently desired to construct the calibration set with components obtained through the same method to have more representative formulations. Netchacovitch et al. used Raman spectroscopy to determine crystalline itraconazole in amorphous solid dispersions prepared by hotmelt extrusion. Calibration set included three levels of concentration and was built by using crystalline API powder, six batches of grinded extrudates with amorphous API, and placebo-

Pan et al. calibrated NIR method for the quantification of low-level Irbesartan Form B from pharmaceutical tablets. Form B is known to have a limited solubility and is formed from Form A via a solution-mediated process. To incorporate physical variability into the calibration set, the sample preparation procedure supposed the use of specifications similar to the manufacturing process. The robustness of the method to process induced physical variability, the effect of tablet hardness, granule size, and atmospheric humidity was evaluated. It was demonstrated that the prediction accuracy was influenced only by relative humidity, generating a positive bias in samples stored at 50%RH. Therefore, the entire calibration and validation was reconsidered by pre-conditioning the samples at 25C and 50%RH for 20 h, prior to recording the spectra and building the model. This way, the robustness of the method was increased to

As the number of factors increases, the calibration set becomes more complex and different strategies have to be applied to avoid correlated responses. If two formulation components C1 and C2 are correlated, a change in the concentration of C1 can be spuriously predicted as a change in C2. In DoE, factors are varied simultaneously in a systematic manner, providing orthogonality, an essential condition for estimating regression coefficients [26]. There are several design types that can be used for calibration purposes, starting from the classic full factorials down to central composite, mixture, or D-optimal designs. Considering more complex formulations, NIR spectroscopy has been applied to determine the amount of amoxicillin in the presence of seven other excipients. By applying a three-factor (API, saccharose, and other excipients) experimental design, the concentration of factors was varied orthogonally [27]. Ferreira et al. used a calibration set prepared according to a DoE with three factors: hydrochlorothyazide, cellulose, and other excipients to train a NIR method for the quantifica-

Li et al. calibrated Raman method to quantify active ingredient content considering the presence of different sources of variability: degradation compound, relative humidity, change of scales, and compression force. Laboratory samples were prepared based on a 32 full-factorial design where the active ingredient ranged between 80 and 120%, from which a subset of samples were spiked with the degradation product, added in two molar ratios. Each powder mixture was compacted at 8 and 30 kN in laboratory scale and three design points were compacted at manufacturing scale [29]. Casian et al. developed NIR and Raman methods for

future expected variations in environmental conditions [21].

tion of the active ingredient in pharmaceutical samples [28].

2.2. Design of experiment strategy

different coefficients [20, 24].

grinded extrudate [25].

Gómez et al. calibrated a Raman method for the content uniformity control of low-dosebreakscored acenocumarol tablets by under and overdosing the powdered commercial medicinal product, by adding either lactose or the active pharmaceutical ingredient to the mixture. Two commercial products with different content uniformity were considered and the two calibration sets included 7 samples in the range of 1–3% (w/w) and 12 samples in the range of 0.35– 1.50% [18]. Creating calibration sets by under-overdosing samples can result in correlated concentrations between API and excipients [19]. Collinearity between concentrations leads to spurious predictions by attributing changes to the correlated formulation component instead of the real contributor [20].

Changing the production scale generates samples that incorporate different types of variability from the primary conditions through which the calibration set was prepared. As laboratoryprepared samples lack manufacturing variability, the accuracy of prediction may be affected for production prediction sets. This limitation has been exceeded by extending the calibration set with production samples [13], adjusting the sampling strategy, pre-conditioning the calibration set to future expected environmental conditions [21], or by mathematically adding process variability to laboratory samples [20].

Blanco et al. developed NIR methods to control individual steps of paracetamol tablet manufacturing, resuming to an intermediate granulation step and tableting. Prior to building a calibration model, both laboratory-prepared samples and industrial production samples were taken into account to evaluate the eventual spectral differences. In case of the granule-active content assay, the calibration set was built solely on laboratory-prepared samples, whereas in the case of tablet assay the differences between laboratory and production samples made the calibration set include both, in order to ensure representativeness. For granule particle size characterization, samples collected over a period of 2 years ensured the presence of future expected variability in prediction set [22].

Blanco et al. used NIR to characterize mirtazapine tablets in terms of content uniformity and tablet hardness. For active ingredient content, the calibration set included production tablets from 20 batches and 34 laboratory-prepared samples, whereas for tablet hardness the laboratory samples were compacted in the range of 300–740 MPa. Including production samples for both responses reduced the systematic errors and gave better predictions [13]. By adding spectra from different manufacturing scales to the calibration set, the spectral variability becomes more representative, an important aspect for prediction accuracy. As the number of manufacturing samples is lower compared to the initial calibration set, proper weighting is necessary to avoid the dominating tendency of the larger dataset. To this regard, Farrel et al. applied Tikhonov regularization as a multi-criterion-based weighting selection method to augment the performance of NIR models regarding their ability to predict production scale products [23].

Blanco et al. proposed a method to incorporate physical variability that originates from production into the calibration. The concept relies on calculating a process spectrum, which added to the laboratory sample spectra incorporates process-related physical changes. The process spectrum represents the difference between the laboratory sample spectrum and the intermediate/final product spectra of an identical composition prepared on a different scale. The variability given by the process spectra can be further increased by multiplying the data with different coefficients [20, 24].

In situations where solid-state transformations occur within the manufacturing process, it is frequently desired to construct the calibration set with components obtained through the same method to have more representative formulations. Netchacovitch et al. used Raman spectroscopy to determine crystalline itraconazole in amorphous solid dispersions prepared by hotmelt extrusion. Calibration set included three levels of concentration and was built by using crystalline API powder, six batches of grinded extrudates with amorphous API, and placebogrinded extrudate [25].

Pan et al. calibrated NIR method for the quantification of low-level Irbesartan Form B from pharmaceutical tablets. Form B is known to have a limited solubility and is formed from Form A via a solution-mediated process. To incorporate physical variability into the calibration set, the sample preparation procedure supposed the use of specifications similar to the manufacturing process. The robustness of the method to process induced physical variability, the effect of tablet hardness, granule size, and atmospheric humidity was evaluated. It was demonstrated that the prediction accuracy was influenced only by relative humidity, generating a positive bias in samples stored at 50%RH. Therefore, the entire calibration and validation was reconsidered by pre-conditioning the samples at 25C and 50%RH for 20 h, prior to recording the spectra and building the model. This way, the robustness of the method was increased to future expected variations in environmental conditions [21].

#### 2.2. Design of experiment strategy

The impact of polymorphism is a well-recognized phenomenon in the pharmaceutical industry, as the differences in crystalline structure of the same active ingredient generate different physical properties that get reflected in the quality of the final medicinal product. Croker et al. developed NIR and Raman methods to quantify FII and FIII of nootropic drug-piracetam from binary mixtures using a calibration set of 15 formulations with FII ranging from 0 to 100% [17]. Gómez et al. calibrated a Raman method for the content uniformity control of low-dosebreakscored acenocumarol tablets by under and overdosing the powdered commercial medicinal product, by adding either lactose or the active pharmaceutical ingredient to the mixture. Two commercial products with different content uniformity were considered and the two calibration sets included 7 samples in the range of 1–3% (w/w) and 12 samples in the range of 0.35– 1.50% [18]. Creating calibration sets by under-overdosing samples can result in correlated concentrations between API and excipients [19]. Collinearity between concentrations leads to spurious predictions by attributing changes to the correlated formulation component instead

38 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Changing the production scale generates samples that incorporate different types of variability from the primary conditions through which the calibration set was prepared. As laboratoryprepared samples lack manufacturing variability, the accuracy of prediction may be affected for production prediction sets. This limitation has been exceeded by extending the calibration set with production samples [13], adjusting the sampling strategy, pre-conditioning the calibration set to future expected environmental conditions [21], or by mathematically adding

Blanco et al. developed NIR methods to control individual steps of paracetamol tablet manufacturing, resuming to an intermediate granulation step and tableting. Prior to building a calibration model, both laboratory-prepared samples and industrial production samples were taken into account to evaluate the eventual spectral differences. In case of the granule-active content assay, the calibration set was built solely on laboratory-prepared samples, whereas in the case of tablet assay the differences between laboratory and production samples made the calibration set include both, in order to ensure representativeness. For granule particle size characterization, samples collected over a period of 2 years ensured the presence of future expected

Blanco et al. used NIR to characterize mirtazapine tablets in terms of content uniformity and tablet hardness. For active ingredient content, the calibration set included production tablets from 20 batches and 34 laboratory-prepared samples, whereas for tablet hardness the laboratory samples were compacted in the range of 300–740 MPa. Including production samples for both responses reduced the systematic errors and gave better predictions [13]. By adding spectra from different manufacturing scales to the calibration set, the spectral variability becomes more representative, an important aspect for prediction accuracy. As the number of manufacturing samples is lower compared to the initial calibration set, proper weighting is necessary to avoid the dominating tendency of the larger dataset. To this regard, Farrel et al. applied Tikhonov regularization as a multi-criterion-based weighting selection method to augment the perfor-

mance of NIR models regarding their ability to predict production scale products [23].

Blanco et al. proposed a method to incorporate physical variability that originates from production into the calibration. The concept relies on calculating a process spectrum, which added to the laboratory sample spectra incorporates process-related physical changes. The process

of the real contributor [20].

variability in prediction set [22].

process variability to laboratory samples [20].

As the number of factors increases, the calibration set becomes more complex and different strategies have to be applied to avoid correlated responses. If two formulation components C1 and C2 are correlated, a change in the concentration of C1 can be spuriously predicted as a change in C2. In DoE, factors are varied simultaneously in a systematic manner, providing orthogonality, an essential condition for estimating regression coefficients [26]. There are several design types that can be used for calibration purposes, starting from the classic full factorials down to central composite, mixture, or D-optimal designs. Considering more complex formulations, NIR spectroscopy has been applied to determine the amount of amoxicillin in the presence of seven other excipients. By applying a three-factor (API, saccharose, and other excipients) experimental design, the concentration of factors was varied orthogonally [27]. Ferreira et al. used a calibration set prepared according to a DoE with three factors: hydrochlorothyazide, cellulose, and other excipients to train a NIR method for the quantification of the active ingredient in pharmaceutical samples [28].

Li et al. calibrated Raman method to quantify active ingredient content considering the presence of different sources of variability: degradation compound, relative humidity, change of scales, and compression force. Laboratory samples were prepared based on a 32 full-factorial design where the active ingredient ranged between 80 and 120%, from which a subset of samples were spiked with the degradation product, added in two molar ratios. Each powder mixture was compacted at 8 and 30 kN in laboratory scale and three design points were compacted at manufacturing scale [29]. Casian et al. developed NIR and Raman methods for the quantification of two APIs found in significantly different concentrations from immediate release tablets. The calibration set was built on a full-factorial design with two factors and five levels with a total of 25 formulations [10]. The use of full-factorial designs is feasible with two factors if five levels of variation are used [52]. Adding one more factor will generate 125 experimental runs that are impractical [26, 53].

quantification of four active ingredients with structural similarity, found in different concentrations. Calibration was built on six formulations, where five factors (four APIs and one diluent) were varied on six levels while avoiding correlations. The performance of the model was

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When DoE is used, correlations are significantly reduced dependent on the type of design, number of factors, and experimental runs. However, an increased number of factors will require a high number of experimental runs to avoid collinearity, which rapidly increases the costs. Several papers have addressed the question of how many samples are needed to ensure a robust calibration [19]. The fact that models with similar performance were developed on a reduced design compared to its full-factorial counterpart suggests the presence of redundant

Saraguca proposed a method that relies on building the model on a limited number of samples and uses the remaining formulations to test the predictive performance in terms of RMSECV and RMSEP. In the following steps, the calibration set was extended by transferring one formulation at a time from the test set until the calculated cross-validation and prediction errors stabilized. The sample selection procedure focused on maximizing the concentration variability

Alam et al. proposed a method for calibration set development in spectral space instead of concentration space. Orthogonality in spectral response will yield a better estimation of coefficients with a minimum number of samples, while orthogonality in concentration space will not necessarily translate into spectral orthogonality, as the contribution of each component to the sample spectrum is different. The method is based on decomposing the pure component spectra of a formulation into orthogonal directions (scores), which will be varied around a model tablet score through DoE. The model tablet score represents the score of the spectra recorded on a target formulation projected onto the orthonormal basis vector of the pure components spectra. After designing the spectral space calibration set, the composition of each

The application of vibrational spectroscopy for in-line monitoring implies the use of fiber optic probes mounted at the interface of the process itself to acquire spectral data with a defined rate. The simplest way to calibrate an in-line method is to acquire real-time spectra through the entire process length along with collecting samples at regular intervals. The response values obtained through reference methods are correlated with the spectral data, considering the process time as a link between the two [38–40]. More extensive calibrations also evaluate the effect of sample presentation, changing process, and formulation parameters, to challenge the

For coating application, the calibration strategy relies on the linear variation of spectral response as the contribution of the coating material increases and the tablet core contribution decreases [41]. Moes et al. developed quantitative NIR method using three batches of tablets by varying the tablet core weight (240–200–160 g) and the amount of coating suspension resulting in different coating thicknesses [42]. Möltgen et al. used five full-scale experimental

improved by adding a set of spectral data from a different production scale [43].

information in full-factorial designs [36].

spectra is retrieved by mathematical means [37].

2.3. Calibration strategy for calibration in-line monitoring methods

of all components [19].

robustness of the methods.

Netchacovitch et al. calibrated a Raman method to quantify low-level polymorphic impurities in a pharmaceutical formulation through a 12-run central-composite experimental design [25]. Central composite designs are extensions of the two-level full-factorial designs that are built by adding symmetrically axial points. Dependent on the position of axial points, factors can be varied on three levels (central composite face-centered design) or five levels (central composite circumscribed) [26].

Short et al. used NIR to evaluate relative density and crushing strength of four component tablets. Compared to other studies, where only the compaction pressure was considered as a factor to induce variability in the investigated response, in this case formulation composition was varied also. The calibration set consisted of 29 formulations (mixture design) with each formulation being compressed at different pressures [30]. Lyndgaard et al. developed a Raman method to quantify paracetamol content from tablets through blisters. The calibration set included 18 formulations, selected on the basis of a ternary mixture design (paracetamol, starch, and sucrose) with each factor being varied on six levels [31]. Igne et al. evaluated the effect of API physical form, excipient particle size, different manufacturer, and changes in environmental conditions on the performance of a NIR model. The calibration samples were prepared according to a 29-run quaternary mixture design with every formulation being compressed at two of five different forces. Only changes in the particle size of lactose produced biased predictions in both ambient and chamber conditions. The authors tested variableselection methods to increase method robustness to raw material variability [32].

Griffen et al. used Raman spectroscopy to quantify all tablet constituents, three active ingredients and two excipients. In this case, the calibration set was built on a first-order (linear) five-level, five-factor mixture design that uniformly covered the concentration ranges of the components. The concentration of individual components ranged from 1 to 85% (w/w) [33]. Mixture designs are well suited for formulation application, where the sum of all ingredients adds up to 100% and where factors cannot be manipulated independently one from another. Porfire et al. used a D-optimal design with three variables and five levels to build a calibration set with 63 formulations with the purpose of quantifying encapsulated simvastatin and two functional excipients Lα-phosphatidylcholine and cholesterol from liposomes [34]. Saraguca et al. developed an NIR method to simultaneously quantify paracetamol and three other excipients from powder blends using a calibration set constructed on a 40-run D-optimal mixture design [19].

A D-optimal design is frequently applied for a high number of factors as it gives a lower number of runs compared to factorial designs. The D-letter originates from its criterion of selecting the best subset of factor combinations from a pool of theoretically possible combinations, which relies on maximizing the X'X matrix Determinant [26]. In another study, Heinz et al. trained NIR and Raman to quantify ternary mixtures of alpha, gamma, and amorphous forms of indomethacin from ternary mixtures using a 13-sample calibration set built on a cubic model experimental design [35]. Lin et al. developed an at-line blend uniformity NIR method for simultaneous quantification of four active ingredients with structural similarity, found in different concentrations. Calibration was built on six formulations, where five factors (four APIs and one diluent) were varied on six levels while avoiding correlations. The performance of the model was improved by adding a set of spectral data from a different production scale [43].

the quantification of two APIs found in significantly different concentrations from immediate release tablets. The calibration set was built on a full-factorial design with two factors and five levels with a total of 25 formulations [10]. The use of full-factorial designs is feasible with two factors if five levels of variation are used [52]. Adding one more factor will generate 125

Netchacovitch et al. calibrated a Raman method to quantify low-level polymorphic impurities in a pharmaceutical formulation through a 12-run central-composite experimental design [25]. Central composite designs are extensions of the two-level full-factorial designs that are built by adding symmetrically axial points. Dependent on the position of axial points, factors can be varied on three levels (central composite face-centered design) or five levels (central composite

Short et al. used NIR to evaluate relative density and crushing strength of four component tablets. Compared to other studies, where only the compaction pressure was considered as a factor to induce variability in the investigated response, in this case formulation composition was varied also. The calibration set consisted of 29 formulations (mixture design) with each formulation being compressed at different pressures [30]. Lyndgaard et al. developed a Raman method to quantify paracetamol content from tablets through blisters. The calibration set included 18 formulations, selected on the basis of a ternary mixture design (paracetamol, starch, and sucrose) with each factor being varied on six levels [31]. Igne et al. evaluated the effect of API physical form, excipient particle size, different manufacturer, and changes in environmental conditions on the performance of a NIR model. The calibration samples were prepared according to a 29-run quaternary mixture design with every formulation being compressed at two of five different forces. Only changes in the particle size of lactose produced biased predictions in both ambient and chamber conditions. The authors tested variable-

selection methods to increase method robustness to raw material variability [32].

using a calibration set constructed on a 40-run D-optimal mixture design [19].

Griffen et al. used Raman spectroscopy to quantify all tablet constituents, three active ingredients and two excipients. In this case, the calibration set was built on a first-order (linear) five-level, five-factor mixture design that uniformly covered the concentration ranges of the components. The concentration of individual components ranged from 1 to 85% (w/w) [33]. Mixture designs are well suited for formulation application, where the sum of all ingredients adds up to 100% and where factors cannot be manipulated independently one from another. Porfire et al. used a D-optimal design with three variables and five levels to build a calibration set with 63 formulations with the purpose of quantifying encapsulated simvastatin and two functional excipients Lα-phosphatidylcholine and cholesterol from liposomes [34]. Saraguca et al. developed an NIR method to simultaneously quantify paracetamol and three other excipients from powder blends

A D-optimal design is frequently applied for a high number of factors as it gives a lower number of runs compared to factorial designs. The D-letter originates from its criterion of selecting the best subset of factor combinations from a pool of theoretically possible combinations, which relies on maximizing the X'X matrix Determinant [26]. In another study, Heinz et al. trained NIR and Raman to quantify ternary mixtures of alpha, gamma, and amorphous forms of indomethacin from ternary mixtures using a 13-sample calibration set built on a cubic model experimental design [35]. Lin et al. developed an at-line blend uniformity NIR method for simultaneous

experimental runs that are impractical [26, 53].

40 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

circumscribed) [26].

When DoE is used, correlations are significantly reduced dependent on the type of design, number of factors, and experimental runs. However, an increased number of factors will require a high number of experimental runs to avoid collinearity, which rapidly increases the costs. Several papers have addressed the question of how many samples are needed to ensure a robust calibration [19]. The fact that models with similar performance were developed on a reduced design compared to its full-factorial counterpart suggests the presence of redundant information in full-factorial designs [36].

Saraguca proposed a method that relies on building the model on a limited number of samples and uses the remaining formulations to test the predictive performance in terms of RMSECV and RMSEP. In the following steps, the calibration set was extended by transferring one formulation at a time from the test set until the calculated cross-validation and prediction errors stabilized. The sample selection procedure focused on maximizing the concentration variability of all components [19].

Alam et al. proposed a method for calibration set development in spectral space instead of concentration space. Orthogonality in spectral response will yield a better estimation of coefficients with a minimum number of samples, while orthogonality in concentration space will not necessarily translate into spectral orthogonality, as the contribution of each component to the sample spectrum is different. The method is based on decomposing the pure component spectra of a formulation into orthogonal directions (scores), which will be varied around a model tablet score through DoE. The model tablet score represents the score of the spectra recorded on a target formulation projected onto the orthonormal basis vector of the pure components spectra. After designing the spectral space calibration set, the composition of each spectra is retrieved by mathematical means [37].

#### 2.3. Calibration strategy for calibration in-line monitoring methods

The application of vibrational spectroscopy for in-line monitoring implies the use of fiber optic probes mounted at the interface of the process itself to acquire spectral data with a defined rate. The simplest way to calibrate an in-line method is to acquire real-time spectra through the entire process length along with collecting samples at regular intervals. The response values obtained through reference methods are correlated with the spectral data, considering the process time as a link between the two [38–40]. More extensive calibrations also evaluate the effect of sample presentation, changing process, and formulation parameters, to challenge the robustness of the methods.

For coating application, the calibration strategy relies on the linear variation of spectral response as the contribution of the coating material increases and the tablet core contribution decreases [41]. Moes et al. developed quantitative NIR method using three batches of tablets by varying the tablet core weight (240–200–160 g) and the amount of coating suspension resulting in different coating thicknesses [42]. Möltgen et al. used five full-scale experimental runs to develop a quantitative NIR method (one run) and to evaluate the effect of changing exhaust air temperature and spray rate (two runs) and the effect of tablet density and flow motion in the coater (two runs). For quantitative calibration, samples were collected through the entire process and analyzed using reference methods [6]. For the quantification of coating thickness by means of Raman spectroscopy, Kauffman et al. calibrated the method by considering film thickness and film composition variables. Tablets were coated on five levels ranging 0.5–6% weight gain by varying their residence time in the coater. As for film composition, three different TiO2 levels were evaluated due to the strong Raman signal of this component offering the potential for an indirect measure [41]. In the case of thin coatings, the generation of a calibration set can become a difficult task and can become limited due to the lack of reference methods. In this situation, an alternative to classical regression methods would be the Science-Based Calibration (SBC) approach, which allows the calibration without a reference method by separating spectral variability into orthogonal (covariance matrix) and predictive parts (related to the coating). Möltgen et al. applied SBC to develop quantitative NIR method for in-line evaluation of thin hydroxypropyl methylcellulose (HPMC) coatings through four experimental runs. For calibration, the pure HPMC spectrum was used as the coating response spectrum and the covariance matrix included hardware, core, water, and process-related noise. The method developed without reference samples predicted accurately coating thickness values in the range of 8–28 μm demonstrating the value of SBC [43].

ensuring similar sampling conditions for calibration as for actual real-time monitoring [9]. For another application, Karande et al. evaluated the effect of different spectral-sampling strategies on the performance of an NIR model, to accurately predict blend components in quaternary mixtures. Calibration samples (24 formulations-D-optimal mixture design) were recorded in three ways: laboratory mixing and static spectral acquisition; IBC (intermediate bulk container) mixing and static spectral acquisition; IBC mixing and dynamic spectral acquisition. Dynamic sampling yielded the best calibration model with highest accuracy, demonstrating

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Based on the presented examples found in literature, the most frequently applied methods to

• One chemical/physical property: formulations with three to five levels of variation for the

• One chemical and one physical property: formulations with three to five levels of variation for the chemical response and for the physical property calibration are considered

• Two chemical/physical properties: any type of DoE (full-factorial, central composite, mix-

• Three chemical/physical properties: simple lattice mixture designs or D-optimal designs. • In-line methods: models built by correlating sampled product properties with in-line collected spectra. Most rigorous studies also investigated the effect of process parameters

The dependence of the NIR spectra on the sample's chemical and physical properties caused by absorption and scatter effects can be an advantage of this type of spectroscopy, but at the same time, the scatter effects caused by sample variations or even by environmental phenomena can create a series of analytical problems. In such cases, each type of interferences has to be considered in the calibration model development. In the following section, the importance of chemical, physical, and environmental interferences will be described, providing insights on specific spectral variations produced by each category and highlighting how to handle them in

Generally, a quality NIR analysis should provide a model that manages a correct interconnection of the spectral variables with the samples properties of interest. At the same time, an ideal calibration model will not react to instrument variation, environmental changes, background interferences, and will be mostly focused on the information of interest. Chemometrics is the science that enables the extraction of relevant information, as well as the reduction of unrelated

Spectral interferences resulting from variable physico-chemical sample properties (e.g., particle size variation and moisture content) or instrumental effects (e.g., path-length variation,

the importance of selecting similar sampling conditions to the actual testing [45].

response that span the desired range of concentration/physical property.

ture design, D-optimal) to avoid collinearity and spurious predictions.

3. Handling chemical, physical, and environmental interferences

design a calibration set were as follows:

on the NIR spectra.

order to increase model robustness [1, 2].

information as well as interfering parameters.

only for target formulation (five levels).

In order to predict granule moisture content in a six-segmented fluid bed dryer through NIR spectroscopy, a calibration set of 20 experiments was applied. Granules were prepared with five moisture levels by varying the drying air temperature and drying time. Each moisture level had four replicates prepared on two different days [3].

Clavaud et al. developed a global regression model for moisture content estimation from freezedried medicine. As expected, the calibration set was extensive, including three types of active ingredient with different concentrations, different vial diameters, and excipient amounts. To include intra- and inter-product variability, 5 batches and 100 samples were used for each product [44]. Martinez et al. calibrated NIR method for in-line quantification of two active ingredients in a batch-blending process by investigating the influence of sample presentation. With regard to this, the high-loading API was used either in the form of a cohesive powder or in a granular form prepared by melt-extrusion. The observed spectral differences were resumed to the polymer wavelength absorption band that coincided with the water region. The offline calibration of the method was built on 13 samples which included both forms of the high-loading API [2].

Wahl et al. evaluated in-line the content uniformity of ternary mixtures with an NIR mounted on the feed frame of a tablet press. For calibration, the active ingredient and two excipients concentrations were varied through eight experiments selected by means of a D-optimal design and two extra runs added to ensure equidistant steps in the content of each component. Spectral data were recorded in a dynamic acquisition mode, simulating real conditions [5].

Karande et al. developed NIR method for real-time monitoring of tableting based on a 105 sample calibration set generated through a simplex lattice design with four factors (chlorpheniramine maleate, lactose, microcrystalline cellulose, and magnesium stearate). Prior to building the calibration, the effect of sampling was evaluated by recording NIR spectra in both static and dynamic conditions. The differences between measurements revealed the importance of ensuring similar sampling conditions for calibration as for actual real-time monitoring [9]. For another application, Karande et al. evaluated the effect of different spectral-sampling strategies on the performance of an NIR model, to accurately predict blend components in quaternary mixtures. Calibration samples (24 formulations-D-optimal mixture design) were recorded in three ways: laboratory mixing and static spectral acquisition; IBC (intermediate bulk container) mixing and static spectral acquisition; IBC mixing and dynamic spectral acquisition. Dynamic sampling yielded the best calibration model with highest accuracy, demonstrating the importance of selecting similar sampling conditions to the actual testing [45].

runs to develop a quantitative NIR method (one run) and to evaluate the effect of changing exhaust air temperature and spray rate (two runs) and the effect of tablet density and flow motion in the coater (two runs). For quantitative calibration, samples were collected through the entire process and analyzed using reference methods [6]. For the quantification of coating thickness by means of Raman spectroscopy, Kauffman et al. calibrated the method by considering film thickness and film composition variables. Tablets were coated on five levels ranging 0.5–6% weight gain by varying their residence time in the coater. As for film composition, three different TiO2 levels were evaluated due to the strong Raman signal of this component offering the potential for an indirect measure [41]. In the case of thin coatings, the generation of a calibration set can become a difficult task and can become limited due to the lack of reference methods. In this situation, an alternative to classical regression methods would be the Science-Based Calibration (SBC) approach, which allows the calibration without a reference method by separating spectral variability into orthogonal (covariance matrix) and predictive parts (related to the coating). Möltgen et al. applied SBC to develop quantitative NIR method for in-line evaluation of thin hydroxypropyl methylcellulose (HPMC) coatings through four experimental runs. For calibration, the pure HPMC spectrum was used as the coating response spectrum and the covariance matrix included hardware, core, water, and process-related noise. The method developed without reference samples predicted accurately coating thickness values

In order to predict granule moisture content in a six-segmented fluid bed dryer through NIR spectroscopy, a calibration set of 20 experiments was applied. Granules were prepared with five moisture levels by varying the drying air temperature and drying time. Each moisture

Clavaud et al. developed a global regression model for moisture content estimation from freezedried medicine. As expected, the calibration set was extensive, including three types of active ingredient with different concentrations, different vial diameters, and excipient amounts. To include intra- and inter-product variability, 5 batches and 100 samples were used for each product [44]. Martinez et al. calibrated NIR method for in-line quantification of two active ingredients in a batch-blending process by investigating the influence of sample presentation. With regard to this, the high-loading API was used either in the form of a cohesive powder or in a granular form prepared by melt-extrusion. The observed spectral differences were resumed to the polymer wavelength absorption band that coincided with the water region. The offline calibration of the

method was built on 13 samples which included both forms of the high-loading API [2].

Wahl et al. evaluated in-line the content uniformity of ternary mixtures with an NIR mounted on the feed frame of a tablet press. For calibration, the active ingredient and two excipients concentrations were varied through eight experiments selected by means of a D-optimal design and two extra runs added to ensure equidistant steps in the content of each component. Spectral data were recorded in a dynamic acquisition mode, simulating real conditions [5].

Karande et al. developed NIR method for real-time monitoring of tableting based on a 105 sample calibration set generated through a simplex lattice design with four factors (chlorpheniramine maleate, lactose, microcrystalline cellulose, and magnesium stearate). Prior to building the calibration, the effect of sampling was evaluated by recording NIR spectra in both static and dynamic conditions. The differences between measurements revealed the importance of

in the range of 8–28 μm demonstrating the value of SBC [43].

42 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

level had four replicates prepared on two different days [3].

Based on the presented examples found in literature, the most frequently applied methods to design a calibration set were as follows:


### 3. Handling chemical, physical, and environmental interferences

The dependence of the NIR spectra on the sample's chemical and physical properties caused by absorption and scatter effects can be an advantage of this type of spectroscopy, but at the same time, the scatter effects caused by sample variations or even by environmental phenomena can create a series of analytical problems. In such cases, each type of interferences has to be considered in the calibration model development. In the following section, the importance of chemical, physical, and environmental interferences will be described, providing insights on specific spectral variations produced by each category and highlighting how to handle them in order to increase model robustness [1, 2].

Generally, a quality NIR analysis should provide a model that manages a correct interconnection of the spectral variables with the samples properties of interest. At the same time, an ideal calibration model will not react to instrument variation, environmental changes, background interferences, and will be mostly focused on the information of interest. Chemometrics is the science that enables the extraction of relevant information, as well as the reduction of unrelated information as well as interfering parameters.

Spectral interferences resulting from variable physico-chemical sample properties (e.g., particle size variation and moisture content) or instrumental effects (e.g., path-length variation, light scattering, and random noise) can be reduced, eliminated, or standardized by using spectral pretreatments, prior to the multivariate data analysis [3]. Since the correct selection of spectral pretreatment can significantly improve the reliability of the model, this topic will be discussed in the following paragraphs. The most common pre-processing techniques can be divided into two groups: pretreatments for spectral normalization and for smoothing/differentiation. The first group achieves spectral normalization through scatter-correction methods. Scatter effects are common for all spectroscopic techniques and the phenomenon appears mostly because of the physical variabilities between samples or path-length variations. Two of those pre-processing concepts are standard normal variate (SNV) and multiplicative scatter correction (MSC) which also normalize the baseline shifts of different samples [4, 5]. The second set of pre-processing methods has the capacity to reduce or remove the noise by smoothing and differentiating the spectral values. The most common spectral derivatives are based on the Savitzky-Golay (SG) [6] and the Norris-Williams algorithms [7].

4. Data pre-processing

predictive ability of the developed model.

redundant information [46].

4.1. Pre-processing methods

4.1.1. Spectral normalization

The main goals of data-pre-processing are the following:

understandable by both humans and machines;

c. detection and removal of outliers and trends; and

a. improvement of the robustness and accuracy of subsequent analyses;

During the development of a multivariate calibration model, systematic variation such as baseline shifts and scatter effects, not relevant for the prediction of the response variables (Y), is present in predictor variables (X). Pre-processing methods are used in order to remove the systematic variation not related to the Y-matrix, which might impair the interpretation or

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b. improved interpretability: raw data are transformed into a format that will be better

d. reduction of the dimensionality of the data mining task and removal of irrelevant and

The methods generally used for data pre-processing are divided into two categories. The first consists of classical pre-processing methods, used for normalization, smoothing, and differentiation. The second is represented by methods for variable selection and dimensionality reduction [47]. Among these methods, the most appropriate has to be chosen, such as to only remove unwanted variation, without excluding or altering chemically relevant information [48].

When used in an inappropriate way, pre-processing may introduce artifacts or cause loss of information. Thus, the purpose of the analysis is important for the selection of the most appropriate pre-processing method, because scattering is disruptive for compound identification and quantitation, but is useful to study the physical properties of the sample. As a consequence, the best pre-processing method, ensuring a correct data analysis and robust results, has to be chosen by testing and comparing the results of different methods [48].

In many analytical methods, the variables measured for a given sample are increased or decreased from their true value by a multiplicative factor, which is called the scaling or gain effect. In spectroscopic methods, the scaling effect arises from path-length effects, scattering effects, source or detector variations, so the relative value of variables should be used during multivariate modeling rather than the absolute measured value. The sample normalization is one of the most important pre-processing methods, which is applied in an attempt to correct for multiplicative scaling effects, the shifts and the trends in baseline and curvilinearity, by identifying some aspect for each sample which should be essentially constant from one sample

to the next, and correcting the scaling of all variables based on this characteristic [48].

Normalization methods can be subdivided into two main groups: simple normalization methods (min-max normalization, one-norm, vector normalization, standard normal variate),

In most cases, in order to obtain best results, there is the need to apply both types of pretreatment techniques one after the other. Peeters et al. tested both types of pre-processings not only to reduce light scattering effects but also to minimize peak shifts of Raman and NIR spectra. They applied SNV, MSC, and first and second derivatives obtained by calculating 15 point quadratic Savitzky-Golay filters, in order to develop a method for the off-line prediction of tablet properties [8]. Sylvester et al. developed an in-line NIR-monitoring method for a freeze-drying process using the SNV pre-processing in order to remove multiplicative interferences caused by scatter and particle size variations and the first Savitzky-Golay derivative to reduce baseline shifts and to improve the spectral resolution [9]. The successful development of a real-time method for monitoring continuous powder flow from a tableting machine feeder was described by Alam et al. Savitzky-Golay derivatization was first applied for smoothing, followed by SNV for scatter correction [10]. Environmental interferences can be caused by sample, instrument, or even laboratory variations; this type of interferences causes misalignments or shifts of the spectra and is commonly overcome by applying alignment/warping techniques to the data [3]. Those methods stretch or compress the signal in order to match it in the best way possible with a given reference spectra [11, 12].

All pre-processing methods have the purpose to reduce the undesirable variability and interferences from the data, but there is always a risk of choosing an inappropriate type or applying a severe pre-processing that would also remove valuable information. Because of this, choosing the correct technique is one of the most important steps in data pre-processing and model development.

A last useful solution to deal with problems caused by interferences is wavelength selection method. The model development can be done based on the specific spectral domain that contains the information of interest. In order to select the domain of interest or to eliminate irrelevant wavelength domains, principal component analysis (PCA) can be performed. Prior to the PCA, the collected spectra should be pre-processed and column centered, then the analysis can be performed on the data matrix. Finally, the variables should be selected according to high peak loadings obtained for all relevant principal components (PCs), and the position of the resulting features should be compared with the original spectrum to validate the selection.

### 4. Data pre-processing

light scattering, and random noise) can be reduced, eliminated, or standardized by using spectral pretreatments, prior to the multivariate data analysis [3]. Since the correct selection of spectral pretreatment can significantly improve the reliability of the model, this topic will be discussed in the following paragraphs. The most common pre-processing techniques can be divided into two groups: pretreatments for spectral normalization and for smoothing/differentiation. The first group achieves spectral normalization through scatter-correction methods. Scatter effects are common for all spectroscopic techniques and the phenomenon appears mostly because of the physical variabilities between samples or path-length variations. Two of those pre-processing concepts are standard normal variate (SNV) and multiplicative scatter correction (MSC) which also normalize the baseline shifts of different samples [4, 5]. The second set of pre-processing methods has the capacity to reduce or remove the noise by smoothing and differentiating the spectral values. The most common spectral derivatives are

In most cases, in order to obtain best results, there is the need to apply both types of pretreatment techniques one after the other. Peeters et al. tested both types of pre-processings not only to reduce light scattering effects but also to minimize peak shifts of Raman and NIR spectra. They applied SNV, MSC, and first and second derivatives obtained by calculating 15 point quadratic Savitzky-Golay filters, in order to develop a method for the off-line prediction of tablet properties [8]. Sylvester et al. developed an in-line NIR-monitoring method for a freeze-drying process using the SNV pre-processing in order to remove multiplicative interferences caused by scatter and particle size variations and the first Savitzky-Golay derivative to reduce baseline shifts and to improve the spectral resolution [9]. The successful development of a real-time method for monitoring continuous powder flow from a tableting machine feeder was described by Alam et al. Savitzky-Golay derivatization was first applied for smoothing, followed by SNV for scatter correction [10]. Environmental interferences can be caused by sample, instrument, or even laboratory variations; this type of interferences causes misalignments or shifts of the spectra and is commonly overcome by applying alignment/warping techniques to the data [3]. Those methods stretch or compress the signal in order to match it

All pre-processing methods have the purpose to reduce the undesirable variability and interferences from the data, but there is always a risk of choosing an inappropriate type or applying a severe pre-processing that would also remove valuable information. Because of this, choosing the correct technique is one of the most important steps in data pre-processing and model

A last useful solution to deal with problems caused by interferences is wavelength selection method. The model development can be done based on the specific spectral domain that contains the information of interest. In order to select the domain of interest or to eliminate irrelevant wavelength domains, principal component analysis (PCA) can be performed. Prior to the PCA, the collected spectra should be pre-processed and column centered, then the analysis can be performed on the data matrix. Finally, the variables should be selected according to high peak loadings obtained for all relevant principal components (PCs), and the position of the resulting features should be compared with the original spectrum to validate

based on the Savitzky-Golay (SG) [6] and the Norris-Williams algorithms [7].

44 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

in the best way possible with a given reference spectra [11, 12].

development.

the selection.

During the development of a multivariate calibration model, systematic variation such as baseline shifts and scatter effects, not relevant for the prediction of the response variables (Y), is present in predictor variables (X). Pre-processing methods are used in order to remove the systematic variation not related to the Y-matrix, which might impair the interpretation or predictive ability of the developed model.

The main goals of data-pre-processing are the following:


The methods generally used for data pre-processing are divided into two categories. The first consists of classical pre-processing methods, used for normalization, smoothing, and differentiation. The second is represented by methods for variable selection and dimensionality reduction [47]. Among these methods, the most appropriate has to be chosen, such as to only remove unwanted variation, without excluding or altering chemically relevant information [48].

When used in an inappropriate way, pre-processing may introduce artifacts or cause loss of information. Thus, the purpose of the analysis is important for the selection of the most appropriate pre-processing method, because scattering is disruptive for compound identification and quantitation, but is useful to study the physical properties of the sample. As a consequence, the best pre-processing method, ensuring a correct data analysis and robust results, has to be chosen by testing and comparing the results of different methods [48].

#### 4.1. Pre-processing methods

#### 4.1.1. Spectral normalization

In many analytical methods, the variables measured for a given sample are increased or decreased from their true value by a multiplicative factor, which is called the scaling or gain effect. In spectroscopic methods, the scaling effect arises from path-length effects, scattering effects, source or detector variations, so the relative value of variables should be used during multivariate modeling rather than the absolute measured value. The sample normalization is one of the most important pre-processing methods, which is applied in an attempt to correct for multiplicative scaling effects, the shifts and the trends in baseline and curvilinearity, by identifying some aspect for each sample which should be essentially constant from one sample to the next, and correcting the scaling of all variables based on this characteristic [48].

Normalization methods can be subdivided into two main groups: simple normalization methods (min-max normalization, one-norm, vector normalization, standard normal variate), requiring only the information from the spectrum to be normalized, and normalization methods requiring the presence of collective spectral data matrices or of reference spectra (multiplicative scatter correction and extended multiplicative signal correction (EMSC) [46]. Among these, the most used scattering correction algorithms include the SNV and MSC. The two pretreatments give similar results, being considered exchangeable, but the results obtained through both algorithms are compared usually, since they may be different [49]. SNV was proposed to reduce multiplicative effects of scattering, particle size, and multicollinearity changes over the NIR spectra. This approach starts with mean centering and consists of dividing mean-centered spectra by the standard deviation over the spectral intensities [50]. SNV normalizes each spectrum returning a mean of 0 and a variance of 1 spectra dataset [48]. The disadvantage is the assumption that multiplicative effects are uniform over the whole spectral range, so artifacts may be introduced by this transformation.

polynomial order. The highest derivative that can be determined depends on the degree of the

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These methods rely on reducing the dimension of the predictor space spanned by a number of variables or wavelengths, in order to find the subspace mainly containing variations related to the response matrix. The orthogonal projection and the variable-selection methods are in this group. Orthogonal signal correction (OSC) and its modified version direct orthogonal signal correction ((D)OSC) are the most common among this group, developed to remove systematic variation in the descriptor matrix, that is not correlated to the response matrix. In other words, the pre-processing is performed in such a way that the removed parts are orthogonal (not linearly related) to the response matrix [53, 54]. The method has the advantage of correcting at

An alternative OSC algorithm was developed by Trygg and Wold and is called orthogonal projection to latent structures (OPLS). The objective of OPLS is the same as of OSC, but the approach is different, i.e., the OPLS method analyzes the variation explained in each PLS component. The non-correlated systematic variation in descriptor matrix is removed, making interpretation of the resulting PLS model easier, and the non-correlated variation can be

Variable-selection techniques consist of selecting particular variables related to the response, instead of removing the interference modeled as a spectrum, the aim being to identify a subset of wavelengths that produces the smallest possible error [56]. Selecting the most correlated wavelengths may lead to better performance in PLS and PCR, but, on the other hand, selection of the most correlated wavelengths may eliminate those that correct for the influence of

In practical applications, combinations of pre-processing methods are usually employed in search for the best algorithm, involving more than one pre-processing step. According to Rinnan et al., several rules may serve as guidelines: scatter correction (except of normalization) should always be performed prior to differentiation; normalization can be used at both ends of the correction, but usually is easier to be assessed if it is done prior to any other strategy; MSC gives a smaller baseline correction than SNV with subsequent de-trending; it is not

The ideal pre-processing strategy should only remove artifacts present in the data, without introducing any unwanted artifacts or variability in the data. When physical properties, that is, tablets' crushing strength, are evaluated through vibrational spectroscopy, typical preprocessing methods such as SNV, MSC, and the derivatives cannot be used, because they lose the baseline-shifting information, which is relevant for the physical properties. The data in this case should be modeled as such or after normalization [16]. Three approaches are described in the literature, for the selection of the most appropriate strategy: the trial-and-error approach;

polynomial used during the fitting [51].

4.1.3. Dimensionality-reduction methods

once multiple artifacts.

analyzed further [55].

interfering compounds or factors [56].

recommended to perform de-trending followed by SNV [51].

visual inspection and the use of data-quality parameters [57].

4.2. Pre-processing strategy

The de-trend method is another approach to correct for baseline shift, which removes the baseline curvature by expressing it as a quadratic function of the wavelengths. The modeled baseline is subtracted from the spectrum, so de-trend can be used after SNV to circumvent any curvilinear trend, where the baseline drift is a function of wavelength [50]. The MSC pretreatment performs a linear regression of each spectrum on a reference spectrum, which is usually the mean of all available spectra, for example, the average spectra of the calibration set, or a generic reference spectrum can also be applied [49].

#### 4.1.2. Smoothing and differentiation

The smoothing algorithms are used in order to correct the spectral noise, while differentiation is used to enhance spectral resolution and to eliminate background absorption. The most common ways to achieve smoothing are the use of noise filters for de-noising and smoothing and Savitzky-Golay smoothing/derivative filters for smoothing/resolution enhancement. Noise filters are specific low-pass filters which can be used to reduce random noise. Their drawback is that the signal-to-noise ratio is increased at the expenses of distorting the signal. The most popular smoothing filters are the zeroth-order SG-smoothing/derivative filter, the binomial filter, and the moving average filter [46].

Derivatives are used for their capability to remove both additive and multiplicative effects in the spectra. The first derivative removes only the baseline; the second derivative removes both baseline and linear trend. The first derivative is estimated as the difference between two subsequent spectral measurement points, while the second-order derivative is estimated as the difference between two successive points of the first-order derivative spectra [51]. The most popular derivation method is SG algorithm, proposed by Golay and Savitzky in 1962 [52]. The method has the advantage that computation of the derivatives and smoothing are carried out in a single step. The algorithm used in this method is based on fitting a polynomial in a symmetric window on the raw data, in order to find the derivative at the center point. The parameters of the polynomial are calculated and the derivative of this function is found, this value being used as the derivative estimate for this center point. The same operation is subsequently applied to all points in the spectra. Two decisions are important to be made in this algorithm, i.e., the window width (width of the subset of the data) and the fitted polynomial order. The highest derivative that can be determined depends on the degree of the polynomial used during the fitting [51].

#### 4.1.3. Dimensionality-reduction methods

requiring only the information from the spectrum to be normalized, and normalization methods requiring the presence of collective spectral data matrices or of reference spectra (multiplicative scatter correction and extended multiplicative signal correction (EMSC) [46]. Among these, the most used scattering correction algorithms include the SNV and MSC. The two pretreatments give similar results, being considered exchangeable, but the results obtained through both algorithms are compared usually, since they may be different [49]. SNV was proposed to reduce multiplicative effects of scattering, particle size, and multicollinearity changes over the NIR spectra. This approach starts with mean centering and consists of dividing mean-centered spectra by the standard deviation over the spectral intensities [50]. SNV normalizes each spectrum returning a mean of 0 and a variance of 1 spectra dataset [48]. The disadvantage is the assumption that multiplicative effects are uniform over the whole

The de-trend method is another approach to correct for baseline shift, which removes the baseline curvature by expressing it as a quadratic function of the wavelengths. The modeled baseline is subtracted from the spectrum, so de-trend can be used after SNV to circumvent any curvilinear trend, where the baseline drift is a function of wavelength [50]. The MSC pretreatment performs a linear regression of each spectrum on a reference spectrum, which is usually the mean of all available spectra, for example, the average spectra of the calibration set,

The smoothing algorithms are used in order to correct the spectral noise, while differentiation is used to enhance spectral resolution and to eliminate background absorption. The most common ways to achieve smoothing are the use of noise filters for de-noising and smoothing and Savitzky-Golay smoothing/derivative filters for smoothing/resolution enhancement. Noise filters are specific low-pass filters which can be used to reduce random noise. Their drawback is that the signal-to-noise ratio is increased at the expenses of distorting the signal. The most popular smoothing filters are the zeroth-order SG-smoothing/derivative filter, the

Derivatives are used for their capability to remove both additive and multiplicative effects in the spectra. The first derivative removes only the baseline; the second derivative removes both baseline and linear trend. The first derivative is estimated as the difference between two subsequent spectral measurement points, while the second-order derivative is estimated as the difference between two successive points of the first-order derivative spectra [51]. The most popular derivation method is SG algorithm, proposed by Golay and Savitzky in 1962 [52]. The method has the advantage that computation of the derivatives and smoothing are carried out in a single step. The algorithm used in this method is based on fitting a polynomial in a symmetric window on the raw data, in order to find the derivative at the center point. The parameters of the polynomial are calculated and the derivative of this function is found, this value being used as the derivative estimate for this center point. The same operation is subsequently applied to all points in the spectra. Two decisions are important to be made in this algorithm, i.e., the window width (width of the subset of the data) and the fitted

spectral range, so artifacts may be introduced by this transformation.

46 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

or a generic reference spectrum can also be applied [49].

binomial filter, and the moving average filter [46].

4.1.2. Smoothing and differentiation

These methods rely on reducing the dimension of the predictor space spanned by a number of variables or wavelengths, in order to find the subspace mainly containing variations related to the response matrix. The orthogonal projection and the variable-selection methods are in this group. Orthogonal signal correction (OSC) and its modified version direct orthogonal signal correction ((D)OSC) are the most common among this group, developed to remove systematic variation in the descriptor matrix, that is not correlated to the response matrix. In other words, the pre-processing is performed in such a way that the removed parts are orthogonal (not linearly related) to the response matrix [53, 54]. The method has the advantage of correcting at once multiple artifacts.

An alternative OSC algorithm was developed by Trygg and Wold and is called orthogonal projection to latent structures (OPLS). The objective of OPLS is the same as of OSC, but the approach is different, i.e., the OPLS method analyzes the variation explained in each PLS component. The non-correlated systematic variation in descriptor matrix is removed, making interpretation of the resulting PLS model easier, and the non-correlated variation can be analyzed further [55].

Variable-selection techniques consist of selecting particular variables related to the response, instead of removing the interference modeled as a spectrum, the aim being to identify a subset of wavelengths that produces the smallest possible error [56]. Selecting the most correlated wavelengths may lead to better performance in PLS and PCR, but, on the other hand, selection of the most correlated wavelengths may eliminate those that correct for the influence of interfering compounds or factors [56].

#### 4.2. Pre-processing strategy

In practical applications, combinations of pre-processing methods are usually employed in search for the best algorithm, involving more than one pre-processing step. According to Rinnan et al., several rules may serve as guidelines: scatter correction (except of normalization) should always be performed prior to differentiation; normalization can be used at both ends of the correction, but usually is easier to be assessed if it is done prior to any other strategy; MSC gives a smaller baseline correction than SNV with subsequent de-trending; it is not recommended to perform de-trending followed by SNV [51].

The ideal pre-processing strategy should only remove artifacts present in the data, without introducing any unwanted artifacts or variability in the data. When physical properties, that is, tablets' crushing strength, are evaluated through vibrational spectroscopy, typical preprocessing methods such as SNV, MSC, and the derivatives cannot be used, because they lose the baseline-shifting information, which is relevant for the physical properties. The data in this case should be modeled as such or after normalization [16]. Three approaches are described in the literature, for the selection of the most appropriate strategy: the trial-and-error approach; visual inspection and the use of data-quality parameters [57].

In the trial-and-error approach, all pre-processing methods are applied to the data and the preprocessed data are used as an input to a calibration model, which is further used to assess the quality of the pre-processing strategy by an internal measure, such as RMSEP or RMSECV [57]. For example, Karande et al. chose among various pre-processing methods through comparing the figures of merit (explained variance, R<sup>2</sup> , RMSEC, and RMSECV) of the developed partial least-squares (PLS1) regression models, for the quantification of micronized drug and excipients in tablets by NIR spectroscopy. The raw calibration spectra were pretreated with SNV followed by first derivative and SNV followed by second derivative pre-processing. All models were developed using the entire spectral range or narrow spectral ranges. The best performance of the calibration method (highest explained variance, lowest RMSEC and RMSECV) was obtained using the whole spectral range, pretreated with SNV followed by first derivative spectral pre-processing [9] . The same approach has been used by Porfire et al. in the attempt to select the best pretreatment method in the development of calibration models for prediction of chemical composition and crushing strength of sustained-release tablets with indapamide. PLS regression was performed for non-processed spectra as well as for spectra treated by various pre-processing methods (i.e., FD, SD, SNV, MSC, FD + SNV, FD + MSC), and the most suitable pretreatment algorithm was chosen based on the results obtained for PLS model validation through cross-validation, i.e., based on its RMSECV and bias [58].

normal area corresponding to 95 or 99% confidence. Subsequently, for a better understanding of the properties of grouped data, a splitting of data into smaller groups according to the nature of the clustering is done, and separate PCA models may be fitted. For the detection of weakly deviating observations (moderate outliers), which are not strong enough to show up as outliers in score plots, the residuals of each observation are used. The detection tool is called DmodX (a notation for distance to the model in X-space). A value of Dmodx is calculated for each observation, and the values are plotted in a control chart where the maximum tolerable distance (Dcrit) for the dataset is given. The plot of DmodX enables an overview of the unsystematic process variation, as moderate outliers have DmodX values

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Before PCA, scaling of data is usually performed, because variables have different numerical ranges so they will have different variance and they will weight differently in the data analysis. The most common approach is the unit variance (UV) scaling, consisting in dividing each variable by its standard deviation. The result is that each variable has equal variance, meaning that the "length" of each variable is identical, although the mean values still

Tôrres et al. used Hotelling's T<sup>2</sup> chart to analyze the NIR spectra of a training (calibration) set for the development of a monitoring method for the stability of captopril in tablets. Before being analyzed by PCA, NIR spectra were smoothed as described by Savitzky-Golay with a 21-point window and second-order polynomial and were processed by MSC for the correction of baseline variation due to non-homogeneity of particle's distribution [60]. The Hotelling's T<sup>2</sup> chart measures the distance from an observation to the center of the samples under normal operating conditions and evaluates whether a particular sample has a systematic deviation from the samples considered to be under statistical control [61]. As all samples from the training set were assumed to be normal, the training chart was not expected to identify systematic deviations in these samples in the training phase, so the number of PC retained in the model was selected to minimize the number of false alarms (false positives and false

Regression analysis is a modeling technique used to investigate the relationship between dependent variables (responses or y's variables) and independent variables (predictor, factors or x's variables). According to the number of variable, three cases can be distinguished:

The objective of a regression method can be achieved by means of a model where the observed result (dependent variables, response, y's variables) is described as a function of independent

negatives) during the training phase of the control charts [60].

1. Simple linear regression—one y and one x variable.

variables (x's variables) and the noise is left as residual.

2. Univariate linear regression—one y and several x's variables.

3. Multivariate linear regression—several y's and several x's variables [62].

higher than Dcrit [59].

remain different [59].

5. Regression methods

In visual inspection method, the effect of pre-processing is assessed before a model is constructed. Thus, because artifacts have been removed during pre-processing, samples should show more spectral overlap after pre-processing in visual inspection, and differences between groups of samples should be more pronounced. However, as visual inspection may be very difficult and not objective, the data are not usually inspected in "spectral mode" but in a lower dimensional space, obtained usually through principal component analysis [57]. PCA reduces the dimensionality of the problem by generating linear combinations of the original variables returning new "latent" variables. Each original variable is weighted by a loading representing the importance of the considered variable on the variance of the data. The variability of the data is expressed by new dimensions called principal components, and the projection of a pixel onto the PCs is called its score. The result of PCA is the decomposition of the pre-processed matrix in a score matrix and a loading matrix [48]. PCA is used for data overview, for example, for detecting outliers, groups, and trends among observations, for evaluating relationships among variables, and between observations and variables. In PCA, data in the matrix X are transferred into a new coordinate system defined by principal components. The direction in variable space occupied by the most varying data points will define the location of the first PC, and the second PC will be given by the largest variation orthogonal to the first component. PCs are extracted until only minor variation is left unexplained by the PC model, each component consisting of a score vector and a loading vector. Observations close to each other in a score plot have similar properties, and variables close to each other in a loading plot are correlated. Thus, the score plot is useful for the detection of strong outliers, clustering, and time trends [59] .

The detection of strong outliers through PCA is done by analyzing the score plot. The strong outliers are removed, as they may have a degrading impact on model quality. A statistic tool called Hotteling's T<sup>2</sup> may be used in conjunction with the score plot for the detection of strong outliers. This tool is a multivariate generalization of Student's t-test, defining the normal area corresponding to 95 or 99% confidence. Subsequently, for a better understanding of the properties of grouped data, a splitting of data into smaller groups according to the nature of the clustering is done, and separate PCA models may be fitted. For the detection of weakly deviating observations (moderate outliers), which are not strong enough to show up as outliers in score plots, the residuals of each observation are used. The detection tool is called DmodX (a notation for distance to the model in X-space). A value of Dmodx is calculated for each observation, and the values are plotted in a control chart where the maximum tolerable distance (Dcrit) for the dataset is given. The plot of DmodX enables an overview of the unsystematic process variation, as moderate outliers have DmodX values higher than Dcrit [59].

Before PCA, scaling of data is usually performed, because variables have different numerical ranges so they will have different variance and they will weight differently in the data analysis. The most common approach is the unit variance (UV) scaling, consisting in dividing each variable by its standard deviation. The result is that each variable has equal variance, meaning that the "length" of each variable is identical, although the mean values still remain different [59].

Tôrres et al. used Hotelling's T<sup>2</sup> chart to analyze the NIR spectra of a training (calibration) set for the development of a monitoring method for the stability of captopril in tablets. Before being analyzed by PCA, NIR spectra were smoothed as described by Savitzky-Golay with a 21-point window and second-order polynomial and were processed by MSC for the correction of baseline variation due to non-homogeneity of particle's distribution [60]. The Hotelling's T<sup>2</sup> chart measures the distance from an observation to the center of the samples under normal operating conditions and evaluates whether a particular sample has a systematic deviation from the samples considered to be under statistical control [61]. As all samples from the training set were assumed to be normal, the training chart was not expected to identify systematic deviations in these samples in the training phase, so the number of PC retained in the model was selected to minimize the number of false alarms (false positives and false negatives) during the training phase of the control charts [60].

### 5. Regression methods

In the trial-and-error approach, all pre-processing methods are applied to the data and the preprocessed data are used as an input to a calibration model, which is further used to assess the quality of the pre-processing strategy by an internal measure, such as RMSEP or RMSECV [57]. For example, Karande et al. chose among various pre-processing methods through comparing

least-squares (PLS1) regression models, for the quantification of micronized drug and excipients in tablets by NIR spectroscopy. The raw calibration spectra were pretreated with SNV followed by first derivative and SNV followed by second derivative pre-processing. All models were developed using the entire spectral range or narrow spectral ranges. The best performance of the calibration method (highest explained variance, lowest RMSEC and RMSECV) was obtained using the whole spectral range, pretreated with SNV followed by first derivative spectral pre-processing [9] . The same approach has been used by Porfire et al. in the attempt to select the best pretreatment method in the development of calibration models for prediction of chemical composition and crushing strength of sustained-release tablets with indapamide. PLS regression was performed for non-processed spectra as well as for spectra treated by various pre-processing methods (i.e., FD, SD, SNV, MSC, FD + SNV, FD + MSC), and the most suitable pretreatment algorithm was chosen based on the results obtained for PLS

model validation through cross-validation, i.e., based on its RMSECV and bias [58].

detection of strong outliers, clustering, and time trends [59] .

In visual inspection method, the effect of pre-processing is assessed before a model is constructed. Thus, because artifacts have been removed during pre-processing, samples should show more spectral overlap after pre-processing in visual inspection, and differences between groups of samples should be more pronounced. However, as visual inspection may be very difficult and not objective, the data are not usually inspected in "spectral mode" but in a lower dimensional space, obtained usually through principal component analysis [57]. PCA reduces the dimensionality of the problem by generating linear combinations of the original variables returning new "latent" variables. Each original variable is weighted by a loading representing the importance of the considered variable on the variance of the data. The variability of the data is expressed by new dimensions called principal components, and the projection of a pixel onto the PCs is called its score. The result of PCA is the decomposition of the pre-processed matrix in a score matrix and a loading matrix [48]. PCA is used for data overview, for example, for detecting outliers, groups, and trends among observations, for evaluating relationships among variables, and between observations and variables. In PCA, data in the matrix X are transferred into a new coordinate system defined by principal components. The direction in variable space occupied by the most varying data points will define the location of the first PC, and the second PC will be given by the largest variation orthogonal to the first component. PCs are extracted until only minor variation is left unexplained by the PC model, each component consisting of a score vector and a loading vector. Observations close to each other in a score plot have similar properties, and variables close to each other in a loading plot are correlated. Thus, the score plot is useful for the

The detection of strong outliers through PCA is done by analyzing the score plot. The strong outliers are removed, as they may have a degrading impact on model quality. A statistic tool called Hotteling's T<sup>2</sup> may be used in conjunction with the score plot for the detection of strong outliers. This tool is a multivariate generalization of Student's t-test, defining the

, RMSEC, and RMSECV) of the developed partial

the figures of merit (explained variance, R<sup>2</sup>

48 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Regression analysis is a modeling technique used to investigate the relationship between dependent variables (responses or y's variables) and independent variables (predictor, factors or x's variables). According to the number of variable, three cases can be distinguished:


The objective of a regression method can be achieved by means of a model where the observed result (dependent variables, response, y's variables) is described as a function of independent variables (x's variables) and the noise is left as residual.

In a regression analysis, the relationship between two data matrix X (BxK) and Y (NxM) are related to each other. A regression model can be written as in a matrix form as

$$\mathbf{Y} = \mathbf{X}\mathbf{B} \tag{1}$$

If not all the x's variables can be controlled, the number of x's variables extends the number of experimental runs or the number of experimental runs is larger than the number of x's variables, the co-linearity between x's variables arises and the orthogonality no longer exists, so the

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51

Except the cases when the calibration of spectroscopic methods is performed following the design of experiment strategy in the other multivariate calibration, the orthogonalities do not exist and the MLR cannot be applied. That is the reason why other regression methods based on latent variables as partial last squares are preferred and become popular. When the calibrations are performed based on latent variables, inside of using the original variables in the regression, a new set of orthogonal (latent) variables is calculated and leads to reduction of the original dimension of x's variables matrix and performs the least-square estimation.

Principal component regression is a regression method based on principal component analysis and it is used when datasets are highly collinear. In a PCA regression, the original set of collinear variables is transformed to a new set of correlated variables. So, the principal component analysis is used to decompose the x's variables into a principal component (orthogonal basis) and a subset of components in order to predict y's variables. The basic idea of the principal component regression is to calculate the principal components and then use some of these components as predictors in a linear regression model fitted using the typical least-

In the case of PCR determination, the relationship between x's variables and y's variables is

where X contains X average; T is a matrix of scores that summarizes the X variables; P is a matrix of loadings showing the influence of the X variables; E is a matrix of residuals (the

The main idea of principal regression is to replace X matrix of row date to a smaller orthogonal score—loading matrix (TPT matrix) that summarized the original X matrix, and then to relate

The core of PCR is that a small number of principal components is enough to explain the variability into the data. In most of the cases, it might be found out that four to six principal

The partial least-squares regression is the most popular method for the creation of models used in the development of NIR and Raman spectrometric methods and is used to develop a linear

components are enough to explain more that 90% of the variance into the data.

link between two matrices, the NIR/Raman spectral data and the reference values.

), called principal components, and a

<sup>X</sup> <sup>¼</sup> <sup>1</sup><sup>X</sup> <sup>þ</sup> TPT <sup>þ</sup> <sup>E</sup> (6)

inverse of XT

X cannot be applied.

5.2. Principal component regression

squares procedure [66, 67].

matrix of residuals (E).

the T-scores to y's variables.

5.3. Partial least squares

achieved by means of a matrix of lower dimension (TPT

deviations between the original and the predicted values) [66].

where Y is the matrix of x's variables; X is the matrix of y's variables; B is the matrix of regression coefficient, B(KxM).

A good estimate of regression coefficient (B matrix) provides a good fit to Y and good prediction of future unknown parameters y<sup>T</sup> . More, the regression coefficient vector should be of mechanistic understanding and interpretable [59, 63, 64].

A large number of regression methods were developed, all with the goal of finding the best estimation of B. In the calibration of spectroscopic methods, only multivariate regression techniques can be applied, and the most used are (1) multiple linear regression (MLR), (2) principal component regression, (3) partial least-squares regression, and (4) orthogonal partial least-squares regression (O-PLS). In the last years, some advanced regression methods as (5) Bayesian ridge regression (Bayes-RR) (6) support vector regression (SVR) or (7) decision tree regression (DTR) have started to be used.

#### 5.1. Multiple linear regression

Multiple linear regression is an extension of simple linear regression model. In the case of MLR determination, the relationship between x's—variables and y's—variables is achieved by means of a model where the responses (y's—variables) are described as a function of analyzed factors (x's—variables) and the noise is left in the residual (ε) (Eq. (1)) [65]

$$y = f(\mathbf{x}\_1, \mathbf{x}\_2, \mathbf{x}\_3, \dots, \mathbf{x}\_n) + \varepsilon \tag{2}$$

The function f is approximated by a polynomial equation (Eq. (3)),

$$y = b\_0 + b\_1 \mathbf{x}\_0 + b\_0 \mathbf{x}\_2 + \dots + b\_0 \mathbf{x}\_n + \varepsilon \tag{3}$$

where bi (i = 1, 2, 3, …,n) are the regression coefficients and describe the effect of each term on the response y.

The polynomial equation (Eq. (3)) can be written in matrix way as follows:

$$y = Xb + \varepsilon \tag{4}$$

where X are the matrix of x's variables and b the vector, and the multiple linear regression is used to determinate vector b.

If there are orthogonalities between x's variables, Eq. (4) can be written as

$$b = \left(\mathbf{X}^T\mathbf{X}\right)^{-1}\mathbf{X}^T\mathbf{y} \tag{5}$$

In this equation, matrix X<sup>T</sup> X become a diagonal matrix and b is easily calculated. If not all the x's variables can be controlled, the number of x's variables extends the number of experimental runs or the number of experimental runs is larger than the number of x's variables, the co-linearity between x's variables arises and the orthogonality no longer exists, so the inverse of XT X cannot be applied.

Except the cases when the calibration of spectroscopic methods is performed following the design of experiment strategy in the other multivariate calibration, the orthogonalities do not exist and the MLR cannot be applied. That is the reason why other regression methods based on latent variables as partial last squares are preferred and become popular. When the calibrations are performed based on latent variables, inside of using the original variables in the regression, a new set of orthogonal (latent) variables is calculated and leads to reduction of the original dimension of x's variables matrix and performs the least-square estimation.

#### 5.2. Principal component regression

In a regression analysis, the relationship between two data matrix X (BxK) and Y (NxM) are

where Y is the matrix of x's variables; X is the matrix of y's variables; B is the matrix of

A good estimate of regression coefficient (B matrix) provides a good fit to Y and good

A large number of regression methods were developed, all with the goal of finding the best estimation of B. In the calibration of spectroscopic methods, only multivariate regression techniques can be applied, and the most used are (1) multiple linear regression (MLR), (2) principal component regression, (3) partial least-squares regression, and (4) orthogonal partial least-squares regression (O-PLS). In the last years, some advanced regression methods as (5) Bayesian ridge regression (Bayes-RR) (6) support vector regression (SVR) or (7) decision tree

Multiple linear regression is an extension of simple linear regression model. In the case of MLR determination, the relationship between x's—variables and y's—variables is achieved by means of a model where the responses (y's—variables) are described as a function of analyzed

where bi (i = 1, 2, 3, …,n) are the regression coefficients and describe the effect of each term on

where X are the matrix of x's variables and b the vector, and the multiple linear regression is

<sup>b</sup> <sup>¼</sup> <sup>X</sup>TX �<sup>1</sup>

X become a diagonal matrix and b is easily calculated.

factors (x's—variables) and the noise is left in the residual (ε) (Eq. (1)) [65]

The polynomial equation (Eq. (3)) can be written in matrix way as follows:

If there are orthogonalities between x's variables, Eq. (4) can be written as

The function f is approximated by a polynomial equation (Eq. (3)),

Y ¼ XB (1)

. More, the regression coefficient vector should be

y ¼ f xð <sup>1</sup>; x2; x3…:; xnÞ þ ε (2)

y ¼ Xb þ ε (4)

XTy (5)

y ¼ b<sup>0</sup> þ b1x<sup>0</sup> þ b0x<sup>2</sup> þ … þ b0xn þ ε (3)

related to each other. A regression model can be written as in a matrix form as

regression coefficient, B(KxM).

prediction of future unknown parameters y<sup>T</sup>

regression (DTR) have started to be used.

5.1. Multiple linear regression

the response y.

used to determinate vector b.

In this equation, matrix X<sup>T</sup>

of mechanistic understanding and interpretable [59, 63, 64].

50 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Principal component regression is a regression method based on principal component analysis and it is used when datasets are highly collinear. In a PCA regression, the original set of collinear variables is transformed to a new set of correlated variables. So, the principal component analysis is used to decompose the x's variables into a principal component (orthogonal basis) and a subset of components in order to predict y's variables. The basic idea of the principal component regression is to calculate the principal components and then use some of these components as predictors in a linear regression model fitted using the typical leastsquares procedure [66, 67].

In the case of PCR determination, the relationship between x's variables and y's variables is achieved by means of a matrix of lower dimension (TPT ), called principal components, and a matrix of residuals (E).

$$X = \mathbf{1}\overline{X} + TP^T + E \tag{6}$$

where X contains X average; T is a matrix of scores that summarizes the X variables; P is a matrix of loadings showing the influence of the X variables; E is a matrix of residuals (the deviations between the original and the predicted values) [66].

The main idea of principal regression is to replace X matrix of row date to a smaller orthogonal score—loading matrix (TPT matrix) that summarized the original X matrix, and then to relate the T-scores to y's variables.

The core of PCR is that a small number of principal components is enough to explain the variability into the data. In most of the cases, it might be found out that four to six principal components are enough to explain more that 90% of the variance into the data.

#### 5.3. Partial least squares

The partial least-squares regression is the most popular method for the creation of models used in the development of NIR and Raman spectrometric methods and is used to develop a linear link between two matrices, the NIR/Raman spectral data and the reference values.

The PLS approach was first proposed by Herman Wold around 1975 for the modeling of complicated datasets in terms of chains of matrices, the so-called path models. PLS regression is preferable to develop calibration models because unlike MLR, it can analyze data with strongly collinear, noisy, and numerous X-variables, and also simultaneously model several response variables [68]. PLS was developed for situation in which the data have more independent variables than observations (the "small n, large p") or/and where collinearity is present among dataset [69].

The PLS finds a multivariate model (linear or polynomial) that describes the relationship between Y matrix (dependent variables) and X matrix (predictor variables) expressed as

$$\mathbf{Y} = \mathbf{f}(\mathbf{X}) + \mathbf{E} \tag{7}$$

An O2-PLS model can be written as

<sup>X</sup> <sup>¼</sup> <sup>1</sup>X<sup>0</sup> <sup>þ</sup> TPT <sup>þ</sup> ToP<sup>T</sup>

<sup>Y</sup> <sup>¼</sup> <sup>1</sup>Y<sup>0</sup> <sup>þ</sup> UCT <sup>þ</sup> UoCT

where X is a contain de X average; Y is a contain de Y average; T is a matrix of scores that summarizes the X variables; U is a matrix of scores that summarizes the Y variables; P is a matrix of weigh that express the correlation between X and U; C is a matrix of weigh that

In the last years, O2-PLS has become the preferred regression technique for the development of

Another regression method recently proposed for multivariate calibration of spectroscopic methods is Bayesian ridge regression. The method presents similarities with least squares,

In a Bayes-RR regression model, higher-level prior Gaussian distributions can be introduced

parameters w. Since this prior distribution is conjugate to the likelihood function, the predictive

The Bayes-RR is a widely used regression technique in machine learning based on the ridge regression [73], and in the last years its performance for the development of excellent models

The support vector machines (SVMs) are a set of learning methods mostly used for classification that can be used as a regression technique which is called the support vector regression. In the last years, SVM started to be used in chemometrics for NIR spectra classification and multivariate calibration. The SVR uses the same principles as the SVM and is based on finding the hyperplane maximizing the margin between classes. The hyperplane maximizing the margin is justified by statistical learning theory endowed with a probabilistic test error bound that is minimized when the margin is maximized. The regression is performed using kernel functions that transform the data into a higher dimensional feature space to make a linear

ð

and the estimated coefficients tend toward zero in order to avoid collinearity [44].

over α<sup>2</sup> and α, and the prediction can be performed by integrating over α<sup>2</sup>

p yjα, <sup>α</sup><sup>2</sup> � � <sup>¼</sup>

for spectroscopic calibration has been proved [72, 74, 75].

express the correlation between Y and T; E, F, HTU, HUT are the matrixes of residuals.

The matrixes TP<sup>T</sup> and UC<sup>T</sup> hold the joint X/Y information overlap [12, 63, 64].

calibration models in NIR and Raman spectroscopy.

5.5. Bayesian ridge regression

distribution is also Gaussian [72]

5.6. Support vector regression (SVR)

<sup>o</sup> þ E (11)

http://dx.doi.org/10.5772/intechopen.72598

53

<sup>O</sup> þ F (12)

, α, and the regression

T ¼ UBu þ HTU (13)

Multivariate Calibration for the Development of Vibrational Spectroscopic Methods

U ¼ TBT þ HUT (14)

p yjw, <sup>α</sup><sup>2</sup> � �p wð Þ <sup>j</sup><sup>α</sup> dw (15)

PLS may be easily understood geometrically if we imagine the matrices X and Y as N points in two spaces. The X-space with K axes, and the Y-space with M axes, where K is the number of columns in X matrix and M the number of columns in Y matrix. The objectives of PLS is to find a latent variable so that the best approximate X-space, the best approximate Y–space, and the greatest possible correlation between X-space and Y space.

A PLS model can be written as

$$X = 1\overline{X} + TP^T + E \tag{8}$$

$$Y = \mathbf{1}\overline{Y} + \mathbf{U}\mathbf{C}^T + F \tag{9}$$

$$T = \mathcal{U} + H \tag{10}$$

where X contains the X average; Y contains the Y average; T is a matrix of scores that summarizes the X variables; U is a matrix of scores that summarizes the Y variables; E, F, H is a matrix of residuals (the deviations between the original and the predicted values) [12].

In a PLS algorithm, there are additional loading called weight. P is the matrix of weigh expressing the correlation between X and U and is used to calculate T. C is the matrix of weigh expressing the correlation between Y and T and is used to calculate U [12, 70].

#### 5.4. Orthogonal partial least squares

OPLS has been developed in order to separate information in the X matrix that is correlated with Y matrix form Y-uncorrelated information. The idea of O-PLS algorithm was to remove systematic variation uncorrelated with the response with the goal and to reduce the number of components in order to increase interpretability of the model [55, 69, 71].

The main idea of O-PLS is to separate the systematic variation in X into two parts, one which is related to both X and Y (co-varying noise) and one which is orthogonal to Y (structured noise). Two O-PLS algorithms were developed, the first (O1-PLS) is unidirectional X ) Y and the second (O2-PLS) is bi-directional X ⇔ Y and is able to separate these different types of variations in both X and Y matrices [63, 64]. The practical result of using O-PLS algorithms inside of PLS is cleaner models that are easier to display and interpret.

An O2-PLS model can be written as

The PLS approach was first proposed by Herman Wold around 1975 for the modeling of complicated datasets in terms of chains of matrices, the so-called path models. PLS regression is preferable to develop calibration models because unlike MLR, it can analyze data with strongly collinear, noisy, and numerous X-variables, and also simultaneously model several response variables [68]. PLS was developed for situation in which the data have more independent variables than observations (the "small n, large p") or/and where collinearity is

The PLS finds a multivariate model (linear or polynomial) that describes the relationship between Y matrix (dependent variables) and X matrix (predictor variables) expressed as

PLS may be easily understood geometrically if we imagine the matrices X and Y as N points in two spaces. The X-space with K axes, and the Y-space with M axes, where K is the number of columns in X matrix and M the number of columns in Y matrix. The objectives of PLS is to find a latent variable so that the best approximate X-space, the best approximate Y–space, and the

where X contains the X average; Y contains the Y average; T is a matrix of scores that summarizes the X variables; U is a matrix of scores that summarizes the Y variables; E, F, H is a matrix of

In a PLS algorithm, there are additional loading called weight. P is the matrix of weigh expressing the correlation between X and U and is used to calculate T. C is the matrix of weigh

OPLS has been developed in order to separate information in the X matrix that is correlated with Y matrix form Y-uncorrelated information. The idea of O-PLS algorithm was to remove systematic variation uncorrelated with the response with the goal and to reduce the number of

The main idea of O-PLS is to separate the systematic variation in X into two parts, one which is related to both X and Y (co-varying noise) and one which is orthogonal to Y (structured noise). Two O-PLS algorithms were developed, the first (O1-PLS) is unidirectional X ) Y and the second (O2-PLS) is bi-directional X ⇔ Y and is able to separate these different types of variations in both X and Y matrices [63, 64]. The practical result of using O-PLS algorithms inside of

residuals (the deviations between the original and the predicted values) [12].

expressing the correlation between Y and T and is used to calculate U [12, 70].

components in order to increase interpretability of the model [55, 69, 71].

PLS is cleaner models that are easier to display and interpret.

greatest possible correlation between X-space and Y space.

52 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Y ¼ fðXÞ þ E (7)

<sup>X</sup> <sup>¼</sup> <sup>1</sup><sup>X</sup> <sup>þ</sup> TPT <sup>þ</sup> <sup>E</sup> (8)

<sup>Y</sup> <sup>¼</sup> <sup>1</sup><sup>Y</sup> <sup>þ</sup> UCT <sup>þ</sup> <sup>F</sup> (9)

T ¼ U þ H (10)

present among dataset [69].

A PLS model can be written as

5.4. Orthogonal partial least squares

$$X = 1\overline{X'} + TP^T + T\_o P\_o^T + E \tag{11}$$

$$Y = 1\overline{Y}' + \mathcal{U}\mathcal{C}^T + \mathcal{U}\_o\mathcal{C}\_O^T + F \tag{12}$$

$$T = \mathcal{U}B\_u + H\_{TL} \tag{13}$$

$$
\Delta U = T B\_T + H\_{UT} \tag{14}
$$

where X is a contain de X average; Y is a contain de Y average; T is a matrix of scores that summarizes the X variables; U is a matrix of scores that summarizes the Y variables; P is a matrix of weigh that express the correlation between X and U; C is a matrix of weigh that express the correlation between Y and T; E, F, HTU, HUT are the matrixes of residuals.

The matrixes TP<sup>T</sup> and UC<sup>T</sup> hold the joint X/Y information overlap [12, 63, 64].

In the last years, O2-PLS has become the preferred regression technique for the development of calibration models in NIR and Raman spectroscopy.

#### 5.5. Bayesian ridge regression

Another regression method recently proposed for multivariate calibration of spectroscopic methods is Bayesian ridge regression. The method presents similarities with least squares, and the estimated coefficients tend toward zero in order to avoid collinearity [44].

In a Bayes-RR regression model, higher-level prior Gaussian distributions can be introduced over α<sup>2</sup> and α, and the prediction can be performed by integrating over α<sup>2</sup> , α, and the regression parameters w. Since this prior distribution is conjugate to the likelihood function, the predictive distribution is also Gaussian [72]

$$p\left(y|\alpha,\alpha^2\right) = \int p\left(y|w,\alpha^2\right)p(w|\alpha)dw\tag{15}$$

The Bayes-RR is a widely used regression technique in machine learning based on the ridge regression [73], and in the last years its performance for the development of excellent models for spectroscopic calibration has been proved [72, 74, 75].

#### 5.6. Support vector regression (SVR)

The support vector machines (SVMs) are a set of learning methods mostly used for classification that can be used as a regression technique which is called the support vector regression. In the last years, SVM started to be used in chemometrics for NIR spectra classification and multivariate calibration. The SVR uses the same principles as the SVM and is based on finding the hyperplane maximizing the margin between classes. The hyperplane maximizing the margin is justified by statistical learning theory endowed with a probabilistic test error bound that is minimized when the margin is maximized. The regression is performed using kernel functions that transform the data into a higher dimensional feature space to make a linear separation possible. The models obtained by SVR are more complex and difficult to interpret in comparison with those obtained by other regression techniques [44, 76, 77].

extrusion process using in-line Raman spectroscopy. International Journal of Pharma-

Multivariate Calibration for the Development of Vibrational Spectroscopic Methods

http://dx.doi.org/10.5772/intechopen.72598

55

[5] Wahl PR, Fruhmann G, Sacher S, Straka G, Sowinski S, Khinast JG. PAT for tableting: Inline monitoring of API and excipients via NIR spectroscopy. European Journal of Phar-

[6] Möltgen C, Puchert T, Menezes JC, Lochmann D, Reich GA. Novel in-line NIR spectroscopy application for the monitoring of tablet film coating in an industrial scale process.

[7] Kauppinen A, Toiviainen M, Lehtonen M, Järvinen K, Paaso J, Juuti M, et al. Validation of a multipoint near-infrared spectroscopy method for in-line moisture content analysis during freeze-drying. Journal of Pharmaceutical and Biomedical Analysis. 2014;95:229-237

[8] Liu R, Li L, Yin W, Xu D, Zang H. Near-infrared spectroscopy monitoring and control of the fluidized bed granulation and coating processes—A review. International Journal of

[9] Karande AD, Wan P, Heng S, Liew CV. In-line quantification of micronized drug and excipients in tablets by near infrared (NIR) spectroscopy: Real time monitoring of

[10] Casian T, Reznek A, Vonica-gligor AL, Van Renterghem J, De Beer T, Tomu I. Development, validation and comparison of near infrared and Raman spectroscopic methods for fast characterization of tablets with amlodipine and valsartan. Talanta. 2017;167:333-343

[11] Taylor P, Gabrielsson J, Trygg J, Gabrielsson J, Trygg J. Recent developments in multivar-

[12] Eriksson L, Byrne T, Johansson E, Trygg J, Vikstrom C. Multi- and Megavariate Data Analysis: Basic Principles and Applications. 3rd ed. Malmo: MKS Umetrics AB; 2013. 1-505 pp [13] Blanco M, Alcal M. Content uniformity and tablet hardness testing of intact pharmaceutical tablets by near infrared spectroscopy A contribution to process analytical technolo-

[14] Mbinze JK, Sacré PY, Yemoa A, Mavar Tayey Mbay J, Habyalimana V, Kalenda N, et al. Development, validation and comparison of NIR and Raman methods for the identification and assay of poor-quality oral quinine drops. Journal of Pharmaceutical and Bio-

[15] Tomuta I, Iovanov R, Bodoki E, Vonica L. Development and validation of NIR-chemometric methods for chemical and pharmaceutical characterization of meloxicam tablets.

[16] Virtanen S, Antikainen O, Yliruusi J. Determination of the crushing strength of intact tablets using Raman spectroscopy. International Journal of Pharmaceutics. 2008;360(1–2):40-46 [17] Croker DM, Hennigan MC, Maher A, Hu Y, Ryder AG, Hodnett BKA. Comparative study of the use of powder X-ray diffraction, Raman and near infrared spectroscopy for

Drug Development and Industrial Pharmacy. 2014;40(4):549-559

iate calibration. Journal of Chemometrics. 2006;36:243-255

gies. Analytica Chimica Acta. 2006;557:353-359

medical Analysis. 2015;111:21-27

tableting process. International Journal of Pharmaceutics. 2010;396(1–2):63-74

ceutics. 2017;517(1–2):119-127

Talanta. 2012;92:26-37

Pharmaceutics. 2017;530(1–2):308-315

maceutics and Biopharmaceutics. 2014;87(2):271-278

#### 5.7. Decision tree regression

Decision tree regression is a type of decision tree algorithm that can be applied to solve regression problems. Decision trees represent one of the main techniques used for discriminant analysis, classification, and prediction in knowledge discovery. It is widely used because it closely resembles human reasoning and is easy to understand. The principle is to compute a regression in a tree structure from breaking down a dataset into smaller and smaller subsets. Recently, some applications in multivariate calibration of spectroscopic methods have been proposed [44, 77–79].

### Acknowledgements

This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS - UEFISCDI, project number PN-III-P2-2.1-BG-2016-0201.

### Author details

Ioan Tomuta\*, Alina Porfire, Tibor Casian and Alexandru Gavan

\*Address all correspondence to: tomutaioan@umfcluj.ro

Department of Pharmaceutical Technology and Biopharmacy, University of Medicine and Pharmacy "Iuliu Hatieganu", Cluj-Napoca, Romania

### References


extrusion process using in-line Raman spectroscopy. International Journal of Pharmaceutics. 2017;517(1–2):119-127

[5] Wahl PR, Fruhmann G, Sacher S, Straka G, Sowinski S, Khinast JG. PAT for tableting: Inline monitoring of API and excipients via NIR spectroscopy. European Journal of Pharmaceutics and Biopharmaceutics. 2014;87(2):271-278

separation possible. The models obtained by SVR are more complex and difficult to interpret

Decision tree regression is a type of decision tree algorithm that can be applied to solve regression problems. Decision trees represent one of the main techniques used for discriminant analysis, classification, and prediction in knowledge discovery. It is widely used because it closely resembles human reasoning and is easy to understand. The principle is to compute a regression in a tree structure from breaking down a dataset into smaller and smaller subsets. Recently, some applications in multivariate calibration of spectroscopic methods have been proposed [44, 77–79].

This work was supported by a grant of the Romanian National Authority for Scientific Research

Department of Pharmaceutical Technology and Biopharmacy, University of Medicine and

[1] Tomuta I, Rus L, Iovanov R, Rus LL. High-throughput NIR-chemometric methods for determination of drug content and pharmaceutical properties of indapamide tablets.

[2] Martínez L, Peinado A, Liesum L. In-line quantification of two active ingredients in a batch blending process by near-infrared spectroscopy : Influence of physical presentation

[3] Fonteyne M, Arruabarrena J, De Beer J, Hellings M, van den Kerkhof T, Burggraeve A, et al. NIR spectroscopic method for the in-line moisture assessment during drying in a six-segmented fluid bed dryer of a continuous tablet production line: Validation of quantifying abilities and uncertainty assessment. Journal of Pharmaceutical and Biomedical

[4] Van Renterghem J, Kumar A, Vervaet C, Paul J, Nopens I, Vander Y, et al. Elucidation and visualization of solid-state transformation and mixing in a pharmaceutical mini hot melt

Journal of Pharmaceutical and Biomedical Analysis. 2013;84:285-292

of the sample. International Journal of Pharmaceutics. 2013;451(1–2):67-75

and Innovation, CNCS - UEFISCDI, project number PN-III-P2-2.1-BG-2016-0201.

Ioan Tomuta\*, Alina Porfire, Tibor Casian and Alexandru Gavan

\*Address all correspondence to: tomutaioan@umfcluj.ro

Pharmacy "Iuliu Hatieganu", Cluj-Napoca, Romania

in comparison with those obtained by other regression techniques [44, 76, 77].

54 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

5.7. Decision tree regression

Acknowledgements

Author details

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**Chapter 4**

Provisional chapter

**Internal Standards for Absolute Quantification of Large**

DOI: 10.5772/intechopen.75569

Internal standardization plays a critical role in the performance of a bioanalytical method. There has been a tremendous increase in the popularity of using liquid chromatography tandem mass spectrometry (LC-MS/MS) methods for quantitative bioanalysis of protein molecules. Protein, being too large to be directly analyzed by LC-MS/MS, is proteolyzed and a characteristic peptide is used as a surrogate analyte for quantification. Internal standardization in small molecules' analysis is straightforward, i.e., either a stable labeled isotope (SIL) form of the analyte or a structural analogue is used. As protein quantification involves protein digestion to yield peptides, there are more options for internal standardization. Currently, internal standard selection is based on the availability of the internal standards and the sample preparation workflow. A SIL-form of the analyte protein is the ideal internal standard. However, its use is limited due to cost and commercial availability. Alternatively, a SIL form the surrogate peptide analyte or a cleavable SIL-peptide can be used as an IS. For preclinical bioanalysis of humanized IgG antibody-based drugs, a universal SIL analogue protein has been effectively used as an internal standard. This chapter focuses on internal standardization for the quantitative analysis of proteins, such

Mass spectrometry, as a quantitative tool, was largely restricted to the evaluation of small molecules until the 1990s. This was due to the lack of good-soft ionization techniques that are required for large molecule quantification. The development of soft ionization techniques such

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

**Molecules (Proteins) from Biological Matrices by LC-**

Large Molecules (Proteins) from Biological Matrices

Internal Standards for Absolute Quantification of

**MS/MS**

by LC-MS/MS

Abstract

1. Introduction

Morse Faria and Matthew S. Halquist

Morse Faria and Matthew S. Halquist

http://dx.doi.org/10.5772/intechopen.75569

Additional information is available at the end of the chapter

as biotherapeutics and biomarkers, using LC-MS/MS.

Keywords: internal standards, protein bioanalysis, LC-MS/MS

Additional information is available at the end of the chapter


#### **Internal Standards for Absolute Quantification of Large Molecules (Proteins) from Biological Matrices by LC-MS/MS** Internal Standards for Absolute Quantification of Large Molecules (Proteins) from Biological Matrices by LC-MS/MS

DOI: 10.5772/intechopen.75569

Morse Faria and Matthew S. Halquist Morse Faria and Matthew S. Halquist

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75569

#### Abstract

[75] Brown PJ, Fearn T, Vannucci M. Bayesian wavelet regression on curves with application to a spectroscopic calibration problem. Journal of the American Statistical Association. 2001;96 (454):398-408 Available from: http://www.tandfonline.com/doi/abs/10.1198/016214501753

60 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

[76] Smola A, Schölkopf B. A tutorial on support vector regression. NeuroCOLT2 Technical Report Series. 1998;73. Available from: http://www.springerlink.com/index/KM7KRM46

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[79] Czajkowski M, Kretowski M. The role of decision tree representation in regression problems—An evolutionary perspective. Applied Soft Computing. 2016;48:458-475. Available

168118

802R2114.pdf

39(4):261-283

from:. DOI: 10.1016/j.asoc.2016.07.007

Internal standardization plays a critical role in the performance of a bioanalytical method. There has been a tremendous increase in the popularity of using liquid chromatography tandem mass spectrometry (LC-MS/MS) methods for quantitative bioanalysis of protein molecules. Protein, being too large to be directly analyzed by LC-MS/MS, is proteolyzed and a characteristic peptide is used as a surrogate analyte for quantification. Internal standardization in small molecules' analysis is straightforward, i.e., either a stable labeled isotope (SIL) form of the analyte or a structural analogue is used. As protein quantification involves protein digestion to yield peptides, there are more options for internal standardization. Currently, internal standard selection is based on the availability of the internal standards and the sample preparation workflow. A SIL-form of the analyte protein is the ideal internal standard. However, its use is limited due to cost and commercial availability. Alternatively, a SIL form the surrogate peptide analyte or a cleavable SIL-peptide can be used as an IS. For preclinical bioanalysis of humanized IgG antibody-based drugs, a universal SIL analogue protein has been effectively used as an internal standard. This chapter focuses on internal standardization for the quantitative analysis of proteins, such as biotherapeutics and biomarkers, using LC-MS/MS.

Keywords: internal standards, protein bioanalysis, LC-MS/MS

### 1. Introduction

Mass spectrometry, as a quantitative tool, was largely restricted to the evaluation of small molecules until the 1990s. This was due to the lack of good-soft ionization techniques that are required for large molecule quantification. The development of soft ionization techniques such

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

as electrospray ionization (ESI) and matrix-assisted laser desorption ionization (MALDI) facilitated the use of mass spectrometry for analysis of peptides and proteins [1, 2]. At the beginning of the twenty-first century, large molecule quantification was restricted to immunoassays. The advancements in mass spectrometric instrumentation and better quantification strategies have resulted in a shift of large molecule analysis from immunoassays to mass spectrometry [1, 2]. In the last decade, several methods have been reported for quantification of protein biomarkers and protein biotherapeutics. This popularity of LC-MS/MS methods can be attributed to its inherent selectivity, high dynamic range, shorter development time, and multiplexing capabilities.

protein analyte proteolysis, and surrogate peptide analyte enrichment. Instrumental analysis comprises of chromatographic separation and mass spectrometric ionization. This section briefly

Internal Standards for Absolute Quantification of Large Molecules (Proteins) from Biological Matrices…

http://dx.doi.org/10.5772/intechopen.75569

63

Selection of a signature peptide is a critical part of method development for protein bioanalysis. Peptides containing amino acid residues with potential post-translational modification (PTM) sites are usually avoided due to a potential change in peptide mass that would affect reproducible quantification. However, if the intended purpose is to quantify a posttranslational modification, a tryptic peptide containing the specific PTM is selected [3–5]. Tryptic peptides containing amino acids susceptible to oxidation such as methionine and tryptophan are avoided as chemical modifications of these molecules can result in a change in its mass and thus can affect method reproducibility. Usually, tryptic peptides containing cysteine residues are avoided as they undergo iodoacetamidation. However, methods using signature peptide containing a cysteine residue have been reported after accounting for any mass change occurring prior to mass spectrometric detection [6, 7]. Missed cleavages can result inconsistent production of the signature peptide in turn impacting quantitation. Peptides containing ragged ends or dibasic ends next to each other (such as in Arg-Arg, Lys-Lys, or

summarizes various process encountered in protein quantification by LC-MS/MS.

Arg-Lys) should be avoided as they are known to result in missed cleavages [8–10].

Biological samples, especially plasma and serum, are complex mixtures comprising of proteins, lipids, and salts in addition to the analyte molecule. Biological samples require pretreatment such as analyte enrichment or proteolysis prior to protein LC-MS/MS analysis. Sample preparation depends on the analyte physiochemical properties as well as the required level of selectivity and sensitivity. For example, proteins having a low molecular weight (<10 kDa), can be analyzed without proteolysis using protein precipitation and/or solid phase extraction. High molecular weight proteins (>10 kDa) require proteolysis to yield peptide fragments compatible for mass spectrometric analysis. These samples may require enrichment before and/or after proteolysis to achieve required detection limits. Routinely used sample

For proteins smaller than 10 kDa, various non-selective protein enrichment techniques can be employed. Partial protein precipitation, using organic solvents along with surfactants, is used as a simple sample purification technique to deplete the endogenous plasma proteins. Partial protein precipitation eliminates larger proteins but leave smaller ones in solution [11–13]. Protein precipitation could have low recovery due to losses as a result co-precipitation, which would be a drawback. As it is simple but a crude clean-up technique, the resulting extracts are usually complex containing high concentration of salts and lipids. Matrix effects are commonly

2.2. Sample preparation techniques for protein quantification LC-MS/MS

preparation techniques are described below.

2.2.1. Non-selective protein enrichment techniques

observed with these extracts, which can be a source of variability.

2.1. Signature peptide selection

Protein quantification using targeted mass spectrometry-based quantification from biological matrices is challenging owing to the high molecular mass and high protein background in biological matrices. Direct LC-MS/MS analysis of an intact protein analyte can be performed on proteins having molecular weights below 10 kDa. Proteins tend to ionize with multiple charges during electrospray ionization resulting in a complex spectrum with many precursor ion peaks corresponding to each charged state. Because of the complex precursor ion spectra, any single chosen precursor ion signal for quantitation will only represent a very small fraction of the total ionized analyte signal. This will result in lower signal response and reduce the sensitivity of the method. The complex ion spectrum also impacts the method specificity due to the presence of many overlapping signals arising from naturally occurring isotopes. In addition, larger protein analytes tend to be undergoing inefficient or non-existent collisioninduced dissociation, in turn, impacting targeted mass spectrometric analysis. These challenges are overcome by enzymatic proteolysis of the analyte protein to yield one or more characteristic peptide fragments (i.e., signature peptides), which can be used as surrogate analyte(s) for quantification. In some methods, immunoaffinity enrichment is used for sample clean particularly for methods requiring detection limits below 100 ng/ml. These enzymatic digestions and immunoaffinity isolations are a potential source of variation and need to be controlled.

An internal standard is added to the sample during absolute quantification to compensate for variability encountered in sample processing and instrumental analysis. For mass spectrometric assays, a stable isotope labeled (SIL)-form of the analyte is an ideal internal standard it mimics the analyte throughout the method. However, SIL-proteins are difficult to produce with sufficient purity, and hence substitute internal standards such as SIL-peptides or protein structural analogues are used. In this chapter, we discuss the commonly used strategies for protein quantification using appropriate internal standards.

### 2. Overview of mass spectrometric-based protein quantification

Before we evaluate the different internal standardization options for protein quantification, it is essential to understand the various sources of variability during protein bioanalysis. Method variability arises during sample preparation or instrumental analysis. Protein bioanalytical quantification can encompass complex sample preparation steps such as protein analyte enrichment, protein analyte proteolysis, and surrogate peptide analyte enrichment. Instrumental analysis comprises of chromatographic separation and mass spectrometric ionization. This section briefly summarizes various process encountered in protein quantification by LC-MS/MS.

#### 2.1. Signature peptide selection

as electrospray ionization (ESI) and matrix-assisted laser desorption ionization (MALDI) facilitated the use of mass spectrometry for analysis of peptides and proteins [1, 2]. At the beginning of the twenty-first century, large molecule quantification was restricted to immunoassays. The advancements in mass spectrometric instrumentation and better quantification strategies have resulted in a shift of large molecule analysis from immunoassays to mass spectrometry [1, 2]. In the last decade, several methods have been reported for quantification of protein biomarkers and protein biotherapeutics. This popularity of LC-MS/MS methods can be attributed to its inherent selectivity, high dynamic range, shorter development time, and multiplexing

62 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Protein quantification using targeted mass spectrometry-based quantification from biological matrices is challenging owing to the high molecular mass and high protein background in biological matrices. Direct LC-MS/MS analysis of an intact protein analyte can be performed on proteins having molecular weights below 10 kDa. Proteins tend to ionize with multiple charges during electrospray ionization resulting in a complex spectrum with many precursor ion peaks corresponding to each charged state. Because of the complex precursor ion spectra, any single chosen precursor ion signal for quantitation will only represent a very small fraction of the total ionized analyte signal. This will result in lower signal response and reduce the sensitivity of the method. The complex ion spectrum also impacts the method specificity due to the presence of many overlapping signals arising from naturally occurring isotopes. In addition, larger protein analytes tend to be undergoing inefficient or non-existent collisioninduced dissociation, in turn, impacting targeted mass spectrometric analysis. These challenges are overcome by enzymatic proteolysis of the analyte protein to yield one or more characteristic peptide fragments (i.e., signature peptides), which can be used as surrogate analyte(s) for quantification. In some methods, immunoaffinity enrichment is used for sample clean particularly for methods requiring detection limits below 100 ng/ml. These enzymatic digestions and immunoaffinity isolations are a potential source of variation and need to be

An internal standard is added to the sample during absolute quantification to compensate for variability encountered in sample processing and instrumental analysis. For mass spectrometric assays, a stable isotope labeled (SIL)-form of the analyte is an ideal internal standard it mimics the analyte throughout the method. However, SIL-proteins are difficult to produce with sufficient purity, and hence substitute internal standards such as SIL-peptides or protein structural analogues are used. In this chapter, we discuss the commonly used strategies for

Before we evaluate the different internal standardization options for protein quantification, it is essential to understand the various sources of variability during protein bioanalysis. Method variability arises during sample preparation or instrumental analysis. Protein bioanalytical quantification can encompass complex sample preparation steps such as protein analyte enrichment,

protein quantification using appropriate internal standards.

2. Overview of mass spectrometric-based protein quantification

capabilities.

controlled.

Selection of a signature peptide is a critical part of method development for protein bioanalysis. Peptides containing amino acid residues with potential post-translational modification (PTM) sites are usually avoided due to a potential change in peptide mass that would affect reproducible quantification. However, if the intended purpose is to quantify a posttranslational modification, a tryptic peptide containing the specific PTM is selected [3–5]. Tryptic peptides containing amino acids susceptible to oxidation such as methionine and tryptophan are avoided as chemical modifications of these molecules can result in a change in its mass and thus can affect method reproducibility. Usually, tryptic peptides containing cysteine residues are avoided as they undergo iodoacetamidation. However, methods using signature peptide containing a cysteine residue have been reported after accounting for any mass change occurring prior to mass spectrometric detection [6, 7]. Missed cleavages can result inconsistent production of the signature peptide in turn impacting quantitation. Peptides containing ragged ends or dibasic ends next to each other (such as in Arg-Arg, Lys-Lys, or Arg-Lys) should be avoided as they are known to result in missed cleavages [8–10].

#### 2.2. Sample preparation techniques for protein quantification LC-MS/MS

Biological samples, especially plasma and serum, are complex mixtures comprising of proteins, lipids, and salts in addition to the analyte molecule. Biological samples require pretreatment such as analyte enrichment or proteolysis prior to protein LC-MS/MS analysis. Sample preparation depends on the analyte physiochemical properties as well as the required level of selectivity and sensitivity. For example, proteins having a low molecular weight (<10 kDa), can be analyzed without proteolysis using protein precipitation and/or solid phase extraction. High molecular weight proteins (>10 kDa) require proteolysis to yield peptide fragments compatible for mass spectrometric analysis. These samples may require enrichment before and/or after proteolysis to achieve required detection limits. Routinely used sample preparation techniques are described below.

#### 2.2.1. Non-selective protein enrichment techniques

For proteins smaller than 10 kDa, various non-selective protein enrichment techniques can be employed. Partial protein precipitation, using organic solvents along with surfactants, is used as a simple sample purification technique to deplete the endogenous plasma proteins. Partial protein precipitation eliminates larger proteins but leave smaller ones in solution [11–13]. Protein precipitation could have low recovery due to losses as a result co-precipitation, which would be a drawback. As it is simple but a crude clean-up technique, the resulting extracts are usually complex containing high concentration of salts and lipids. Matrix effects are commonly observed with these extracts, which can be a source of variability.

Solid phase extraction (SPE) is another purification technique that is employed solely or along with other purification techniques for sample clean up wherein the analyte is a smaller protein or peptide [12, 14–17]. Several mixed mode SPE cartridges, combining reversed phase stationary phase along with strong cation exchange or weak anion exchange, are commercially available for peptide analysis. These are usually available in 96-well microelution plate format. Microelution SPE offers many advantages including increased sensitivity due to low elution volumes, analysis of limited volume samples, significantly cleaner samples compared to extracts obtained after protein precipitation and higher reproducibility. The low elution volume avoids the need for sample extract evaporation and reconstitution, which can result in peptide instability.

available antibodies while biotherapeutic drug molecules have specific antibodies developed for immuno-purification or screening during early pharmaceutical discovery and development. Due to the high specificity of this enrichment process, only a SIL-protein internal standard can be used an internal standard. However, in methods using a capture antibody, that has an epitope present on or near the signature peptide region of the analyte protein, an external SIL-peptide

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65

Anderson et al. introduced the stable isotope standards with capture by anti-peptide antibodies (SISCAPA) strategy wherein immunocapture enrichment is directed toward a signature peptide after digestion using anti-peptide antibodies [35]. This technique allows high sensitivity and precision. However, these signature peptide-specific antibodies may not be commercially available and require inhouse development increasing method development cost and time. Some methods have employed this type of immunocapture online using specialized columns containing analyte-specific antibodies [29, 36–38]. This workflow is extensively used for multiplexed biomarker assays [24, 39]. Methods using dual enrichment, i.e., analyte protein enrichment and surrogate peptide enrichment post digestion, have also been reported. Multiple enrichment steps require the selection of an appropriate internal standard to compensate

The majority of the biotherapeutic drugs are monoclonal antibodies or antibody-based molecules such as antibody drug conjugates. Antibodies have a constant tail region also known as the fragment crystallizable region (Fc region) and a variable region also referred to as antigenbinding region (Fab) region. The Fab region contains the complementarity determining region. Antibody-based drugs can be isolated using Protein A or G coated supports to bind to the Fc. This technique requires minimum time and resources for development and can achieve high throughput with adequate sensitivity. If additional selectivity is required, anti-Fc antibodies may be used depending on the analyte and the biological matrix. This technique is useful for the quantitation of humanized biotherapeutic drugs in animal models. Quantitation of humanized biotherapeutic drugs in human biological matrices requires the use of anti-idiotypic antibodies as capture agents to achieve significant detection limits. In some methods, the target antigen is used as a binding agent for the selective capture. Dubios et al. described an immunoaffinity coupled LC-MS/MS method wherein the analyte Cetuximab was isolated

using its target antigen (soluble epidermal growth factor) as a capture reagent [40].

Most protein quantitative LC-MS/MS methods involve enzymatic digestion of the proteins to yield smaller peptides which can be easily quantified by commercially available quantitative mass spectrometers. A typical protein digestion procedure involves denaturation, reduction, and alkylation followed by proteolysis. Denaturation is carried out to unfold the protein so that it can be easily accessible to the proteolytic enzyme. Urea is the most commonly used for denaturation during protein quantification. Alternatively, denaturation has been achieved using

can be used as an internal standard [34].

2.2.4. Enzymatic proteolysis

2.2.3.2. Immunocapture using peptide-specific antibodies

for method variability arising within each enrichment step.

2.2.3.3. Non-antibody capture of antibody-based biotherapeutic drugs

#### 2.2.2. Abundant protein depletion

Several commercial kits are available which use immunoaffinity depletion to selectively remove serum albumin, immunoglobulins, and other high abundant proteins from biological matrices [18–21]. These kits have shown to reduce protein content by up to 85% [22]. The enrichment technique is best suited for methods that have multiple protein analytes typically seen in biomarker research. The high costs of these kits and recovery issues have been the major drawback of this approach [23, 24]. Abundant protein depletion has been used in several biomarker quantification methods [23, 25, 26]. Liu et al. showed that isopropanol with 1.0% trichloroacetic acid was effective in removing 95% of the total albumin in human plasma samples while retaining 60–100% of the three analyte proteins that were evaluated. The recovery using this approach was found to be better than commercially available albumin depletion kits [27].

#### 2.2.3. Immunoaffinity enrichment

Use of immuno (or affinity) capture for isolation of the analyte protein or its signature peptide is a highly selective enrichment technique. Combing the selectivity of an immunoaffinity capture with the selectivity of a LC-MS/MS system can allow a 1000-fold enrichment in comparison to conventional techniques [24]. Although this technique requires specialized antibodies, it provides sufficient purification to achieve quantification of low abundance proteins from plasma [24, 28–31]. Low recoveries and cross reactivities are some of the issues seen during immunocapture enrichment [32, 33]. Immunoaffinity isolations may be carried out with single or multiple antibodies depending on the availability of analyte-specific antibodies and the desired detection limits. The capture antibodies are immobilized in a 96-well plate or on to the surface of magnetic beads prior to the immunocapture. This immobilization is achieved using biotinylated antibodies and streptavidin-coated plates or magnetic beads. Alternatively, Protein A or G coated supports may be used for immobilizing the antibody using the Fc region of the antibody. The wide variety of immunocapture techniques can roughly be categorized into three categories based on the type of capture reagent.

#### 2.2.3.1. Immunocatpture using protein-specific antibodies

The simplest approach is to use monoclonal or polyclonal antibody that is specific to the target analyte for immunocapture enrichment. Most of the protein biomarkers will have commercially available antibodies while biotherapeutic drug molecules have specific antibodies developed for immuno-purification or screening during early pharmaceutical discovery and development. Due to the high specificity of this enrichment process, only a SIL-protein internal standard can be used an internal standard. However, in methods using a capture antibody, that has an epitope present on or near the signature peptide region of the analyte protein, an external SIL-peptide can be used as an internal standard [34].

#### 2.2.3.2. Immunocapture using peptide-specific antibodies

Solid phase extraction (SPE) is another purification technique that is employed solely or along with other purification techniques for sample clean up wherein the analyte is a smaller protein or peptide [12, 14–17]. Several mixed mode SPE cartridges, combining reversed phase stationary phase along with strong cation exchange or weak anion exchange, are commercially available for peptide analysis. These are usually available in 96-well microelution plate format. Microelution SPE offers many advantages including increased sensitivity due to low elution volumes, analysis of limited volume samples, significantly cleaner samples compared to extracts obtained after protein precipitation and higher reproducibility. The low elution volume avoids the need for sample extract evaporation and reconstitution, which can result in

64 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Several commercial kits are available which use immunoaffinity depletion to selectively remove serum albumin, immunoglobulins, and other high abundant proteins from biological matrices [18–21]. These kits have shown to reduce protein content by up to 85% [22]. The enrichment technique is best suited for methods that have multiple protein analytes typically seen in biomarker research. The high costs of these kits and recovery issues have been the major drawback of this approach [23, 24]. Abundant protein depletion has been used in several biomarker quantification methods [23, 25, 26]. Liu et al. showed that isopropanol with 1.0% trichloroacetic acid was effective in removing 95% of the total albumin in human plasma samples while retaining 60–100% of the three analyte proteins that were evaluated. The recovery using this approach was found to be better than commercially available albumin

Use of immuno (or affinity) capture for isolation of the analyte protein or its signature peptide is a highly selective enrichment technique. Combing the selectivity of an immunoaffinity capture with the selectivity of a LC-MS/MS system can allow a 1000-fold enrichment in comparison to conventional techniques [24]. Although this technique requires specialized antibodies, it provides sufficient purification to achieve quantification of low abundance proteins from plasma [24, 28–31]. Low recoveries and cross reactivities are some of the issues seen during immunocapture enrichment [32, 33]. Immunoaffinity isolations may be carried out with single or multiple antibodies depending on the availability of analyte-specific antibodies and the desired detection limits. The capture antibodies are immobilized in a 96-well plate or on to the surface of magnetic beads prior to the immunocapture. This immobilization is achieved using biotinylated antibodies and streptavidin-coated plates or magnetic beads. Alternatively, Protein A or G coated supports may be used for immobilizing the antibody using the Fc region of the antibody. The wide variety of immunocapture techniques can

roughly be categorized into three categories based on the type of capture reagent.

The simplest approach is to use monoclonal or polyclonal antibody that is specific to the target analyte for immunocapture enrichment. Most of the protein biomarkers will have commercially

2.2.3.1. Immunocatpture using protein-specific antibodies

peptide instability.

depletion kits [27].

2.2.3. Immunoaffinity enrichment

2.2.2. Abundant protein depletion

Anderson et al. introduced the stable isotope standards with capture by anti-peptide antibodies (SISCAPA) strategy wherein immunocapture enrichment is directed toward a signature peptide after digestion using anti-peptide antibodies [35]. This technique allows high sensitivity and precision. However, these signature peptide-specific antibodies may not be commercially available and require inhouse development increasing method development cost and time. Some methods have employed this type of immunocapture online using specialized columns containing analyte-specific antibodies [29, 36–38]. This workflow is extensively used for multiplexed biomarker assays [24, 39]. Methods using dual enrichment, i.e., analyte protein enrichment and surrogate peptide enrichment post digestion, have also been reported. Multiple enrichment steps require the selection of an appropriate internal standard to compensate for method variability arising within each enrichment step.

#### 2.2.3.3. Non-antibody capture of antibody-based biotherapeutic drugs

The majority of the biotherapeutic drugs are monoclonal antibodies or antibody-based molecules such as antibody drug conjugates. Antibodies have a constant tail region also known as the fragment crystallizable region (Fc region) and a variable region also referred to as antigenbinding region (Fab) region. The Fab region contains the complementarity determining region. Antibody-based drugs can be isolated using Protein A or G coated supports to bind to the Fc. This technique requires minimum time and resources for development and can achieve high throughput with adequate sensitivity. If additional selectivity is required, anti-Fc antibodies may be used depending on the analyte and the biological matrix. This technique is useful for the quantitation of humanized biotherapeutic drugs in animal models. Quantitation of humanized biotherapeutic drugs in human biological matrices requires the use of anti-idiotypic antibodies as capture agents to achieve significant detection limits. In some methods, the target antigen is used as a binding agent for the selective capture. Dubios et al. described an immunoaffinity coupled LC-MS/MS method wherein the analyte Cetuximab was isolated using its target antigen (soluble epidermal growth factor) as a capture reagent [40].

#### 2.2.4. Enzymatic proteolysis

Most protein quantitative LC-MS/MS methods involve enzymatic digestion of the proteins to yield smaller peptides which can be easily quantified by commercially available quantitative mass spectrometers. A typical protein digestion procedure involves denaturation, reduction, and alkylation followed by proteolysis. Denaturation is carried out to unfold the protein so that it can be easily accessible to the proteolytic enzyme. Urea is the most commonly used for denaturation during protein quantification. Alternatively, denaturation has been achieved using other chaotropic agents such as guanidine HCl, surfactants such as sodium deoxycholate, organic solvents such as methanol and heat (95C) [13, 17, 26, 41, 42]. RapiGest SF, an acidlabile surfactant, is a Waters proprietary product that has gained high popularity for protein bioanalysis due to its compatibility with mass spectrometric detectors. This detergent is easily precipitated out by lowering the pH during the termination step of the enzymatic digestions. Reduction of the protein is carried out using dithiothreitol or TCEP (tris(2-carboxyethyl)phosphine) to break the disulfide linkages between cysteine residues. The resulting free thiol groups are then derivatized using an alkylating agent such as iodoacetamide or iodoacetic acid in order to prevent reformation of disulfide linkages.

2.4. Mass spectrometric detection

variability.

Triple quadrupole (QQQ) and Quadrapole Ion Trap (QTrap) using the multiple reaction monitoring (MRM) mode are the most widely used mass analyzers for protein quantification. Proteins and peptides under electrospray conditions generally ionize to several charge states. For smaller peptides and proteins, [M + 2H]2+ is usually the most abundant species, however, for larger molecules, [M + 3H]3+, [M + 4H]4+, and so on may also form, distributing the signal over several charge states and reducing the achievable limits of quantification. It is essential that the charge distribution across multiple samples is reproducible or will introduce method

Internal Standards for Absolute Quantification of Large Molecules (Proteins) from Biological Matrices…

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67

MRM mode allows measurement of multiple transitions and can be used for quantification of multiple analytes. Besides the signature peptide used for quantitative evaluation, additional characteristic peptides maybe monitored as monitoring peptides or qualitative peptides. Based on their location in the protein amino acid sequence, these monitoring peptides can provide

Mass spectrometric detection using electrospray ionization is highly susceptible to matrix effects. Samples with elevated concentrations of phospholipids, such as glycerophosphocholines and lysophosphatidylcholines, exhibit increase in ionization suppression when compared to normal plasma [55]. Lipid-related interference is generally not an issue with immunocapture-based methods, but it can be source of concern with methods that use non-

Internal standards need to track the analyte during all stages of sample analysis that includes sample preparation, chromatographic separation, and detection. Immunoaffinity capture, enzymatic proteolysis, and mass spectrometric ionization are the three major steps that are susceptible to variability during protein bioanalysis by LC-MS/MS. The internal standard may be added at different step(s) of the extraction process depending on the availability of the internal standards and the sample extraction workflow. Figure 1 describes various commonly used workflows for protein quantification and the internal standard (IS) options. Protein internal standards are added prior to analyte protein enrichment. Protein analyte enrichment can be immunoaffinity isolations or a non-selective process such as partial protein precipitation, SPE, and abundant protein removal. Smaller proteins can be directly analyzed after protein analyte enrichment. Larger proteins are proteolyzed to yield signature peptide(s) that can be used as surrogate analytes. Peptide internal standards when added prior to enzymatic proteolysis can only track peptide instability and volume recovery during the proteolytic process as we well mass spectrometric ionization during analysis. Additionally, cleavable internal standard peptides may be able to track the digestion variability when added prior to proteolytic incubations. Methods requiring low detection limits utilize peptide enrichment post enzymatic proteolysis. SIL-peptides are required to track immunoaffinity-based peptide enrichment processes. Cur-

valuable insights about the integrity of the analyte protein.

selective isolations such as partial protein precipitation.

3. Internal standardization for protein bioanalytical methods

rently used internal standards for protein bioanalysis are described below.

Trypsin is the most commonly used enzyme for protein digestions primarily as tryptic peptides have a c-terminal basic residue that favors ionization. In addition, average tryptic peptides have lengths suitable for detection on commonly used quantitative mass spectrometers. However, other enzymes such Lys-C, Arg-C, pepsin, chymotrypsin have been used when a specific cleavage is required [43–46]. To improve digestion efficiency, different approaches have been illustrated including high temperature, microwave-assisted digestion, and use of organic solvents [31, 47].

The "pellet digestion" method is a simplified method in which the proteins are precipitated using an organic solvent like acetonitrile to form a pellet and the supernatant containing interfering molecules such as phospholipids are discarded. This method provides an easy, efficient way of performing a fast clean-up and has resulted in improved digestion efficiency in comparison to direct digestions [48–51].

#### 2.3. Chromatographic separation

Liquid chromatography is used for separation of the protein or peptide mixture prior to mass spectrometric detection. For most peptide and protein analytes, reversed-phase column chemistry, typically C18 columns, allows separation of structurally and chemically similar molecules using mobile phases that are compatible with ESI. Hydrophilic interaction liquid chromatography (HILIC) has also been used to separate hydrophilic peptides. The mechanism of separation for small molecules is based on partitioning between the mobile and stationary phases. However, proteins and large peptides are not able to fully penetrate the pores and instead adsorb to the surface, and are desorbed at a critical concentration of organic solvent. Columns with larger pore stationary phases (300 Å) allow improved penetration of larger molecules as well as the use of higher flow rates with reduced band broadening, and therefore provide greater selectivity for some peptides and proteins.

Two-dimensional chromatographic separations, such as ion-exchange chromatography (IEC)- RPLC or RPLC-HILIC, have been utilized to fractionate and clean up samples, thus improving sensitivity of detection [16, 24, 46, 52, 53]. Additionally, many reported methods have used column trapping prior to analytical separation. The trap column retains the analytes and removes salts and other highly hydrophilic peptides [25, 28–31, 39, 54]. Some methods have used columns with antibodies for online immunoaffinity LC has been reported to achieve exceptional selectivity with minimal sample clean-up [31, 37, 38].

#### 2.4. Mass spectrometric detection

other chaotropic agents such as guanidine HCl, surfactants such as sodium deoxycholate, organic solvents such as methanol and heat (95C) [13, 17, 26, 41, 42]. RapiGest SF, an acidlabile surfactant, is a Waters proprietary product that has gained high popularity for protein bioanalysis due to its compatibility with mass spectrometric detectors. This detergent is easily precipitated out by lowering the pH during the termination step of the enzymatic digestions. Reduction of the protein is carried out using dithiothreitol or TCEP (tris(2-carboxyethyl)phosphine) to break the disulfide linkages between cysteine residues. The resulting free thiol groups are then derivatized using an alkylating agent such as iodoacetamide or iodoacetic

Trypsin is the most commonly used enzyme for protein digestions primarily as tryptic peptides have a c-terminal basic residue that favors ionization. In addition, average tryptic peptides have lengths suitable for detection on commonly used quantitative mass spectrometers. However, other enzymes such Lys-C, Arg-C, pepsin, chymotrypsin have been used when a specific cleavage is required [43–46]. To improve digestion efficiency, different approaches have been illustrated including high temperature, microwave-assisted digestion, and use of

The "pellet digestion" method is a simplified method in which the proteins are precipitated using an organic solvent like acetonitrile to form a pellet and the supernatant containing interfering molecules such as phospholipids are discarded. This method provides an easy, efficient way of performing a fast clean-up and has resulted in improved digestion efficiency

Liquid chromatography is used for separation of the protein or peptide mixture prior to mass spectrometric detection. For most peptide and protein analytes, reversed-phase column chemistry, typically C18 columns, allows separation of structurally and chemically similar molecules using mobile phases that are compatible with ESI. Hydrophilic interaction liquid chromatography (HILIC) has also been used to separate hydrophilic peptides. The mechanism of separation for small molecules is based on partitioning between the mobile and stationary phases. However, proteins and large peptides are not able to fully penetrate the pores and instead adsorb to the surface, and are desorbed at a critical concentration of organic solvent. Columns with larger pore stationary phases (300 Å) allow improved penetration of larger molecules as well as the use of higher flow rates with reduced band broadening, and therefore

Two-dimensional chromatographic separations, such as ion-exchange chromatography (IEC)- RPLC or RPLC-HILIC, have been utilized to fractionate and clean up samples, thus improving sensitivity of detection [16, 24, 46, 52, 53]. Additionally, many reported methods have used column trapping prior to analytical separation. The trap column retains the analytes and removes salts and other highly hydrophilic peptides [25, 28–31, 39, 54]. Some methods have used columns with antibodies for online immunoaffinity LC has been reported to achieve

acid in order to prevent reformation of disulfide linkages.

66 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

organic solvents [31, 47].

in comparison to direct digestions [48–51].

provide greater selectivity for some peptides and proteins.

exceptional selectivity with minimal sample clean-up [31, 37, 38].

2.3. Chromatographic separation

Triple quadrupole (QQQ) and Quadrapole Ion Trap (QTrap) using the multiple reaction monitoring (MRM) mode are the most widely used mass analyzers for protein quantification. Proteins and peptides under electrospray conditions generally ionize to several charge states. For smaller peptides and proteins, [M + 2H]2+ is usually the most abundant species, however, for larger molecules, [M + 3H]3+, [M + 4H]4+, and so on may also form, distributing the signal over several charge states and reducing the achievable limits of quantification. It is essential that the charge distribution across multiple samples is reproducible or will introduce method variability.

MRM mode allows measurement of multiple transitions and can be used for quantification of multiple analytes. Besides the signature peptide used for quantitative evaluation, additional characteristic peptides maybe monitored as monitoring peptides or qualitative peptides. Based on their location in the protein amino acid sequence, these monitoring peptides can provide valuable insights about the integrity of the analyte protein.

Mass spectrometric detection using electrospray ionization is highly susceptible to matrix effects. Samples with elevated concentrations of phospholipids, such as glycerophosphocholines and lysophosphatidylcholines, exhibit increase in ionization suppression when compared to normal plasma [55]. Lipid-related interference is generally not an issue with immunocapture-based methods, but it can be source of concern with methods that use nonselective isolations such as partial protein precipitation.

### 3. Internal standardization for protein bioanalytical methods

Internal standards need to track the analyte during all stages of sample analysis that includes sample preparation, chromatographic separation, and detection. Immunoaffinity capture, enzymatic proteolysis, and mass spectrometric ionization are the three major steps that are susceptible to variability during protein bioanalysis by LC-MS/MS. The internal standard may be added at different step(s) of the extraction process depending on the availability of the internal standards and the sample extraction workflow. Figure 1 describes various commonly used workflows for protein quantification and the internal standard (IS) options. Protein internal standards are added prior to analyte protein enrichment. Protein analyte enrichment can be immunoaffinity isolations or a non-selective process such as partial protein precipitation, SPE, and abundant protein removal. Smaller proteins can be directly analyzed after protein analyte enrichment. Larger proteins are proteolyzed to yield signature peptide(s) that can be used as surrogate analytes. Peptide internal standards when added prior to enzymatic proteolysis can only track peptide instability and volume recovery during the proteolytic process as we well mass spectrometric ionization during analysis. Additionally, cleavable internal standard peptides may be able to track the digestion variability when added prior to proteolytic incubations. Methods requiring low detection limits utilize peptide enrichment post enzymatic proteolysis. SIL-peptides are required to track immunoaffinity-based peptide enrichment processes. Currently used internal standards for protein bioanalysis are described below.

more fundamental precursors which serve as carbon or nitrogen sources for the synthesis of

Internal Standards for Absolute Quantification of Large Molecules (Proteins) from Biological Matrices…

SILAC is a popular technique for production of SIL-proteins by incorporation of SIL-amino acids into the target protein. This technique is popularly known as stable isotope labeling by amino acids in cell culture (SILAC) [57] or stable isotope labeling with amino acids (SILAA) [58]. SILAC is a straightforward procedure in which essential amino acids are left out of culture media and replaced by deuterated, carbon-13, and/or nitrogen-15 labeled variants of these amino acids. After multiple cell duplication cycles, these SIL amino acids get incorporated in the entire proteome. Heavy labeled variants of lysine and arginine that provide ample spacing between isotopic envelopes of light and heavy tryptic peptides (e.g., 10 Da using 13C6

tion of SIL-proteins using SILAC. Arginine and lysine on an average they occur at every tenth position in a protein sequence. Trypsin, the major proteolytic enzyme used in protein quantification assays, cleaves at lysine and arginine ensuring that at least one of the labeled amino is

Cell culture production is highly useful for generating SIL-labeled proteins for biothereapeutics. Biotherapeutics are produced by genetically modified cell lines, yeast or bacteria. To obtain a SIL-protein, the cells producing the biotherapeutic protein are grown in a medium containing labeled precursors for the desired protein. The stable isotope labeled amino acids gets incorporated in the proteins, thus resulting in production of a SIL-protein. These SIL-proteins are then

The cell culture method is an easy process of producing labeled proteins, but requires a cell culture equipment and a sterile laboratory. A major disadvantage is that in cell culture other endogenous proteins will be simultaneously produced having the incorporated label, and hence a more elaborate purification is required. Also, incomplete labeling can occur when the pools of labeled amino acids are diluted with amino acids newly synthesized by the cell.

SIL-proteins can also be made by in vitro protein synthesis in a cell free system [59]. Cell-free translation systems are largely supernatants obtained by centrifugation of the crude lysate of either E. coli, wheat germ, or rabbit reticulocytes at 30,000 g. The cell lysate supernatants, also referred to as S30 fraction, contain the cell's protein synthetic machinery consisting of ribo-

Cell-free systems can be operated in three different modes: batch mode, continuous flow cellfree (CFCF) mode, and CECF mode. In batch mode, the reaction is carried out in a tube to which all components of the reaction are added. It is easy to step-up and can be useful for fast and easy production of small amounts of protein. Its disadvantage is it is a closed system and

The CFCF mode is an open system which requires the continuous supply of fresh substrates and removal of by-products by a continuous flow of a feeding solution into a reaction chamber. The CFCF mode was first developed by Spirin and co-workers [60]. The total volume of the

somes, translation factors, aminoacyl-tRNA synthetases, and tRNAs.

15N2-Lys) are the most commonly used amino acids for produc-

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69

amino acids prior to their incorporation into protein.

15N4-Arg and 8 Da using 13C6

present on each tryptic peptide.

3.1.1.2. Cell-free production

hence has limited capacity.

purified and can be used as internal standards.

Figure 1. Internal standardization strategies for different LC-MS/MS protein quantification workflows.

#### 3.1. Protein internal standards

#### 3.1.1. Stable isotope labeled protein internal standard

A stable isotope labeled (SIL) form of the analyte protein is the most ideal IS for absolute quantification of proteins. As the analyte protein and SIL-protein internal standards have the same physiochemical behavior, this IS will be able to track the analyte protein throughout the entire analytical procedure. SIL-proteins are added at the start of the sample extraction and can account for immunoaffinity isolation(s), enzymatic digestion, pre-analytical treatments as well as the mass spectrometric ionization.

The EMA guidelines recommend the use of a SIL-protein IS whenever possible for LC-MS/MS methods. However, a major restriction in the use of SIL-proteins as internal standards for protein quantification is their commercial unavailability or the high cost of production. The complex structure consisting of specific intramolecular folding of amino acid chains as well as intramolecular di-sulfide linkages and presence of post translational modifications makes it difficult to synthesize these proteins in a reproducible manner. If the analyte protein is small, a SIL form of the protein can be chemically synthesized using solid-phase synthesis [16, 56]. However, for most protein analytes, the production of its isotopic labeled form requires a cellular environment. Two methods are described below for the generation of isotopically labeled proteins: metabolic labeling using whole cells and the cell-free approach using cell lysates.

#### 3.1.1.1. Cell culture production

All cell-based labeling approaches rely on the metabolic conversion of labeled precursors into a protein. The labeled precursors used in cell-based systems may be amino acids or they may be more fundamental precursors which serve as carbon or nitrogen sources for the synthesis of amino acids prior to their incorporation into protein.

SILAC is a popular technique for production of SIL-proteins by incorporation of SIL-amino acids into the target protein. This technique is popularly known as stable isotope labeling by amino acids in cell culture (SILAC) [57] or stable isotope labeling with amino acids (SILAA) [58]. SILAC is a straightforward procedure in which essential amino acids are left out of culture media and replaced by deuterated, carbon-13, and/or nitrogen-15 labeled variants of these amino acids. After multiple cell duplication cycles, these SIL amino acids get incorporated in the entire proteome. Heavy labeled variants of lysine and arginine that provide ample spacing between isotopic envelopes of light and heavy tryptic peptides (e.g., 10 Da using 13C6 15N4-Arg and 8 Da using 13C6 15N2-Lys) are the most commonly used amino acids for production of SIL-proteins using SILAC. Arginine and lysine on an average they occur at every tenth position in a protein sequence. Trypsin, the major proteolytic enzyme used in protein quantification assays, cleaves at lysine and arginine ensuring that at least one of the labeled amino is present on each tryptic peptide.

Cell culture production is highly useful for generating SIL-labeled proteins for biothereapeutics. Biotherapeutics are produced by genetically modified cell lines, yeast or bacteria. To obtain a SIL-protein, the cells producing the biotherapeutic protein are grown in a medium containing labeled precursors for the desired protein. The stable isotope labeled amino acids gets incorporated in the proteins, thus resulting in production of a SIL-protein. These SIL-proteins are then purified and can be used as internal standards.

The cell culture method is an easy process of producing labeled proteins, but requires a cell culture equipment and a sterile laboratory. A major disadvantage is that in cell culture other endogenous proteins will be simultaneously produced having the incorporated label, and hence a more elaborate purification is required. Also, incomplete labeling can occur when the pools of labeled amino acids are diluted with amino acids newly synthesized by the cell.

#### 3.1.1.2. Cell-free production

3.1. Protein internal standards

as the mass spectrometric ionization.

3.1.1.1. Cell culture production

3.1.1. Stable isotope labeled protein internal standard

A stable isotope labeled (SIL) form of the analyte protein is the most ideal IS for absolute quantification of proteins. As the analyte protein and SIL-protein internal standards have the same physiochemical behavior, this IS will be able to track the analyte protein throughout the entire analytical procedure. SIL-proteins are added at the start of the sample extraction and can account for immunoaffinity isolation(s), enzymatic digestion, pre-analytical treatments as well

Figure 1. Internal standardization strategies for different LC-MS/MS protein quantification workflows.

68 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

The EMA guidelines recommend the use of a SIL-protein IS whenever possible for LC-MS/MS methods. However, a major restriction in the use of SIL-proteins as internal standards for protein quantification is their commercial unavailability or the high cost of production. The complex structure consisting of specific intramolecular folding of amino acid chains as well as intramolecular di-sulfide linkages and presence of post translational modifications makes it difficult to synthesize these proteins in a reproducible manner. If the analyte protein is small, a SIL form of the protein can be chemically synthesized using solid-phase synthesis [16, 56]. However, for most protein analytes, the production of its isotopic labeled form requires a cellular environment. Two methods are described below for the generation of isotopically labeled proteins: metabolic

All cell-based labeling approaches rely on the metabolic conversion of labeled precursors into a protein. The labeled precursors used in cell-based systems may be amino acids or they may be

labeling using whole cells and the cell-free approach using cell lysates.

SIL-proteins can also be made by in vitro protein synthesis in a cell free system [59]. Cell-free translation systems are largely supernatants obtained by centrifugation of the crude lysate of either E. coli, wheat germ, or rabbit reticulocytes at 30,000 g. The cell lysate supernatants, also referred to as S30 fraction, contain the cell's protein synthetic machinery consisting of ribosomes, translation factors, aminoacyl-tRNA synthetases, and tRNAs.

Cell-free systems can be operated in three different modes: batch mode, continuous flow cellfree (CFCF) mode, and CECF mode. In batch mode, the reaction is carried out in a tube to which all components of the reaction are added. It is easy to step-up and can be useful for fast and easy production of small amounts of protein. Its disadvantage is it is a closed system and hence has limited capacity.

The CFCF mode is an open system which requires the continuous supply of fresh substrates and removal of by-products by a continuous flow of a feeding solution into a reaction chamber. The CFCF mode was first developed by Spirin and co-workers [60]. The total volume of the reaction is maintained constant by having the volume flowing out of the chamber equal to the volume flowing in. This system can be used for continuous production of labeled proteins.

can be used as an internal standard. SILu™Mab internal standard is a commercially available stable labeled IgG1 monoclonal antibody and has been metabolically labeled with 13C6

internal standard in quantitation of humanized biotherapeutics in non-human biological matrices. Table 1 lists out the various characteristic SIL-peptides that can be generated after

The universal applicability of SILu™Mab is exemplified in an immunoaffinity coupled LC-MS/ MS method reported by Kaur et al. [61]. A generic method was developed for mAb-1 and its universal applicability was demonstrated with the additional six mAbs. SILu™Mab was used as the common internal standard in all seven methods. The extraction involved immunoaffinity enrichment followed by tryptic digestion. For three mAbs, the immunoaffinity capture was carried out using anti-human Fc antibody attached to magnetic beads. This immunoaffinity capture allows selective binding to a humanized mAb in nonclinical matrices. Alternatively, for remaining four mAbs, the affinity enrichment was performed using a less selective reagent, Protein A/G. After immunocapture, the analyte and IS bound to the magnetic beads were denatured, reduced, and alkylated. The isolated analyte mAb and IS were digested with trypsin prior to LC-MS/MS analysis. The method for mAb-1 in cynomolgus serum was found to have a linear response over the nominal concentration range of 0.100 to 25.0 μg/ml with high precision (%CV < 3%) and good accuracy (%DFN 9%). The high precision and accuracy of the method validates the effectiveness of the internal standard to compensate for any variability during extraction and analysis. The method performance was evaluated with additional six mAb as well as in rat and mouse sera. All the assays showed good precision (%CV < 20%) and accuracy

The generic method, using a universal internal standard that tracks the analyte throughout extraction and instrumental analysis, circumvents the method development challenges for biotherapeutic mAbs. This internal standard use is restricted to non-human biological matrices. In human matrices, the signature peptide will lose its selectivity due to the presence of high

Universal SIL-peptide Antibody isotype Peptide location DTLMISR\* IgG1, IgG2, IgG3, IgG4 Heavy chain FNWYVDGVEVHNAK\* IgG1 Heavy chain VVSVLTVLHQDWLNGK IgG1, IgG3, IgG4 Heavy chain NQVSLTCLVK\* IgG1, IgG2, IgG3, IgG4 Heavy chain GFYPSDIAVEWESNGQPENNYK\* IgG1, IgG4 Heavy chain AGVETTTPSK\* IgG1, IgG2, IgG3, IgG4 Light chain (Lamda) YAASSYLSLTPEQWK\* IgG1, IgG2, IgG3, IgG4 Light chain (Lamda)

15N4–Arginine or 13C6

15N2–Lysine).

15N2-Lysine was expressed in CHO cells. SILu™Mab is used as a universal

Internal Standards for Absolute Quantification of Large Molecules (Proteins) from Biological Matrices…

Arginine and 13C6

(%DFN 20%).

\*

concentrations of endogenous mAbs.

Stable isotope labeled amino acid (13C6

Table 1. Tryptic SIL-peptides of SILu™Mab.

proteolysis of SILu™Mab with trypsin.

15N4–

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The CECF mode is an open system with two chambers separated by a semi-permeable membrane. The first chamber is the feeding chamber and contains the substrates and the energy system. The second chamber is the reaction chamber and contains the enzymes and DNA. The substrates permeate through the semipermeable membrane and are converted to proteins in the reaction chamber. This can be easily set-up using a simple dialysis bag as the reaction chamber. The bag can be immersed in a feeding solution inside of a tube larger than the dialysis bag creating a simple two-chamber device.

#### 3.1.2. Derivatized protein internal standard

Derivatization allows one to easily generate a protein internal standard that is physiochemically like the analyte protein. Winther et al. reported an LC-MS/MS method for quantification of progastrin-releasing peptide (ProGRP), a small cell lung cancer biomarker, in human serum using an acetylated form of the protein as an internal standard [30]. The IS was made in-house by specific acetylation of the lysine side chains in ProGRP (31–98) by using N-hydroxysuccinimide-based ester acetic acid N-hydroxysuccinimide (AA-NHS) as the acetylating reactant. The acetylated ProGRP (31–98) signature peptide NLLGLIEAK gets converted to NLLGLIEAKacENR, which was used as a peptide internal standard. The extraction procedure involved protein precipitation with acetonitrile followed by pellet digestion with trypsin prior to analysis.

This acetylated ProGRP internal standard mimicked the analyte ProGRP through extraction steps including tryptic digestion and hence compensated for any variations during extraction. However, acetylation of the IS-peptide, results in chromatographic differences between the signature peptide and IS-peptide. Differences in retention time can result differences in ionization due to co-eluting matrix interferences. The derivatization also caused ionization differences in the precursor ion charge states. NLLGLIEAK had +2 as the most dominant charge state while NLLGLIEAKacENR had +3 as the most dominant charge state of the precursor ion. The addition of IS to the samples improved the coefficient for both the linear and the polynomial calibration curve and the intra- and inter-day accuracy. However, the high intra-day precision values (%CV of 12–25.2%) displayed some unaccounted variability in turn questioning the performance of the internal standard in this method. An important consideration while using derivatized internal standards is to ensure that impurities of underivatized analyte protein or derivatizing reagent are not present in the purified internal standard.

#### 3.1.3. Universal stable isotope label protein internal standard for quantification of antibody-based biotherapeutics in non-human matrix

Drug development involves bioanalytical testing in non-human species. During bioanalysis of humanized IgG antibody based biotherapeutics in animals, selected peptides from the constant region (Fc) of the antibody can be used as signature peptides. These peptides will be present in the humanized immunoglobulin (IgG)-based biotherapeutic drugs, but will not be present in antibodies found in the animal biological fluids. In methods using signature peptides obtained from the constant region, a stable labeled analogue monoclonal antibody (mAb) can be used as an internal standard. SILu™Mab internal standard is a commercially available stable labeled IgG1 monoclonal antibody and has been metabolically labeled with 13C6 15N4– Arginine and 13C6 15N2-Lysine was expressed in CHO cells. SILu™Mab is used as a universal internal standard in quantitation of humanized biotherapeutics in non-human biological matrices. Table 1 lists out the various characteristic SIL-peptides that can be generated after proteolysis of SILu™Mab with trypsin.

The universal applicability of SILu™Mab is exemplified in an immunoaffinity coupled LC-MS/ MS method reported by Kaur et al. [61]. A generic method was developed for mAb-1 and its universal applicability was demonstrated with the additional six mAbs. SILu™Mab was used as the common internal standard in all seven methods. The extraction involved immunoaffinity enrichment followed by tryptic digestion. For three mAbs, the immunoaffinity capture was carried out using anti-human Fc antibody attached to magnetic beads. This immunoaffinity capture allows selective binding to a humanized mAb in nonclinical matrices. Alternatively, for remaining four mAbs, the affinity enrichment was performed using a less selective reagent, Protein A/G. After immunocapture, the analyte and IS bound to the magnetic beads were denatured, reduced, and alkylated. The isolated analyte mAb and IS were digested with trypsin prior to LC-MS/MS analysis. The method for mAb-1 in cynomolgus serum was found to have a linear response over the nominal concentration range of 0.100 to 25.0 μg/ml with high precision (%CV < 3%) and good accuracy (%DFN 9%). The high precision and accuracy of the method validates the effectiveness of the internal standard to compensate for any variability during extraction and analysis. The method performance was evaluated with additional six mAb as well as in rat and mouse sera. All the assays showed good precision (%CV < 20%) and accuracy (%DFN 20%).

The generic method, using a universal internal standard that tracks the analyte throughout extraction and instrumental analysis, circumvents the method development challenges for biotherapeutic mAbs. This internal standard use is restricted to non-human biological matrices. In human matrices, the signature peptide will lose its selectivity due to the presence of high concentrations of endogenous mAbs.


Table 1. Tryptic SIL-peptides of SILu™Mab.

reaction is maintained constant by having the volume flowing out of the chamber equal to the volume flowing in. This system can be used for continuous production of labeled proteins.

The CECF mode is an open system with two chambers separated by a semi-permeable membrane. The first chamber is the feeding chamber and contains the substrates and the energy system. The second chamber is the reaction chamber and contains the enzymes and DNA. The substrates permeate through the semipermeable membrane and are converted to proteins in the reaction chamber. This can be easily set-up using a simple dialysis bag as the reaction chamber. The bag can be immersed in a feeding solution inside of a tube larger than the

Derivatization allows one to easily generate a protein internal standard that is physiochemically like the analyte protein. Winther et al. reported an LC-MS/MS method for quantification of progastrin-releasing peptide (ProGRP), a small cell lung cancer biomarker, in human serum using an acetylated form of the protein as an internal standard [30]. The IS was made in-house by specific acetylation of the lysine side chains in ProGRP (31–98) by using N-hydroxysuccinimide-based ester acetic acid N-hydroxysuccinimide (AA-NHS) as the acetylating reactant. The acetylated ProGRP (31–98) signature peptide NLLGLIEAK gets converted to NLLGLIEAKacENR, which was used as a peptide internal standard. The extraction procedure involved protein precipitation

This acetylated ProGRP internal standard mimicked the analyte ProGRP through extraction steps including tryptic digestion and hence compensated for any variations during extraction. However, acetylation of the IS-peptide, results in chromatographic differences between the signature peptide and IS-peptide. Differences in retention time can result differences in ionization due to co-eluting matrix interferences. The derivatization also caused ionization differences in the precursor ion charge states. NLLGLIEAK had +2 as the most dominant charge state while NLLGLIEAKacENR had +3 as the most dominant charge state of the precursor ion. The addition of IS to the samples improved the coefficient for both the linear and the polynomial calibration curve and the intra- and inter-day accuracy. However, the high intra-day precision values (%CV of 12–25.2%) displayed some unaccounted variability in turn questioning the performance of the internal standard in this method. An important consideration while using derivatized internal standards is to ensure that impurities of underivatized analyte protein or derivatizing reagent are not present in the purified internal standard.

3.1.3. Universal stable isotope label protein internal standard for quantification of antibody-based

Drug development involves bioanalytical testing in non-human species. During bioanalysis of humanized IgG antibody based biotherapeutics in animals, selected peptides from the constant region (Fc) of the antibody can be used as signature peptides. These peptides will be present in the humanized immunoglobulin (IgG)-based biotherapeutic drugs, but will not be present in antibodies found in the animal biological fluids. In methods using signature peptides obtained from the constant region, a stable labeled analogue monoclonal antibody (mAb)

with acetonitrile followed by pellet digestion with trypsin prior to analysis.

dialysis bag creating a simple two-chamber device.

70 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

3.1.2. Derivatized protein internal standard

biotherapeutics in non-human matrix

#### 3.1.4. Analogue proteins as internal standards

A structural protein analogue can also be used as an internal standard. This internal standard is the least favorable as it may not truly mimic the protein analyte during proteolysis or the signature peptide during mass spectrometric ionization. The advantage of using an analogue protein is ease of availability and low cost. As it accounts for volume loses, it can be an appropriate IS for methods that involve simple sample preparation such as partial protein precipitation. An unlabeled analogue protein is chosen based on the similarities in physiochemical properties, such as size, hydrophobicity, and isoelectric point, with the analyte protein and its surrogate peptides obtained after proteolysis. Some methods have been reported wherein the chosen internal standard was able to track the analyte efficiently throughout the method.

steps. The major advantage of using a SIL-peptide is that these can be synthetized at relatively

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A SIL-peptide internal standard can be added before and after proteolysis. However, if the signature peptide is suspected to undergo degradation, it is recommended to add the SILpeptide prior to digestion. Also, if a recombinant form of the protein is not available, protein concentrations are calculated stoichiometrically, solely based on the known molar concentration of the SIL-peptide used. In such instances, the internal standard is added post digestion to

Variation in digestion efficiency can be accounted for with the use of an extended SIL-peptide which has cleavable groups flanking either side of side of a SIL-peptide [29, 64, 65]. Generally, the cleavable groups consist of three to six amino acids residues from the original protein sequence at both the N- and C- terminus [29, 65, 66]. The addition of an extended SIL-peptide IS prior to digestion provides a more cost-effective alternative to compensate for variability in digestion efficiency, peptide stability, volume recovery, and mass spectrometric ionization.

Barnindge et al. were first to report the comparison between SIL-peptide/non-cleavable peptide (NCP) and a dual cleavable peptide (DCP) or "extended SIL-peptide" as internal standards to track protein digestions [64]. They synthesized two peptides each containing a signature peptide sequence from amino acids 318 to 323 in human serum albumin (HSA). The non-cleavable peptide (NCP) was labeled with a stable isotope labeled alanine residue, i.e., NYA\*EAK, whereas the other peptide had two tryptic cleavage sites and two stable isotope labeled alanine residues, i.e., DVAK-NYA\*EA\*K-DVFLG. Different concentrations of HSA were digested along with equimolar concentrations of NCP and DCP. Prior to digestion the samples were reduced for 30 min at 30C using 10 mM dithiothreitol (DTT) followed by alkylation using a concentration of 30 mM iodoacetamide (IAA) with the reaction going to completion in the dark at room temperature for 30 min. Each sample was then digested with trypsin for 12 h at 30C in a shaking water bath using an enzyme-to-substrate ratio of 1:10. The reaction is terminated after 12 h with trifluoroacetic acid. The samples were analyzed using LC-MS/MS. The results showed that a cleavable internal standard peptide could give similar results to a non-cleavable internal standard peptide. Timed digest experiments showed that the digestion rates for dual cleavable peptide and analyte protein, i.e., HSA were different with the DCP proteolysis coming to completion faster (approximately 1 min) than HSA (approximately 20 min). From these results, they concluded that although an internal standard with a cleavage site provides understanding of the digestion process, a SIL-peptide truly cannot

obtain reproducible peptide quantification [24, 63].

3.2.2. Extended stable isotope labeled peptide internal standard

replicate the proteolysis conditions experienced by the analyte protein.

In another study, Faria et al. compared the performance of a SIL-peptide and extended SILpeptide as internal standards for quantification of human osteopontin [67]. Digestion studies showed that the signature peptide production had a biphasic pattern. This pattern was attributed to the degradation of the signature peptide during digestion with trypsin due to suspected chymotrypsin-like activity. The digestion profile of the protein analyte had three phases, i.e., the "formation phase," the "transition phase," and the "degradation phase." The

low cost.

Halquist et al. reported an LC-MS/MS method for quantification of Alefacept, a therapeutic protein for treatment of psoriasis, in human plasma using horse heart myoglobin a protein analogue internal standard [11]. The method used partial protein precipitation to selectively precipitate background proteins while retaining the analyte protein and the internal standard protein in solution. The isolated proteins were proteolyzed using trypsin. A 20-h-incubation was chosen for proteolysis to ensure least digestion variability for both proteins. The signature peptides from analyte and IS were then separated using reversed phase chromatography and detected using tandem mass spectrometry with electrospray ionization. The chromatographic gradient conditions were adjusted to ensure the surrogate analyte peptide and the IS-peptide had the same retention time. This enabled the IS-peptide to compensate for any matrix effects during ionization.

#### 3.2. Peptide internal standards

#### 3.2.1. Stable isotope labeled peptide internal standard

When a SIL-protein is unavailable for use as an internal standard, a stable isotope labeled form of the signature peptide can be used. A SIL form of the signature peptide (SIL-peptide) is the most commonly used internal standard during protein quantification. SIL-IS peptides are variants of the signature peptides having one or more stable isotope labeled amino acids. Stable isotope labeled amino acids are obtained by substitution of certain atoms (N,C,H) with their heavy variants. The most frequently used stable isotopes are 13C (carbon-13), 15N (nitrogen-15), and <sup>2</sup> H (deuterium). A SIL-peptide can be created by using solid-phase peptide synthesis [56, 62]. Due to the widespread use of SIL-peptides for protein bioanalysis, several laboratories provide commercial services for production of customized SIL-peptides at reasonable prices.

SIL-peptides are physiochemically identical to the signature peptide but can be easily distinguished on a mass spectrometer due to the mass shift from the heavier isotopes. A minimum mass difference of at least 6 Da between SIL-peptides and the signature peptide is recommended. This will ensure an adequate resolution between the mass of SIL-peptide and signature peptide even for peptides having a dominant charge state of +2. SIL peptides can effectively compensate for extraction recovery, peptide instability and LC-MS/MS variability. However, unlike a SIL-protein it does not track immunoaffinity and proteolytic digestion steps. The major advantage of using a SIL-peptide is that these can be synthetized at relatively low cost.

A SIL-peptide internal standard can be added before and after proteolysis. However, if the signature peptide is suspected to undergo degradation, it is recommended to add the SILpeptide prior to digestion. Also, if a recombinant form of the protein is not available, protein concentrations are calculated stoichiometrically, solely based on the known molar concentration of the SIL-peptide used. In such instances, the internal standard is added post digestion to obtain reproducible peptide quantification [24, 63].

#### 3.2.2. Extended stable isotope labeled peptide internal standard

3.1.4. Analogue proteins as internal standards

72 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

during ionization.

gen-15), and <sup>2</sup>

able prices.

3.2. Peptide internal standards

3.2.1. Stable isotope labeled peptide internal standard

A structural protein analogue can also be used as an internal standard. This internal standard is the least favorable as it may not truly mimic the protein analyte during proteolysis or the signature peptide during mass spectrometric ionization. The advantage of using an analogue protein is ease of availability and low cost. As it accounts for volume loses, it can be an appropriate IS for methods that involve simple sample preparation such as partial protein precipitation. An unlabeled analogue protein is chosen based on the similarities in physiochemical properties, such as size, hydrophobicity, and isoelectric point, with the analyte protein and its surrogate peptides obtained after proteolysis. Some methods have been reported wherein the chosen internal standard was able to track the analyte efficiently throughout the method.

Halquist et al. reported an LC-MS/MS method for quantification of Alefacept, a therapeutic protein for treatment of psoriasis, in human plasma using horse heart myoglobin a protein analogue internal standard [11]. The method used partial protein precipitation to selectively precipitate background proteins while retaining the analyte protein and the internal standard protein in solution. The isolated proteins were proteolyzed using trypsin. A 20-h-incubation was chosen for proteolysis to ensure least digestion variability for both proteins. The signature peptides from analyte and IS were then separated using reversed phase chromatography and detected using tandem mass spectrometry with electrospray ionization. The chromatographic gradient conditions were adjusted to ensure the surrogate analyte peptide and the IS-peptide had the same retention time. This enabled the IS-peptide to compensate for any matrix effects

When a SIL-protein is unavailable for use as an internal standard, a stable isotope labeled form of the signature peptide can be used. A SIL form of the signature peptide (SIL-peptide) is the most commonly used internal standard during protein quantification. SIL-IS peptides are variants of the signature peptides having one or more stable isotope labeled amino acids. Stable isotope labeled amino acids are obtained by substitution of certain atoms (N,C,H) with their heavy variants. The most frequently used stable isotopes are 13C (carbon-13), 15N (nitro-

synthesis [56, 62]. Due to the widespread use of SIL-peptides for protein bioanalysis, several laboratories provide commercial services for production of customized SIL-peptides at reason-

SIL-peptides are physiochemically identical to the signature peptide but can be easily distinguished on a mass spectrometer due to the mass shift from the heavier isotopes. A minimum mass difference of at least 6 Da between SIL-peptides and the signature peptide is recommended. This will ensure an adequate resolution between the mass of SIL-peptide and signature peptide even for peptides having a dominant charge state of +2. SIL peptides can effectively compensate for extraction recovery, peptide instability and LC-MS/MS variability. However, unlike a SIL-protein it does not track immunoaffinity and proteolytic digestion

H (deuterium). A SIL-peptide can be created by using solid-phase peptide

Variation in digestion efficiency can be accounted for with the use of an extended SIL-peptide which has cleavable groups flanking either side of side of a SIL-peptide [29, 64, 65]. Generally, the cleavable groups consist of three to six amino acids residues from the original protein sequence at both the N- and C- terminus [29, 65, 66]. The addition of an extended SIL-peptide IS prior to digestion provides a more cost-effective alternative to compensate for variability in digestion efficiency, peptide stability, volume recovery, and mass spectrometric ionization.

Barnindge et al. were first to report the comparison between SIL-peptide/non-cleavable peptide (NCP) and a dual cleavable peptide (DCP) or "extended SIL-peptide" as internal standards to track protein digestions [64]. They synthesized two peptides each containing a signature peptide sequence from amino acids 318 to 323 in human serum albumin (HSA). The non-cleavable peptide (NCP) was labeled with a stable isotope labeled alanine residue, i.e., NYA\*EAK, whereas the other peptide had two tryptic cleavage sites and two stable isotope labeled alanine residues, i.e., DVAK-NYA\*EA\*K-DVFLG. Different concentrations of HSA were digested along with equimolar concentrations of NCP and DCP. Prior to digestion the samples were reduced for 30 min at 30C using 10 mM dithiothreitol (DTT) followed by alkylation using a concentration of 30 mM iodoacetamide (IAA) with the reaction going to completion in the dark at room temperature for 30 min. Each sample was then digested with trypsin for 12 h at 30C in a shaking water bath using an enzyme-to-substrate ratio of 1:10. The reaction is terminated after 12 h with trifluoroacetic acid. The samples were analyzed using LC-MS/MS. The results showed that a cleavable internal standard peptide could give similar results to a non-cleavable internal standard peptide. Timed digest experiments showed that the digestion rates for dual cleavable peptide and analyte protein, i.e., HSA were different with the DCP proteolysis coming to completion faster (approximately 1 min) than HSA (approximately 20 min). From these results, they concluded that although an internal standard with a cleavage site provides understanding of the digestion process, a SIL-peptide truly cannot replicate the proteolysis conditions experienced by the analyte protein.

In another study, Faria et al. compared the performance of a SIL-peptide and extended SILpeptide as internal standards for quantification of human osteopontin [67]. Digestion studies showed that the signature peptide production had a biphasic pattern. This pattern was attributed to the degradation of the signature peptide during digestion with trypsin due to suspected chymotrypsin-like activity. The digestion profile of the protein analyte had three phases, i.e., the "formation phase," the "transition phase," and the "degradation phase." The formation phase was between 0 and 5 h which was dominant in the formation of signature peptide. The transition phase was between 5 and 10 h where signature peptide formation and degradation processes occur at similar rates. The degradation phase was beyond 10 h in which the degradation of the signature peptide was the most dominant phenomenon. In order to track the analyte protein digestion profile, a SIL-peptide IS and extended SIL-peptide IS were added. From Figure 2, we can see that the recombinant protein and the extended SIL-peptide internal standard had similar digestion profiles as they both undergo formation and degradation. SIL-peptide only undergoes degradation and hence only mimics the analyte protein digestion profile during the degradation phase. Validation studies showed that under controlled conditions and long digestion time there was no significant difference in precision when either of the internal standards was used for quantification. However, when trypsin activity was forcibly varied, the extended SIL peptide had higher precision. This difference was more pronounced when digestion was carried out at shorter time intervals.

prior to use. Synthetic IS peptides with stable isotopic labeled antikeyhole limpet hemocyanin leucine (L\*), NQVSL\*TCL\*VK and REEMTKNQVSL\*TCL\*VKGFYPSD (six flanking amino acids), were commercially obtained and used as SIL-IS peptide and extended SIL-IS peptide, respectively. The evaluation was carried out in rat plasma and cynomolgus monkey serum.

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SIL-protein IS was added to each sample prior to extraction. The analyte mAb and SIL-protein mAb were immunocaptured using an antihuman crystallizable fragment (anti-Fc) that recognizes human mAb biotherapeutics but not the endogenous immunoglobulins in the preclinical sample. After immunocapture, the analytes were eluted with 200 μL of 50% MeOH and 3% formic acid in water. Samples with IS-peptides were spiked either with SIL-peptide or extended SIL-peptide. The eluate was evaporated to dryness. SIL-peptide and extended SILpeptide were added to samples with IS-peptides. The samples were reconstituted for reduction and alkylation. The samples were then digested with trypsin. After termination of the proteo-

For the comparison experiment, three sets of QCs each from αDA-G2, αDA-G1, or αK-G2 were analyzed in three replicates along with the three internal standards. The results can be seen in Figure 3. Overall, all three mAb were quantified accurately (Bias within 20%) and precisely (%CV within 20%) using the SIL-protein IS. For the extended peptide SIL-IS, the αDA-G2 QCs were also well within 20%. The mid and high QC values of the αDA-G1 were near the 20% threshold but not the LQC or the QCs of the αK-G2. For the peptide SIL-IS, the QC values of αDA-G2 were marginally acceptable, with higher variability and imprecision for αDA-G1 and the worst results for αK-G2. In addition, the whole molecule IS peak response within the runs was more precise (15.5% CV) than those of the extended SIL-peptide IS (28.1% CV) or the peptide IS (27.7% CV), N = 32. From this data, we can be seen that the whole Ab IS can effectively compensate for any variability during extraction and LC-MS/MS analysis. If the immunocapture and digestion steps were optimized to have high reproducibility, then the

In another study, Bronsema et al. evaluated different internal standardization strategies for quantification of a small protein, salmon calcitonin, which could be analyzed both with and without and digestion [69]. Salmon calcitonin comprises of 32 amino acid and has a molecular weight of 3431.9 Da. Eight internal standardization approaches were compared with respect to accuracy and precision in work flows with and without digestion. Both analogue IS standard proteins (eel and human calcitonin), SIL-salmon calcitonin, SIL-salmon calcitonin signature peptide [1–11], and the cleavable SIL-salmon calcitonin peptide [1–11] were commercially obtained. 18O-labeled form of the signature peptide was synthesized in-house by isotope

The samples were extracted using three different workflows. In work flow A, the samples were extracted using only SPE prior to LC-MS/MS analysis. In workflow B, the samples were either extracted using SPE and the extracts were digested with trypsin prior to analysis. In workflow C, the samples were enriched using SPE, digested with trypsin and then derivatized prior to analysis. Derivatization was performed with a solution containing 10% of deuterated or unlabeled formaldehyde and 10% pyridine-borane complex in methanol. Waters Oasis MCX SPE cartridges were used post derivatization the clean-up prior to LC-MS/MS analysis in work

lytic reaction, the extracts were analyzed using LC-MS/MS.

synthetic peptide ISs may be adequate for quantification.

exchange with18 O-labeled water.

#### 3.3. Comparison of protein SIL-IS versus peptides IS

Li et al. evaluated the use of SIL-protein, SIL-peptide, and extended SIL-peptide as internal standard for quantification of monoclonal antibodies in preclinical biological matrix by LC-MS/ MS [68]. The evaluation was carried out with four mAbs of the same IgG2 isotype as the SIL-IS: αDA-G2, (KLH)-120.6-G2 (αK-G2), 827-435-G2 (827-G2), and anti-DNP-3B1-G2 (αDB-G2). In addition, the test was extended to four more mAbs of a different isotype IgG1: anti-DNP-3A4-F-G1 (αDAG1), anti-KLH-120.6-G1 (αK-G1), 655-341-G1 (655-G1), and anti-DNP-3B1-G1 (αDB-G1). Stable isotope labeled human antidinitrophenol (DNP) IgG2 mAb was used as the IS as it is unlikely to be present endogenously in preclinical species. The whole molecule SIL-IS of clone anti-DNP-3A4-F-G2 (αDA-G2) was produced in cell culture, purified, and characterized

Figure 2. Comparison of digestion profiles of recombinant OPN along with internal standards, i.e., SIL-peptide and extended SIL-peptide. Reprinted from [67]. Copyright (2015) with permission from Elsevier.

prior to use. Synthetic IS peptides with stable isotopic labeled antikeyhole limpet hemocyanin leucine (L\*), NQVSL\*TCL\*VK and REEMTKNQVSL\*TCL\*VKGFYPSD (six flanking amino acids), were commercially obtained and used as SIL-IS peptide and extended SIL-IS peptide, respectively. The evaluation was carried out in rat plasma and cynomolgus monkey serum.

formation phase was between 0 and 5 h which was dominant in the formation of signature peptide. The transition phase was between 5 and 10 h where signature peptide formation and degradation processes occur at similar rates. The degradation phase was beyond 10 h in which the degradation of the signature peptide was the most dominant phenomenon. In order to track the analyte protein digestion profile, a SIL-peptide IS and extended SIL-peptide IS were added. From Figure 2, we can see that the recombinant protein and the extended SIL-peptide internal standard had similar digestion profiles as they both undergo formation and degradation. SIL-peptide only undergoes degradation and hence only mimics the analyte protein digestion profile during the degradation phase. Validation studies showed that under controlled conditions and long digestion time there was no significant difference in precision when either of the internal standards was used for quantification. However, when trypsin activity was forcibly varied, the extended SIL peptide had higher precision. This difference

was more pronounced when digestion was carried out at shorter time intervals.

Li et al. evaluated the use of SIL-protein, SIL-peptide, and extended SIL-peptide as internal standard for quantification of monoclonal antibodies in preclinical biological matrix by LC-MS/ MS [68]. The evaluation was carried out with four mAbs of the same IgG2 isotype as the SIL-IS: αDA-G2, (KLH)-120.6-G2 (αK-G2), 827-435-G2 (827-G2), and anti-DNP-3B1-G2 (αDB-G2). In addition, the test was extended to four more mAbs of a different isotype IgG1: anti-DNP-3A4-F-G1 (αDAG1), anti-KLH-120.6-G1 (αK-G1), 655-341-G1 (655-G1), and anti-DNP-3B1-G1 (αDB-G1). Stable isotope labeled human antidinitrophenol (DNP) IgG2 mAb was used as the IS as it is unlikely to be present endogenously in preclinical species. The whole molecule SIL-IS of clone anti-DNP-3A4-F-G2 (αDA-G2) was produced in cell culture, purified, and characterized

Figure 2. Comparison of digestion profiles of recombinant OPN along with internal standards, i.e., SIL-peptide and

extended SIL-peptide. Reprinted from [67]. Copyright (2015) with permission from Elsevier.

3.3. Comparison of protein SIL-IS versus peptides IS

74 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

SIL-protein IS was added to each sample prior to extraction. The analyte mAb and SIL-protein mAb were immunocaptured using an antihuman crystallizable fragment (anti-Fc) that recognizes human mAb biotherapeutics but not the endogenous immunoglobulins in the preclinical sample. After immunocapture, the analytes were eluted with 200 μL of 50% MeOH and 3% formic acid in water. Samples with IS-peptides were spiked either with SIL-peptide or extended SIL-peptide. The eluate was evaporated to dryness. SIL-peptide and extended SILpeptide were added to samples with IS-peptides. The samples were reconstituted for reduction and alkylation. The samples were then digested with trypsin. After termination of the proteolytic reaction, the extracts were analyzed using LC-MS/MS.

For the comparison experiment, three sets of QCs each from αDA-G2, αDA-G1, or αK-G2 were analyzed in three replicates along with the three internal standards. The results can be seen in Figure 3. Overall, all three mAb were quantified accurately (Bias within 20%) and precisely (%CV within 20%) using the SIL-protein IS. For the extended peptide SIL-IS, the αDA-G2 QCs were also well within 20%. The mid and high QC values of the αDA-G1 were near the 20% threshold but not the LQC or the QCs of the αK-G2. For the peptide SIL-IS, the QC values of αDA-G2 were marginally acceptable, with higher variability and imprecision for αDA-G1 and the worst results for αK-G2. In addition, the whole molecule IS peak response within the runs was more precise (15.5% CV) than those of the extended SIL-peptide IS (28.1% CV) or the peptide IS (27.7% CV), N = 32. From this data, we can be seen that the whole Ab IS can effectively compensate for any variability during extraction and LC-MS/MS analysis. If the immunocapture and digestion steps were optimized to have high reproducibility, then the synthetic peptide ISs may be adequate for quantification.

In another study, Bronsema et al. evaluated different internal standardization strategies for quantification of a small protein, salmon calcitonin, which could be analyzed both with and without and digestion [69]. Salmon calcitonin comprises of 32 amino acid and has a molecular weight of 3431.9 Da. Eight internal standardization approaches were compared with respect to accuracy and precision in work flows with and without digestion. Both analogue IS standard proteins (eel and human calcitonin), SIL-salmon calcitonin, SIL-salmon calcitonin signature peptide [1–11], and the cleavable SIL-salmon calcitonin peptide [1–11] were commercially obtained. 18O-labeled form of the signature peptide was synthesized in-house by isotope exchange with18 O-labeled water.

The samples were extracted using three different workflows. In work flow A, the samples were extracted using only SPE prior to LC-MS/MS analysis. In workflow B, the samples were either extracted using SPE and the extracts were digested with trypsin prior to analysis. In workflow C, the samples were enriched using SPE, digested with trypsin and then derivatized prior to analysis. Derivatization was performed with a solution containing 10% of deuterated or unlabeled formaldehyde and 10% pyridine-borane complex in methanol. Waters Oasis MCX SPE cartridges were used post derivatization the clean-up prior to LC-MS/MS analysis in work

Figure 3. Accuracy and precision of QCs from 3 mAbs obtained with three different SIL-IS's. (a)–(c): Accuracy of whole SIL-IS, flanking SIL-IS, and peptide SIL-IS, respectively. (d)–(f): Precision of whole SIL-IS, flanking SIL-IS, and peptide SIL-IS, respectively. The dashed lines of 20% are the thresholds of acceptance commonly used by LBAs. αDA-G2, αK-G2, and αDA-G1 QCs are represented by blue, red, and green color bars, respectively. Reprinted with permission from [68]. Copyright (2013) American Chemical Society.

and are expected to cover the digestion step, and (2) B-after referring to internal standards that are SIL or structural analogue forms of the signature peptide and will only cover the postdigestion part of the analysis (B-after). Eel calcitonin was not used in this workflow as an internal standard as it yields a signature peptide same as salmon calcitonin. Besides human calcitonin (added before and after digestion), all other approaches tested in workflow B, including the omission of an internal standard, generated acceptable results, which shows that in this workflow all steps were well under control. Again, the best results in terms of precision and accuracy were obtained when SIL-salmon calcitonin [1–32], cleavable SIL peptide internal standard and SIL peptide [1–11] were used as internal standards. Since there was no difference between the performance of a SIL-calcitonin, cleavable SIL-peptide and that of a SIL-peptide for workflow B, it was concluded that the digestion step did not negatively impact method performance. This observation possibly can be attributed to the small size of the analyte protein and absence of any tertiary or quaternary structure. The commercially obtained SIL peptide internal standard and the in-house prepared 18O-labeled form performed comparably in workflow, thus indicating that the 18O-labeled peptide can be used as an economical

Figure 4. Precision (expressed as error bars) and accuracy for 10 different internal standardization approaches according to workflows A–C as compared to the same workflow without internal standard. The results were obtained by 6-fold analysis of the 100 and 1000 pg/mL samples. The dotted lines indicate the acceptable 15% accuracy limits as set by the FDA-guidance. In workflow B, internal standards were either added before or after the digestion step. Reprinted with

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In workflow C (quantification of digested and derivatized analyte), it was seen that using a differentially labeled internal standard slightly improved assay performance compared to the results without internal standard. Precision and accuracy of this internal standardization

alternative to a chemically synthesized SIL peptide.

permission from [69]. Copyright (2013) American Chemical Society.

flow C. Internal standards were added at different stages depending on the workflow and internal standard characteristics. The results of precision and accuracy studies using a series of internal standardization routes as per workflows A through C, compared to the same workflows without internal standard, are illustrated in Figure 4.

Using workflow A (quantification of the intact analyte) without an internal standard had too much variability at 100 pg/mL, resulting in a bias outside the acceptance criterion of 15%. When SIL-salmon calcitonin was used as internal standard, accuracy, and precision improved significantly at both high and low concentrations. This finding was consistent with the expected performance of SIL-protein IS. The first analogue protein IS, i.e., eel calcitonin (90% sequence homology) introduced high variability at the lower level. When human calcitonin (50% sequence homology) was used as an internal standard, the method performance was severely hampered. Both precision and accuracy were inferior to the results obtained without any internal standard. This illustrates that this internal standard did not correct for variability but rather introduced it into the assay.

In workflow B (quantification of the digested analyte), two internal standardization processes were used, i.e., (1) B-before referring to internal standards that are added prior to digestion Internal Standards for Absolute Quantification of Large Molecules (Proteins) from Biological Matrices… http://dx.doi.org/10.5772/intechopen.75569 77

Figure 4. Precision (expressed as error bars) and accuracy for 10 different internal standardization approaches according to workflows A–C as compared to the same workflow without internal standard. The results were obtained by 6-fold analysis of the 100 and 1000 pg/mL samples. The dotted lines indicate the acceptable 15% accuracy limits as set by the FDA-guidance. In workflow B, internal standards were either added before or after the digestion step. Reprinted with permission from [69]. Copyright (2013) American Chemical Society.

and are expected to cover the digestion step, and (2) B-after referring to internal standards that are SIL or structural analogue forms of the signature peptide and will only cover the postdigestion part of the analysis (B-after). Eel calcitonin was not used in this workflow as an internal standard as it yields a signature peptide same as salmon calcitonin. Besides human calcitonin (added before and after digestion), all other approaches tested in workflow B, including the omission of an internal standard, generated acceptable results, which shows that in this workflow all steps were well under control. Again, the best results in terms of precision and accuracy were obtained when SIL-salmon calcitonin [1–32], cleavable SIL peptide internal standard and SIL peptide [1–11] were used as internal standards. Since there was no difference between the performance of a SIL-calcitonin, cleavable SIL-peptide and that of a SIL-peptide for workflow B, it was concluded that the digestion step did not negatively impact method performance. This observation possibly can be attributed to the small size of the analyte protein and absence of any tertiary or quaternary structure. The commercially obtained SIL peptide internal standard and the in-house prepared 18O-labeled form performed comparably in workflow, thus indicating that the 18O-labeled peptide can be used as an economical alternative to a chemically synthesized SIL peptide.

flow C. Internal standards were added at different stages depending on the workflow and internal standard characteristics. The results of precision and accuracy studies using a series of internal standardization routes as per workflows A through C, compared to the same

Figure 3. Accuracy and precision of QCs from 3 mAbs obtained with three different SIL-IS's. (a)–(c): Accuracy of whole SIL-IS, flanking SIL-IS, and peptide SIL-IS, respectively. (d)–(f): Precision of whole SIL-IS, flanking SIL-IS, and peptide SIL-IS, respectively. The dashed lines of 20% are the thresholds of acceptance commonly used by LBAs. αDA-G2, αK-G2, and αDA-G1 QCs are represented by blue, red, and green color bars, respectively. Reprinted with permission from [68].

Using workflow A (quantification of the intact analyte) without an internal standard had too much variability at 100 pg/mL, resulting in a bias outside the acceptance criterion of 15%. When SIL-salmon calcitonin was used as internal standard, accuracy, and precision improved significantly at both high and low concentrations. This finding was consistent with the expected performance of SIL-protein IS. The first analogue protein IS, i.e., eel calcitonin (90% sequence homology) introduced high variability at the lower level. When human calcitonin (50% sequence homology) was used as an internal standard, the method performance was severely hampered. Both precision and accuracy were inferior to the results obtained without any internal standard. This illustrates that this internal standard did not correct for variability

In workflow B (quantification of the digested analyte), two internal standardization processes were used, i.e., (1) B-before referring to internal standards that are added prior to digestion

workflows without internal standard, are illustrated in Figure 4.

76 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

but rather introduced it into the assay.

Copyright (2013) American Chemical Society.

In workflow C (quantification of digested and derivatized analyte), it was seen that using a differentially labeled internal standard slightly improved assay performance compared to the results without internal standard. Precision and accuracy of this internal standardization

approach were comparable to the SIL peptide and 18O-labeled peptide approaches for workflow B, which do not include a derivatization and second SPE step. Workflow C is more laborious and has multiple steps without any internal standards, and therefore will have a higher risk of experimental variability.

[2] Rauh M. LC–MS/MS for protein and peptide quantification in clinical chemistry. Journal

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deployment of a QconCAT strategy. Proteomics. Aug. 2011;11(15):2957-2970

peptide immunoaffinity LC-MS/MS. Analytical Chemistry. 2013;85(11):5522-5529

Academy of Sciences of the United States of America. Jun. 2003;100(12):6940-6945

of Chromatography B. Feb. 2012;883–884:59-67

Methods. Mar. 2005;35(3):265-273

405(7):2321-2331

879(11–12)

2011;25(2):281-290

### 4. Conclusions

Precision and accuracy of bioanalysis is ultimately improved through internal standardization. The selection of an internal standard is often dictated based upon availability, time, and cost. While SIL-proteins are considered the ideal internal standard, their availability often limits their use. SIL-peptides and extended SIL-peptides are readily available, and serve as good alternatives to SIL-proteins. When using SIL-peptide, it is essential that sample preparation steps, i.e., enrichment and enzymatic digestions that are not tracked by the peptide internal standards are optimized to limit their variability. In the absence of SIL-IS standard, an analogue protein or peptide may be used as an internal standard. The use of stable isotope labeled analogue monoclonal antibody as a universal internal standard has enabled rapid development of accurate and precise methods for quantitative bioanalysis of biotherapeutics in nonhuman species.

### Conflict of interest

The views and opinions in this chapter represent those of the authors only.

### Author details

Morse Faria<sup>1</sup> and Matthew S. Halquist<sup>2</sup> \*

\*Address all correspondence to: halquistms@vcu.edu


### References

[1] Makawita S, Diamandis EP. The bottleneck in the cancer biomarker pipeline and protein quantification through mass spectrometry-based approaches: Current strategies for candidate verification. Clinical Chemistry. Feb. 2010;56(2):212-222

[2] Rauh M. LC–MS/MS for protein and peptide quantification in clinical chemistry. Journal of Chromatography B. Feb. 2012;883–884:59-67

approach were comparable to the SIL peptide and 18O-labeled peptide approaches for workflow B, which do not include a derivatization and second SPE step. Workflow C is more laborious and has multiple steps without any internal standards, and therefore will have a

Precision and accuracy of bioanalysis is ultimately improved through internal standardization. The selection of an internal standard is often dictated based upon availability, time, and cost. While SIL-proteins are considered the ideal internal standard, their availability often limits their use. SIL-peptides and extended SIL-peptides are readily available, and serve as good alternatives to SIL-proteins. When using SIL-peptide, it is essential that sample preparation steps, i.e., enrichment and enzymatic digestions that are not tracked by the peptide internal standards are optimized to limit their variability. In the absence of SIL-IS standard, an analogue protein or peptide may be used as an internal standard. The use of stable isotope labeled analogue monoclonal antibody as a universal internal standard has enabled rapid development of accurate and precise methods for quantitative bioanalysis of biotherapeutics in non-

The views and opinions in this chapter represent those of the authors only.

\*

didate verification. Clinical Chemistry. Feb. 2010;56(2):212-222

2 Department of Pharmaceutics, Virginia Commonwealth University, Richmond, VA, USA

[1] Makawita S, Diamandis EP. The bottleneck in the cancer biomarker pipeline and protein quantification through mass spectrometry-based approaches: Current strategies for can-

higher risk of experimental variability.

78 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

4. Conclusions

human species.

Conflict of interest

Author details

References

Morse Faria<sup>1</sup> and Matthew S. Halquist<sup>2</sup>

\*Address all correspondence to: halquistms@vcu.edu

1 Chromatographic Sciences, PPD, Richmond, VA, USA


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**Chapter 5**

Provisional chapter

**Calibration Methods of Laser-Induced Breakdown**

DOI: 10.5772/intechopen.72888

Calibration Methods of Laser-Induced Breakdown

Laser-induced breakdown spectroscopy (LIBS) has gained great attention over the past two decades due to its many advantages, such as needless sample preparation, capability of remote measurement and fast multielement simultaneous analysis. However, because of its inherent uncertainty features of plasma, it is still a big challenge for LIBS community worldwide to realize high sensitivity and accurate quantitative analysis. Currently, many chemometric analytical methods have been applied to LIBS calibration analysis, including univariate regression, multivariate regression, principal component regression (PCR), partial least squares regression (PLSR) and so on. In addition, appropriate sample and spectral pretreatment can effectively improve the analytical performance (i.e., limit of detection (LOD), accuracy and repeatability) of LIBS. In this chapter, we briefly summarize the progress of these calibration methods and their applications

Keywords: laser-induced breakdown spectroscopy, sample and spectral pretreatment, calibration methods, chemometrics, calibration-free laser-induced breakdown

Laser-induced breakdown spectroscopy (LIBS), also sometimes called laser-induced plasma spectroscopy (LIPS), has developed rapidly as an analytical technique over the past two decades. LIBS is a kind of atomic emission spectroscopy, which uses a high-energy pulsed laser as the excitation source. The laser is focused on the sample surface, thereby evaporating and atomizing the sample and generating a plasma. The light emitted by the plasma is detected by a spectrometer. One can obtain sample composition and concentration information by analyzing the plasma

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

**Spectroscopy**

Spectroscopy

Abstract

spectroscopy

1. Introduction

Hongbo Fu, Junwei Jia, Huadong Wang,

Hongbo Fu, Junwei Jia, Huadong Wang,

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

on LIBS and provide our recommendations.

Zhibo Ni and Fengzhong Dong

Zhibo Ni and Fengzhong Dong

http://dx.doi.org/10.5772/intechopen.72888


Provisional chapter

### **Calibration Methods of Laser-Induced Breakdown Spectroscopy** Calibration Methods of Laser-Induced Breakdown

DOI: 10.5772/intechopen.72888

Hongbo Fu, Junwei Jia, Huadong Wang, Zhibo Ni and Fengzhong Dong Hongbo Fu, Junwei Jia, Huadong Wang,

Additional information is available at the end of the chapter Zhibo Ni and Fengzhong Dong

http://dx.doi.org/10.5772/intechopen.72888 Additional information is available at the end of the chapter

#### Abstract

Spectroscopy

serum and plasma in the presence of antithyroglobulin autoantibodies. Clinical Chemis-

[67] Faria M, Halquist MS, Yuan M, Mylott W, Jenkins RG, Karnes HT. Comparison of a stable isotope labeled (SIL) peptide and an extended SIL peptide as internal standards to track digestion variability of an unstable signature peptide during quantification of a cancer biomarker, human osteopontin, from plasma using capill. Journal of Chromatography, B:

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Analytical Technologies in the Biomedical and Life Sciences. 2015;1001

clinical studies. Analytical Chemistry. Feb. 2012;84(3):1267-1273

84 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

try. Jun. 2013;59(6):982-990

2013;85(20):9528-9535

Laser-induced breakdown spectroscopy (LIBS) has gained great attention over the past two decades due to its many advantages, such as needless sample preparation, capability of remote measurement and fast multielement simultaneous analysis. However, because of its inherent uncertainty features of plasma, it is still a big challenge for LIBS community worldwide to realize high sensitivity and accurate quantitative analysis. Currently, many chemometric analytical methods have been applied to LIBS calibration analysis, including univariate regression, multivariate regression, principal component regression (PCR), partial least squares regression (PLSR) and so on. In addition, appropriate sample and spectral pretreatment can effectively improve the analytical performance (i.e., limit of detection (LOD), accuracy and repeatability) of LIBS. In this chapter, we briefly summarize the progress of these calibration methods and their applications on LIBS and provide our recommendations.

Keywords: laser-induced breakdown spectroscopy, sample and spectral pretreatment, calibration methods, chemometrics, calibration-free laser-induced breakdown spectroscopy

#### 1. Introduction

Laser-induced breakdown spectroscopy (LIBS), also sometimes called laser-induced plasma spectroscopy (LIPS), has developed rapidly as an analytical technique over the past two decades. LIBS is a kind of atomic emission spectroscopy, which uses a high-energy pulsed laser as the excitation source. The laser is focused on the sample surface, thereby evaporating and atomizing the sample and generating a plasma. The light emitted by the plasma is detected by a spectrometer. One can obtain sample composition and concentration information by analyzing the plasma

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

1. Simple equipment: few instruments, low cost and easy integration.

4. Various samples: samples can be gas, aerosols, liquids and solids.

its different depths of the sample composition and content.

sample, so all elements in the sample can be analyzed simultaneously.

has broad application prospects.

without processing the sample.

in 1963–2016.

2. Noncontact analysis: LIBS uses pulsed laser as the excitation source, which makes it noncontact analysis, especially in the dangerous environment or space exploration field,

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3. No sample preparation: LIBS directly focused pulsed laser bombardment of the sample

5. Nondestructive analysis: The laser converges to the surface of the sample, and only a small amount of the sample is excited. It can be considered as nondestructive or near nondestructive.

6. Three-dimensional analysis: LIBS can collect laser at different positions on the sample surface or repeat measurements at the same location to analyze the sample surface and

7. Total element analysis: The laser energy can simultaneously excite all the elements in the

8. Remote analysis: The long-distance analysis of the LIBS can be achieved by remotely transmitting the laser energy and collecting the plasma emission spectrum through the fiber.

9. Online analysis: LIBS is a very fast technology that provides analytical results in seconds, making it particularly suitable for rapid analysis or online industrial monitoring.

Figure 2. The number of articles published in the Web of Science search by laser-induced breakdown spectroscopy (LIBS)

Figure 1. A schematic of a general apparatus for laser-induced breakdown spectroscopy illustrating the principal components.

emission spectra. LIBS most commonly used experimental instruments such as mainly lasers, spectrometers, detectors and computers, as shown in Figure 1.

The laser which is the most widely used in LIBS is the Nd:YAG solid-state lasers operated in the Q-switch mode. Typically, it is operated at the fundamental wavelength of 1064 nm, pulse energy is 30–100 mJ, pulse width is 5~15 ns and repetition rate is 1~10 Hz. In addition, the researchers tested the effects of lasers of different types and parameters on the LIBS. Trautner et al. [1] investigated polyethylene (PE) and a rubber material from tire production by employing 157 nm F2 laser and 532 nm Nd:YAG laser ablation in nitrogen and argon gas background or in air. The effects of laser wavelength on depth resolution of thin-film solar cell are investigated by Choi et al. [2] using an ultraviolet (λ = 266 nm) and a visible (λ = 532 nm) nanosecond Nd:YAG lasers. Labutin et al. [3] summarize nearly two decades of studies on femtosecond laser-induced breakdown spectrometry (fs-LIBS). Picosecond pulse train and nanosecond pulse were compared for laser ablation and LIBS measurements by Lednev et al. [4].

Spectrometers disperse the emitted radiation of the laser-induced plasma to get a spectrum in terms of intensity as a function of the wavelength. The dominant spectrometer types used for LIBS are multichannel fiber spectrometer and echelle spectrometer coupled with an intensified CCD. The echelle spectrometer offers a wide spectral range, a high spectral resolution, and the possibility of time-resolved. The plasma parameters (plasma temperature and electron density) are constantly changing with respect to the delay time, and an echelle spectrometer with time resolution is needed when calculating these parameters. However, time-resolved broadband spectrometers are expensive and strongly dependent on external circumstances. The multichannel fiber spectrometer is robust and reliable for the use in mobile and portable LIBS instruments, providing an accredited spectral resolution, but their integration time is typically much longer than the plasma lifetime.

In recent years, with the rapid development of lasers, spectrometers and detectors and the urgent demand of in situ and online analysis, LIBS has developed rapidly. Compared with many other types of elemental analysis techniques, LIBS has obvious advantages:


emission spectra. LIBS most commonly used experimental instruments such as mainly lasers,

Figure 1. A schematic of a general apparatus for laser-induced breakdown spectroscopy illustrating the principal components.

The laser which is the most widely used in LIBS is the Nd:YAG solid-state lasers operated in the Q-switch mode. Typically, it is operated at the fundamental wavelength of 1064 nm, pulse energy is 30–100 mJ, pulse width is 5~15 ns and repetition rate is 1~10 Hz. In addition, the researchers tested the effects of lasers of different types and parameters on the LIBS. Trautner et al. [1] investigated polyethylene (PE) and a rubber material from tire production by employing 157 nm F2 laser and 532 nm Nd:YAG laser ablation in nitrogen and argon gas background or in air. The effects of laser wavelength on depth resolution of thin-film solar cell are investigated by Choi et al. [2] using an ultraviolet (λ = 266 nm) and a visible (λ = 532 nm) nanosecond Nd:YAG lasers. Labutin et al. [3] summarize nearly two decades of studies on femtosecond laser-induced breakdown spectrometry (fs-LIBS). Picosecond pulse train and nanosecond pulse were com-

Spectrometers disperse the emitted radiation of the laser-induced plasma to get a spectrum in terms of intensity as a function of the wavelength. The dominant spectrometer types used for LIBS are multichannel fiber spectrometer and echelle spectrometer coupled with an intensified CCD. The echelle spectrometer offers a wide spectral range, a high spectral resolution, and the possibility of time-resolved. The plasma parameters (plasma temperature and electron density) are constantly changing with respect to the delay time, and an echelle spectrometer with time resolution is needed when calculating these parameters. However, time-resolved broadband spectrometers are expensive and strongly dependent on external circumstances. The multichannel fiber spectrometer is robust and reliable for the use in mobile and portable LIBS instruments, providing an accredited spectral resolution, but their integration time is typically

In recent years, with the rapid development of lasers, spectrometers and detectors and the urgent demand of in situ and online analysis, LIBS has developed rapidly. Compared with

many other types of elemental analysis techniques, LIBS has obvious advantages:

spectrometers, detectors and computers, as shown in Figure 1.

86 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

pared for laser ablation and LIBS measurements by Lednev et al. [4].

much longer than the plasma lifetime.


Figure 2. The number of articles published in the Web of Science search by laser-induced breakdown spectroscopy (LIBS) in 1963–2016.

Because of many advantages of LIBS, it has been applied to a number of analytical domains, for example, various alloys [5–7], slags [8, 9], soil [10], rocks [11, 12] and isotopes [13]. We searched for all scientific papers from 1963 to 2016 on Web of Science with laser-induced breakdown spectroscopy (LIBS). The statistical results are presented in Figure 2. It can be seen that LIBS has developed rapidly since 1990.

research results show that the continuous background of the Al plasma emission spectra induced by 800 nm femtosecond pulse laser is strongly polarized. The use of a polarizer can effectively filter the continuous spectrum, thus improving the signal-to-noise ratio and the

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In order to increase the stability of the signal, the analyte signal intensity can be normalized using a parameter representative of the actual plasma conditions. In general, there are three main standardized methods [27]: (1) normalization by using the intensity of an internal standard line; (2) normalization by using a reference signal; and (3) compensation for the plasma conditions. Castro et al. [28] used 12 different types of data normalization to reduce the interference matrix and to improve the calibration models. Their findings show that the application of normalization modes was useful to compensate for the differences among sample matrices. Models without normalization presented two- to fivefold higher errors. Karki et al. [29] studied the analytical performance of six different spectrum normalization techniques, namely internal normalization, normalization with total light, normalization with background along with their three-point smoothing methods for quantification of Cr, Mn and Ni in stainless steel. The final results show the superiority of internal normalization technique over normalization with total light and normalization with background techniques irrespective of whether it is Cr, Ni or Mn analysis. Wang et al. presented three spectrum standardized methods in order to improve the reproducibility of LIBS measurements which are named the spectrum standardization approach [30], the sampled spectrum standardization approach [31] and the multivariate spectrum standardization method, respectively. In spectral standardization, a particular example is the use of acoustic signals

LIBS can excite all the elements of the spectrum of the sample, so reliable and fast identification of emission lines in laser ablation of multicomponent samples is crucial. Labutin et al. [35] applied an algorithm to automatically identify emission lines in LIBS. The algorithm is implemented by three parts: simulation of the set of spectra corresponding to different temperature and electron density, searching the best correlated pair of a model spectrum and an experimental one, and attributing the peaks with certain lines. Ukwatta et al. [36] consider the problem of element detection as a multilabel classification problem, using support vector machines (SVMs) and artificial neural networks (ANNs) for multielement classification. The proposed algorithm is evaluated by using the LIBS image obtained from the experiment. The accuracy of the machine learning method to identify the elements correctly can reach 99%. Mateo et al. [37] developed the software package SALIPS, which can quickly and semiautomatically identify the spectrum peak and give the element composition of the analytical sample. The software package simulates the spectrum by using the relative intensity of the atomic line in the NIST database. In order to facilitate visual compar-

ison, it can present both the simulated and experimental spectra on the same plot.

signal-to-back ratio of the characteristic spectrum.

[32, 33] or laser-induced plasma image [34].

2.4. Automatic identification of emission lines

2.3. Spectral normalization

### 2. Pretreatment of samples and spectra

#### 2.1. Sample pretreatment

One of the most widely cited advantages of LIBS is that it does not require sample preparation, but this may also be the biggest limitation for improving its consistancy. In general, LIBS performance may be enhanced using two main approaches: pretreatment of samples and spectra. Many homogeneous solid samples require no sample preparation, for example, glass, alloy and plastic. For powder samples (e.g., cement [14], soil [10] and coal [15]) which can press the cake directly, it must be consistent with the standard sample preparation process used for calibration during the pressing process. Comparing with solid samples, the direct analysis of liquid samples by using LIBS has many disadvantages: splash, less excitation and fluctuation of liquid level. The simplest way to change a liquid sample into a solid sample is to freeze it [16, 17]. Sobral et al. [18] investigated the detection sensitivity of Cu, Mg, Pb, Hg, Cd, Cr and Fe traces in water and ice samples under the same experimental conditions by using LIBS. Another effective way that can be used for liquid analysis in a solid matrix configuration consists of using an absorbent substrate, for example, plant fiber spunlace nonwoven [19], absorbent paper [20], thin wood sample [21, 22] and membranebased filter paper [23]. Now LIBS analysis of aerosols is mainly of two categories: direct analysis and enrichment. However, the detection limit and the statistical results of the direct analysis are still relatively poor. On the other hand, the substrate-based collection does not provide as instantaneous information and does allow one to achieve lower detection limits by increasing the sample flow rates and sampling times.

#### 2.2. Correction and removal of continuum background

The detected plasma emission spectrum at a given wavelength in a spectrum is the sum of the analyte signal and the continuum background. The analyte signal is often overwhelmed by the continuum background, which interferes the true intensity of signal and compromises spectral clarity and hence reduces the accuracy of quantitative analysis. Zou et al. [24] developed a modified algorithm of background removal based on wavelet transform for spectrum correction and applied to low-alloy steel samples. This method can effectively improve the quality of the signals and the accuracy of the regression model. Sun et al. [25] presented a method that can automatically estimate and correct varying continuum background emission. Simulations and experiments were made to successfully prove the efficiency of the method. The proposed method scarcely needs people's intervention and can automatically and flexibly estimate varying continuum backgrounds over a very wide spectrum range. Another way to deduct a continuous background is to add a polarizer to the collected light path. Penczak et al.'s [26] research results show that the continuous background of the Al plasma emission spectra induced by 800 nm femtosecond pulse laser is strongly polarized. The use of a polarizer can effectively filter the continuous spectrum, thus improving the signal-to-noise ratio and the signal-to-back ratio of the characteristic spectrum.

#### 2.3. Spectral normalization

Because of many advantages of LIBS, it has been applied to a number of analytical domains, for example, various alloys [5–7], slags [8, 9], soil [10], rocks [11, 12] and isotopes [13]. We searched for all scientific papers from 1963 to 2016 on Web of Science with laser-induced breakdown spectroscopy (LIBS). The statistical results are presented in Figure 2. It can be seen that LIBS has

One of the most widely cited advantages of LIBS is that it does not require sample preparation, but this may also be the biggest limitation for improving its consistancy. In general, LIBS performance may be enhanced using two main approaches: pretreatment of samples and spectra. Many homogeneous solid samples require no sample preparation, for example, glass, alloy and plastic. For powder samples (e.g., cement [14], soil [10] and coal [15]) which can press the cake directly, it must be consistent with the standard sample preparation process used for calibration during the pressing process. Comparing with solid samples, the direct analysis of liquid samples by using LIBS has many disadvantages: splash, less excitation and fluctuation of liquid level. The simplest way to change a liquid sample into a solid sample is to freeze it [16, 17]. Sobral et al. [18] investigated the detection sensitivity of Cu, Mg, Pb, Hg, Cd, Cr and Fe traces in water and ice samples under the same experimental conditions by using LIBS. Another effective way that can be used for liquid analysis in a solid matrix configuration consists of using an absorbent substrate, for example, plant fiber spunlace nonwoven [19], absorbent paper [20], thin wood sample [21, 22] and membranebased filter paper [23]. Now LIBS analysis of aerosols is mainly of two categories: direct analysis and enrichment. However, the detection limit and the statistical results of the direct analysis are still relatively poor. On the other hand, the substrate-based collection does not provide as instantaneous information and does allow one to achieve lower detection limits

The detected plasma emission spectrum at a given wavelength in a spectrum is the sum of the analyte signal and the continuum background. The analyte signal is often overwhelmed by the continuum background, which interferes the true intensity of signal and compromises spectral clarity and hence reduces the accuracy of quantitative analysis. Zou et al. [24] developed a modified algorithm of background removal based on wavelet transform for spectrum correction and applied to low-alloy steel samples. This method can effectively improve the quality of the signals and the accuracy of the regression model. Sun et al. [25] presented a method that can automatically estimate and correct varying continuum background emission. Simulations and experiments were made to successfully prove the efficiency of the method. The proposed method scarcely needs people's intervention and can automatically and flexibly estimate varying continuum backgrounds over a very wide spectrum range. Another way to deduct a continuous background is to add a polarizer to the collected light path. Penczak et al.'s [26]

developed rapidly since 1990.

2.1. Sample pretreatment

2. Pretreatment of samples and spectra

88 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

by increasing the sample flow rates and sampling times.

2.2. Correction and removal of continuum background

In order to increase the stability of the signal, the analyte signal intensity can be normalized using a parameter representative of the actual plasma conditions. In general, there are three main standardized methods [27]: (1) normalization by using the intensity of an internal standard line; (2) normalization by using a reference signal; and (3) compensation for the plasma conditions. Castro et al. [28] used 12 different types of data normalization to reduce the interference matrix and to improve the calibration models. Their findings show that the application of normalization modes was useful to compensate for the differences among sample matrices. Models without normalization presented two- to fivefold higher errors. Karki et al. [29] studied the analytical performance of six different spectrum normalization techniques, namely internal normalization, normalization with total light, normalization with background along with their three-point smoothing methods for quantification of Cr, Mn and Ni in stainless steel. The final results show the superiority of internal normalization technique over normalization with total light and normalization with background techniques irrespective of whether it is Cr, Ni or Mn analysis. Wang et al. presented three spectrum standardized methods in order to improve the reproducibility of LIBS measurements which are named the spectrum standardization approach [30], the sampled spectrum standardization approach [31] and the multivariate spectrum standardization method, respectively. In spectral standardization, a particular example is the use of acoustic signals [32, 33] or laser-induced plasma image [34].

#### 2.4. Automatic identification of emission lines

LIBS can excite all the elements of the spectrum of the sample, so reliable and fast identification of emission lines in laser ablation of multicomponent samples is crucial. Labutin et al. [35] applied an algorithm to automatically identify emission lines in LIBS. The algorithm is implemented by three parts: simulation of the set of spectra corresponding to different temperature and electron density, searching the best correlated pair of a model spectrum and an experimental one, and attributing the peaks with certain lines. Ukwatta et al. [36] consider the problem of element detection as a multilabel classification problem, using support vector machines (SVMs) and artificial neural networks (ANNs) for multielement classification. The proposed algorithm is evaluated by using the LIBS image obtained from the experiment. The accuracy of the machine learning method to identify the elements correctly can reach 99%. Mateo et al. [37] developed the software package SALIPS, which can quickly and semiautomatically identify the spectrum peak and give the element composition of the analytical sample. The software package simulates the spectrum by using the relative intensity of the atomic line in the NIST database. In order to facilitate visual comparison, it can present both the simulated and experimental spectra on the same plot.

#### 3. Calibration methods of LIBS

A number of calibration methods have been applied to various research fields and physical state samples of LIBS quantitative analysis. We cannot involve all published research articles, and only a few of the most commonly used calibration methods are reviewed.

#### 3.1. Univariate analysis

The fitting area intensity I corresponding to the transition between lower level El and upper level Eu of an atomic species α can be expressed as:

$$I = F N\_{\alpha}^{I} A\_{\text{ul}} \frac{\mathcal{g}\_{u}}{\mathcal{U}\_{\alpha}^{I}(T)} \exp\left(-\frac{E\_{u}}{\mathbf{k}\_{\text{B}}T}\right) \tag{1}$$

where F is the experimental parameter, N<sup>I</sup> <sup>α</sup> is the atomic number density, Aul is the transition probability, gu is the upper-level degeneracy and <sup>U</sup><sup>I</sup> <sup>α</sup>ð Þ T is the partition function at the temperature T. For the same sample, if the temperature and density of each laser-induced plasma are constant, then I is proportional to the elemental concentration C. If there are a series of samples with different C, one can establish a calibration line between spectral intensity and element concentration.

$$C\_i = b\_0 + b\_1 I\_i + e\_i \tag{2}$$

data and consequently a fast first knowledge about the prediction ability of the model since poor correlation necessarily implies poor predictive ability. However, it should be noticed that a model with a value of R<sup>2</sup> close to 1 may indeed have a poor accuracy for

Precision is described by the standard deviation (SD), the relative standard deviation (RSD in %)

Pn i¼1

RSDð Þ¼ % SD

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

N

C

Pn i¼1

In order to describe the lower limits of a quantitative model, the limit of detection (LOD) can

LOD ¼ 3

For LIBS, the line of an element is not one. If there are m variables and n samples, then

where σ is the standard deviation of the background and C=I is the reciprocal of the slope of the calibration curve. The calculated values of LOD for different elements are presented in

Ci � <sup>C</sup> � �<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

n

σC

Cb<sup>i</sup> � Ci � �<sup>2</sup>

vuuut (6)

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vuuut (8)

� 100 (7)

<sup>I</sup> (9)

and the root-mean-square error (RMSE), which can be expressed as:

Figure 3. Simple linear regression calibration curves for Ce [38].

SD ¼

RMSE ¼

be calculated by the following equation:

prediction [39].

Table 1.

3.2. Multivariate analysis

3.2.1. Multiple linear regression

where b<sup>0</sup> and b<sup>1</sup> are model parameters, ei is the random error and i is the number of samples. The parameter Cb<sup>i</sup> is the estimate value of Ci, namely

$$
\dot{C}\_i = b\_0 + b\_1 I\_i \tag{3}
$$

and

$$
\mathbf{e}\_i = \dot{\mathbf{C}}\_i - \mathbf{C}\_i \tag{4}
$$

In the regression analysis, the best estimate of b<sup>0</sup> and b<sup>1</sup> is obtained based on a set of I and C, which makes the Cb and C to the nearest degree. For example, Bhatt et al. [38] choose Ce II 413.38, 418.65, and 439.16 nm to establish a univariate linear calibration curve, as shown in Figure 3.

Correlation coefficient R, also called the Pearson coefficient, is often used to denote the correlation between I and C, which is defined as:

$$\mathbf{R} = \frac{\sum\_{i=1}^{n} \left(I\_i - \overline{I}\right) \left(\mathbf{C}\_i - \overline{\mathbf{C}}\right)}{\sqrt{\sum\_{i=1}^{n} \left(I\_i - \overline{I}\right)^2} \sqrt{\sum\_{i=1}^{n} \left(\mathbf{C}\_i - \overline{\mathbf{C}}\right)^2}}\tag{5}$$

Correlation coefficient j j R ≤ 1, and it is closer to 1, indicating the better relevance. Most of the LIBS papers report R<sup>2</sup> which provides fast information about the correlation of the

Figure 3. Simple linear regression calibration curves for Ce [38].

3. Calibration methods of LIBS

level Eu of an atomic species α can be expressed as:

probability, gu is the upper-level degeneracy and <sup>U</sup><sup>I</sup>

The parameter Cb<sup>i</sup> is the estimate value of Ci, namely

lation between I and C, which is defined as:

R ¼

where F is the experimental parameter, N<sup>I</sup>

3.1. Univariate analysis

concentration.

and

A number of calibration methods have been applied to various research fields and physical state samples of LIBS quantitative analysis. We cannot involve all published research articles,

The fitting area intensity I corresponding to the transition between lower level El and upper

gu UI

ature T. For the same sample, if the temperature and density of each laser-induced plasma are constant, then I is proportional to the elemental concentration C. If there are a series of samples with different C, one can establish a calibration line between spectral intensity and element

where b<sup>0</sup> and b<sup>1</sup> are model parameters, ei is the random error and i is the number of samples.

In the regression analysis, the best estimate of b<sup>0</sup> and b<sup>1</sup> is obtained based on a set of I and C, which makes the Cb and C to the nearest degree. For example, Bhatt et al. [38] choose Ce II 413.38, 418.65, and 439.16 nm to establish a univariate linear calibration curve, as shown in Figure 3.

Correlation coefficient R, also called the Pearson coefficient, is often used to denote the corre-

Ii � <sup>I</sup> � � Ci � <sup>C</sup> � �

Ci � <sup>C</sup> � �<sup>2</sup>

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn i¼1

Pn i¼1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn i¼1

Ii � <sup>I</sup> � �<sup>2</sup>

Correlation coefficient j j R ≤ 1, and it is closer to 1, indicating the better relevance. Most of the LIBS papers report R<sup>2</sup> which provides fast information about the correlation of the

<sup>α</sup>ð Þ <sup>T</sup> exp � Eu

kBT � �

<sup>α</sup> is the atomic number density, Aul is the transition

Ci ¼ b<sup>0</sup> þ b1Ii þ ei (2)

Cb<sup>i</sup> ¼ b<sup>0</sup> þ b1Ii (3)

ei ¼ Cb<sup>i</sup> � Ci (4)

<sup>s</sup> (5)

<sup>α</sup>ð Þ T is the partition function at the temper-

(1)

and only a few of the most commonly used calibration methods are reviewed.

90 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

<sup>I</sup> <sup>¼</sup> FN<sup>I</sup>

<sup>α</sup>Aul

data and consequently a fast first knowledge about the prediction ability of the model since poor correlation necessarily implies poor predictive ability. However, it should be noticed that a model with a value of R<sup>2</sup> close to 1 may indeed have a poor accuracy for prediction [39].

Precision is described by the standard deviation (SD), the relative standard deviation (RSD in %) and the root-mean-square error (RMSE), which can be expressed as:

$$\text{SD} = \sqrt{\frac{\sum\_{i=1}^{n} \left(\mathbf{C}\_{i} - \overline{\mathbf{C}}\right)^{2}}{N}} \tag{6}$$

$$\text{RSD}(\%) = \frac{\text{SD}}{\overline{\text{C}}} \times 100\tag{7}$$

$$\text{RMSE} = \sqrt{\frac{\sum\_{i=1}^{n} \left(\widehat{\mathbf{C}}\_{i} - \mathbf{C}\_{i}\right)^{2}}{n}} \tag{8}$$

In order to describe the lower limits of a quantitative model, the limit of detection (LOD) can be calculated by the following equation:

$$LOD = 3\frac{\sigma \mathbb{C}}{I} \tag{9}$$

where σ is the standard deviation of the background and C=I is the reciprocal of the slope of the calibration curve. The calculated values of LOD for different elements are presented in Table 1.

#### 3.2. Multivariate analysis

#### 3.2.1. Multiple linear regression

For LIBS, the line of an element is not one. If there are m variables and n samples, then


Table 1. Limit of detection (LOD) estimated for different elements.

$$\mathbf{C}\_{i} = b\_{0} + b\_{1}I\_{i1} + \dots + b\_{m}I\_{im} + e\_{i} \qquad (i = 1, 2, \dots, n), \tag{10}$$

$$Q = \sum\_{i=1}^{n} e\_i^2 = \sum\_{i=1}^{n} \left(\mathbb{C}\_i - \widehat{\mathbb{C}}\_i\right)^2 \tag{11}$$

Principal component analysis can transform a set of variables that may have correlation into a set of linearly uncorrelated variables by orthogonal transformation. The variable after the conversion is called the principal component. Principal component regression (PCR) is a regression analysis method for analyzing multiple regression and is based on PCA. In general, predicting the concentration by PCR can be divided into three steps: first, the PCA is performed on the data (spectral) matrix of the original independent variables, and the appropriate number of principal components is selected by finding the eigenvalue, eigenvector, variance contribution rate and cumulative contribution rate. Second, the selected principal component is analyzed by the ordinary least-squares method. Finally, the strongest possible correlations between the orthogonal PC scores and elemental composition are established. When selecting principal components by PCR, only the independent variables are taken into account, and the dependent variables are ignored. It can reduce the dimension of variables and address the problem of multiple collinearity but cannot distinguish noise when there is a lot of noise in the independent variable (signal) and lose some information of the original variables,

Calibrate method Input variables R<sup>2</sup> Predicted value (μg/g) Relative error (%)

S2:140.308 7.771

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S2:132.129 13.147

S2:132.687 12.780

S2:159.965 5.151

Unary ICr 0.007 S1:138.208 7.674

Binary ICr,IPCr 0.887 S1:143.649 11.913

Ternary ICr,IPCr,ICa 0.890 S1:142.413 10.950

Quaternary ICr,IPCr,ICa,IPCa 0.987 S1:133.659 4.130

Table 2. Quantitative results of Cr by different linear regression methods.

Death et al. [41] applied PCR to determine the elemental composition of a series of run-of-mine (ROM) iron ore samples. LIBS spectral data were recorded in three separate spectral regions (250 nm, 400 nm and 750 nm) to measure major, minor and trace components of the iron ore sample pellets. Background stripping, normalization and spectral cleaning were applied to minimize RSD of the LIBS data. PCR analysis was used to produce calibration models of Fe, Al, Si, Mn, K and P. Independent LIBS measurement data are used to verify these calibration models. The model R<sup>2</sup> for Fe, Al, Si and K is 0.99, 0.98, 0.99 and 0.84, respectively. As an

The main purpose of PCR is to extract relevant information hidden in the spectral line and then used to predict the concentration. This approach allows one to use only those independent variables, and the noise will be eliminated, so as to improve the quality of the predictive model. However, PCR still has some defects, and some useful variables whose correlation is very small are easily missed when the principal component is selected. If we choose for

so a better regression model will not be obtained.

3.2.3. Partial least squares regression

example, PCR calibration model of Fe is shown in Figure 4 [41].

where I is the intensity of different spectral lines from the same element, ei is residual, Q is the sum of squares of the residuals and Cb<sup>i</sup> is the estimate value of Ci. One can get b0, b1, …,bm when Q value achieves the minimum value.

For example, Chen et al. [40] used the multiple linear regression method to quantitatively analyze chromium in potatoes. The characteristic line of Cr can be considered that the concentration of Cr (Ci) has a relationship with the intensity of Cr and/or the other corresponding elements. They normalize the quantitative analysis of Cr by considering the influence of the Ca matrix. Four independent variables (ICr, IPCr, ICa and IPCa) are used to test the performance of different linear regression methods, where ICr is the intensity of Cr I 425.43 nm, IPCr is the sum of three Cr lines (Cr I:425.43, Cr I 427.48 and Cr I 428.97 nm), ICa is the intensity of Ca I 431.86 nm and IPCa is the sum of five Ca lines (Ca I 422.67, Ca I 428.30, Ca I 430.25, Ca I 430.77, and Ca I 431.86 nm). Different combinations of the four independent variables were selected for unary, binary, ternary and quaternary linear regression analyses. The results of quantitative analysis of Cr element by the linear regression method with different variables are indicated in Table 2.

#### 3.2.2. Principal component regression

In the LIBS quantitative analysis, the calculated concentration is affected by the lines of objective elements and other elements. In the study of empirical questions, in order to analyze the problem comprehensively and systematically, one must consider many spectral lines of many elements. Because each line reflects the information of the element concentration in varying degrees, and the lines have a certain correlation with each other, the information reflected in the calculation overlaps to some extent. In the study of multivariate problems by statistical methods, too many variables will increase the amount of calculation and increase the complexity of the problem. It is hoped that the variables involved in the process of quantitative analysis are less and the amount of information is more. Principal component analysis (PCA) is adapted to this requirement and is an ideal tool for solving such problems.


Table 2. Quantitative results of Cr by different linear regression methods.

Ci ¼ b<sup>0</sup> þ b1Ii<sup>1</sup> þ … þ bmIim þ ei ð Þ i ¼ 1; 2;…; n , (10)

(11)

Ci � Cb<sup>i</sup> � �<sup>2</sup>

where I is the intensity of different spectral lines from the same element, ei is residual, Q is the sum of squares of the residuals and Cb<sup>i</sup> is the estimate value of Ci. One can get b0, b1, …,bm when

For example, Chen et al. [40] used the multiple linear regression method to quantitatively analyze chromium in potatoes. The characteristic line of Cr can be considered that the concentration of Cr (Ci) has a relationship with the intensity of Cr and/or the other corresponding elements. They normalize the quantitative analysis of Cr by considering the influence of the Ca matrix. Four independent variables (ICr, IPCr, ICa and IPCa) are used to test the performance of different linear regression methods, where ICr is the intensity of Cr I 425.43 nm, IPCr is the sum of three Cr lines (Cr I:425.43, Cr I 427.48 and Cr I 428.97 nm), ICa is the intensity of Ca I 431.86 nm and IPCa is the sum of five Ca lines (Ca I 422.67, Ca I 428.30, Ca I 430.25, Ca I 430.77, and Ca I 431.86 nm). Different combinations of the four independent variables were selected for unary, binary, ternary and quaternary linear regression analyses. The results of quantitative analysis of Cr element by the linear regression method with different variables are

In the LIBS quantitative analysis, the calculated concentration is affected by the lines of objective elements and other elements. In the study of empirical questions, in order to analyze the problem comprehensively and systematically, one must consider many spectral lines of many elements. Because each line reflects the information of the element concentration in varying degrees, and the lines have a certain correlation with each other, the information reflected in the calculation overlaps to some extent. In the study of multivariate problems by statistical methods, too many variables will increase the amount of calculation and increase the complexity of the problem. It is hoped that the variables involved in the process of quantitative analysis are less and the amount of information is more. Principal component analysis (PCA) is adapted to this requirement and is an ideal tool for solving such problems.

<sup>Q</sup> <sup>¼</sup> <sup>X</sup><sup>n</sup> i¼1 e 2 <sup>i</sup> <sup>¼</sup> <sup>X</sup><sup>n</sup> i¼1

Q value achieves the minimum value.

Elements LOD (%) Ce 0.098 Eu 0.052 Gd 0.077 Nd 0.047 Sm 0.25 Y 0.036

92 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Table 1. Limit of detection (LOD) estimated for different elements.

indicated in Table 2.

3.2.2. Principal component regression

Principal component analysis can transform a set of variables that may have correlation into a set of linearly uncorrelated variables by orthogonal transformation. The variable after the conversion is called the principal component. Principal component regression (PCR) is a regression analysis method for analyzing multiple regression and is based on PCA. In general, predicting the concentration by PCR can be divided into three steps: first, the PCA is performed on the data (spectral) matrix of the original independent variables, and the appropriate number of principal components is selected by finding the eigenvalue, eigenvector, variance contribution rate and cumulative contribution rate. Second, the selected principal component is analyzed by the ordinary least-squares method. Finally, the strongest possible correlations between the orthogonal PC scores and elemental composition are established. When selecting principal components by PCR, only the independent variables are taken into account, and the dependent variables are ignored. It can reduce the dimension of variables and address the problem of multiple collinearity but cannot distinguish noise when there is a lot of noise in the independent variable (signal) and lose some information of the original variables, so a better regression model will not be obtained.

Death et al. [41] applied PCR to determine the elemental composition of a series of run-of-mine (ROM) iron ore samples. LIBS spectral data were recorded in three separate spectral regions (250 nm, 400 nm and 750 nm) to measure major, minor and trace components of the iron ore sample pellets. Background stripping, normalization and spectral cleaning were applied to minimize RSD of the LIBS data. PCR analysis was used to produce calibration models of Fe, Al, Si, Mn, K and P. Independent LIBS measurement data are used to verify these calibration models. The model R<sup>2</sup> for Fe, Al, Si and K is 0.99, 0.98, 0.99 and 0.84, respectively. As an example, PCR calibration model of Fe is shown in Figure 4 [41].

#### 3.2.3. Partial least squares regression

The main purpose of PCR is to extract relevant information hidden in the spectral line and then used to predict the concentration. This approach allows one to use only those independent variables, and the noise will be eliminated, so as to improve the quality of the predictive model. However, PCR still has some defects, and some useful variables whose correlation is very small are easily missed when the principal component is selected. If we choose for

multiple linear regression analysis. Both PLS and PCA try to extract the maximum information reflecting the data variation, but PCA only considers one independent variable matrix, while PLS has a response matrix, so it has predictive function. PLS avoids potential problems such as nonnormal distribution of data, factor indeterminacy and unidentifiable models. PLS has two types (PLS-1 and PLS-2), and PLS-1 corresponds to the case where there is only one dependent variable. PLS-2 corresponds to the case where there are several dependent variables. Although PLSR is more complex than PCR, and the tendency of overfitting is stronger, better results can be obtained by using PLS to analyze low-precision data or high-

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The input variable of PLS can be characteristic spectral lines [42], partial spectral region [43] or full spectrum [44]. Amador-Hernandez et al. [45] used PLS-1 to quantify gold and silver gold and silver in Au-Ag-Cu alloys. The influence of spectral region (266–340 nm, 266–269/326– 340 nm and 269–313 nm), laser energy (3 mJ, 8 mJ), background correction and integration

To overcome the poor precision of the calibration curve methods and the limitations of nonlinear problems, scholars have proposed the use of statistical methods for the quantitative analysis by LIBS. Artificial neural networks (ANNs) are computing systems inspired by the biological neural networks that constitute animal brains. Such systems learn (progressively improve performance) to do tasks by considering examples, generally without task-specific programming. The following outstanding advantages of artificial neural networks have attracted great attention in recent years: (1) it can fully approximate any complex nonlinear relationship; (2) all the quantitative or qualitative information is stored in the neurons in the network, so it has strong robustness and fault tolerance; (3) ANNS adopts the parallel distribution processing method, so that it can perform a large number of operations quickly; (4) ANNS can learn and adapt to unknown or uncertain system; and (5) it can handle both quantitative and qualitative information at the same time. An artificial neuron network (ANN) is a computational model based on the structure and functions of biological neural networks. Artificial neural networks usually contain input layer,

time on the quantitative analysis of PLS was studied, respectively (Table 3).

hidden layer (competitive layer) and output layer, as shown in Figure 5.

Figure 5. Schematic of the three-layer artificial neural network [46].

complexity systems.

3.2.4. Artificial neural network

Figure 4. PCR calibration model determined for iron using the 250-nm LIBS data.

each component, it is too difficult. Partial least squares regression (PLSR) is a new multivariate statistical data analysis method. It mainly studies the regression modeling of multiple dependent variables to multiple independent variables. PLSR is more effective, especially when the variables are highly linearly correlated. In addition, PLSR solves the problem that the number of samples is less than the number of variables. Partial least squares (PLS) is the advantage of three analytical methods, which are PCA, canonical correlation analysis and


Values in brackets correspond to number of factors if different from three.

WBC = without background correction. BC = with background correction

Table 3. Standard error of calibration (SEP) and prediction (SEV, in italics) estimated during the determination of silver for autoscaled data.

multiple linear regression analysis. Both PLS and PCA try to extract the maximum information reflecting the data variation, but PCA only considers one independent variable matrix, while PLS has a response matrix, so it has predictive function. PLS avoids potential problems such as nonnormal distribution of data, factor indeterminacy and unidentifiable models. PLS has two types (PLS-1 and PLS-2), and PLS-1 corresponds to the case where there is only one dependent variable. PLS-2 corresponds to the case where there are several dependent variables. Although PLSR is more complex than PCR, and the tendency of overfitting is stronger, better results can be obtained by using PLS to analyze low-precision data or highcomplexity systems.

The input variable of PLS can be characteristic spectral lines [42], partial spectral region [43] or full spectrum [44]. Amador-Hernandez et al. [45] used PLS-1 to quantify gold and silver gold and silver in Au-Ag-Cu alloys. The influence of spectral region (266–340 nm, 266–269/326– 340 nm and 269–313 nm), laser energy (3 mJ, 8 mJ), background correction and integration time on the quantitative analysis of PLS was studied, respectively (Table 3).

#### 3.2.4. Artificial neural network

each component, it is too difficult. Partial least squares regression (PLSR) is a new multivariate statistical data analysis method. It mainly studies the regression modeling of multiple dependent variables to multiple independent variables. PLSR is more effective, especially when the variables are highly linearly correlated. In addition, PLSR solves the problem that the number of samples is less than the number of variables. Partial least squares (PLS) is the advantage of three analytical methods, which are PCA, canonical correlation analysis and

Integrated spectra WBC 3.47 3.27 3.27 2.74 (2) 2.72 (2) 2.63 (2)

Time-resolved spectra WBC 3.11 2.27 3 2.02 2.73 (2) 3.96 (2)

Table 3. Standard error of calibration (SEP) and prediction (SEV, in italics) estimated during the determination of silver

Region I Region II Region III

8 mJ 3 mJ 8 mJ 3 mJ 8 mJ 3 mJ

4 3.67 3.76 3.36 2.92 2.85

2.22 2.54 2.03 2.67 2.78 2.57

3.46 2.51 3.4 2.22 3.09 4.36

3.36 2.56 3.57 3.31 2.9 4.57

BC 1.97 2.27 2.56 2.27 2.58 (2) 2.09 (2)

BC 3.07 2.32 3.13 2.23 2.47 (2) 3.73 (2)

Figure 4. PCR calibration model determined for iron using the 250-nm LIBS data.

94 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Values in brackets correspond to number of factors if different from three. WBC = without background correction. BC = with background correction

for autoscaled data.

To overcome the poor precision of the calibration curve methods and the limitations of nonlinear problems, scholars have proposed the use of statistical methods for the quantitative analysis by LIBS. Artificial neural networks (ANNs) are computing systems inspired by the biological neural networks that constitute animal brains. Such systems learn (progressively improve performance) to do tasks by considering examples, generally without task-specific programming. The following outstanding advantages of artificial neural networks have attracted great attention in recent years: (1) it can fully approximate any complex nonlinear relationship; (2) all the quantitative or qualitative information is stored in the neurons in the network, so it has strong robustness and fault tolerance; (3) ANNS adopts the parallel distribution processing method, so that it can perform a large number of operations quickly; (4) ANNS can learn and adapt to unknown or uncertain system; and (5) it can handle both quantitative and qualitative information at the same time. An artificial neuron network (ANN) is a computational model based on the structure and functions of biological neural networks. Artificial neural networks usually contain input layer, hidden layer (competitive layer) and output layer, as shown in Figure 5.

Figure 5. Schematic of the three-layer artificial neural network [46].

For example, El Haddad et al. [46] used an artificial neuron network to analyze the heavy metals in soil and predict the concentration of element. They used average relative error of calibration REC (%) and the average relative error of prediction REP (%) to evaluate the predictive quality of the ANN models. REC and REP were preferred to RMSE because they provide percentage instead of absolute values. Before using the artificial neural network, it is necessary to optimize the parameters such as the number of neurons and training times.

$$\text{REC}(\%) = \frac{100}{N\_{\mathcal{C}}} \sum\_{i=1}^{N\_{\mathcal{C}}} \frac{|c\_i - \widehat{c}\_i|}{c\_i} \tag{12}$$

$$\text{REP}(\%) = \frac{100}{N\_p} \sum\_{i=1}^{N\_p} \frac{|c\_i - \widehat{c}\_i|}{c\_i} \tag{13}$$

3.3. Calibration-free laser-induced breakdown spectroscopy

represent the results of a linear best fit of the Al(I), Mn(II) and Mg(II) data [48].

Figure 6. The calibration curve of Cr by the SVR model with segmental spectra input.

LIBS offers a strong potential for analysis in situ and in real time, not requiring complex sample preparation. This allows it to be applied quickly and extensively to qualitative analysis, but quantitative analysis is very difficult. Even with a given experimental configuration, the laser-induced breakdown spectrum is not only dependent on the concentration of the analyte but also dependent on the composition of the matrix and their polymerization state. Matrix effects play an important role in quantitative analysis of LIBS. In order to overcome the matrix

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Figure 7. Boltzmann plot containing some data resulting from the analysis of an aluminum alloy. The three lines

where Nc is the number of samples in the calibration and Np is the number of samples in the prediction sets, respectively (Table 4).

#### 3.2.5. Support vector regression

The neural network structure design depends on the designer's experience and prior knowledge, while support vector machine (SVM) is based on statistical theory, which has a strict theoretical and mathematical basis. The neural network learning algorithm lacks quantitative analysis and complete theoretical support, and it also needs a lot of samples to learn. SVM is often used to pattern recognition, classification and regression analysis of small samples, nonlinear and high-dimensional data and can achieve very good results. SVM is based on the principle of structural risk minimization, which can ensure that the learning machine has a good generalization ability. SVM for regression prediction is called support vector regression (SVR). SVR also can guarantee the global optimality of the algorithm and avoid the local minimum problem that the neural network cannot solve. Therefore, when there are a small number of samples, it is better to use SVR instead of neural network. It is important to note that the selection of optimized significant penalty parameter C and the kernel parameter of RBF-δ is more sensitive for the SVR model.

For example, Gu et al. [47] used three segmental spectra of 393–397 nm, 422–423 nm and 425– 427 nm as the input variables of SVR model to predict the content of Cr in soil samples. They got better predictive results that <sup>R</sup><sup>2</sup> <sup>¼</sup> <sup>0</sup>:999 and the absolute relative error is 2.61% and the slope of the calibration curve is closer to 1, as shown in Figure 6.


Table 4. Average relative errors of calibration (REC) and prediction (REP).

Figure 6. The calibration curve of Cr by the SVR model with segmental spectra input.

#### 3.3. Calibration-free laser-induced breakdown spectroscopy

For example, El Haddad et al. [46] used an artificial neuron network to analyze the heavy metals in soil and predict the concentration of element. They used average relative error of calibration REC (%) and the average relative error of prediction REP (%) to evaluate the predictive quality of the ANN models. REC and REP were preferred to RMSE because they provide percentage instead of absolute values. Before using the artificial neural network, it is necessary to optimize the parameters such as the number of neurons and training times.

> Nc X Nc

Np X Np

where Nc is the number of samples in the calibration and Np is the number of samples in the

The neural network structure design depends on the designer's experience and prior knowledge, while support vector machine (SVM) is based on statistical theory, which has a strict theoretical and mathematical basis. The neural network learning algorithm lacks quantitative analysis and complete theoretical support, and it also needs a lot of samples to learn. SVM is often used to pattern recognition, classification and regression analysis of small samples, nonlinear and high-dimensional data and can achieve very good results. SVM is based on the principle of structural risk minimization, which can ensure that the learning machine has a good generalization ability. SVM for regression prediction is called support vector regression (SVR). SVR also can guarantee the global optimality of the algorithm and avoid the local minimum problem that the neural network cannot solve. Therefore, when there are a small number of samples, it is better to use SVR instead of neural network. It is important to note that the selection of optimized significant penalty parameter C and the kernel parameter of

For example, Gu et al. [47] used three segmental spectra of 393–397 nm, 422–423 nm and 425– 427 nm as the input variables of SVR model to predict the content of Cr in soil samples. They got better predictive results that <sup>R</sup><sup>2</sup> <sup>¼</sup> <sup>0</sup>:999 and the absolute relative error is 2.61% and the

Output Input element REC (%) REP (%) Al Al, Ca, Ba, Fe, Ti 18.7 � 0.8 19.3 � 2.1 Ca Ca, Ba, Fe, Ti 9.4 � 0.4 15.2 � 0.8 Fe Fe, Ba, Ca, Ti 15.5 � 0.6 16.8 � 0.9

i¼1

i¼1

<sup>∣</sup>ci �bci<sup>∣</sup> ci

<sup>∣</sup>ci �bci<sup>∣</sup> ci

(12)

(13)

RECð Þ¼ % <sup>100</sup>

96 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

REPð Þ¼ % <sup>100</sup>

prediction sets, respectively (Table 4).

RBF-δ is more sensitive for the SVR model.

slope of the calibration curve is closer to 1, as shown in Figure 6.

Table 4. Average relative errors of calibration (REC) and prediction (REP).

3.2.5. Support vector regression

LIBS offers a strong potential for analysis in situ and in real time, not requiring complex sample preparation. This allows it to be applied quickly and extensively to qualitative analysis, but quantitative analysis is very difficult. Even with a given experimental configuration, the laser-induced breakdown spectrum is not only dependent on the concentration of the analyte but also dependent on the composition of the matrix and their polymerization state. Matrix effects play an important role in quantitative analysis of LIBS. In order to overcome the matrix

Figure 7. Boltzmann plot containing some data resulting from the analysis of an aluminum alloy. The three lines represent the results of a linear best fit of the Al(I), Mn(II) and Mg(II) data [48].

effect, Ciucci et al. [48] proposed the calibration-free laser-induced breakdown spectroscopy (CF-LIBS) approach which takes the matrix into account as a part of the analytical problem. In local thermodynamic equilibrium (LTE), excited levels are populated according to the Boltzmann distribution and ionization states are populated according to the Saha-Boltzmann equilibrium equation. Each spectral line is represented as a point in a Boltzmann plane where the slope and intercept correspond to the plasma temperature and the concentration of the corresponding element, respectively (Figure 7).

Ciucci et al. [48] proposed CF-LIBS for the first time and used it for quantitative analysis of the composition of metallic alloys and quantitative determination of the composition of the atmosphere. CF-LIBS has been applied to many samples, such as aluminum alloys, steel and iron alloys, precious alloys for jewelry, copper alloys, archeological copper artifacts, glasses, pigments on roman frescoes and on parchments, soils and rocks, meteorites, coral skeletons and human hair. However, the accuracy of CF-LIBS is still not high.

### 4. The comparison of calibration methods

LIBS is an analytical technique that can inspire all the elements in the sample. Univariate analysis uses only partial spectral information and suffers from the strong effects of plasma instability. More importantly, strong matrix effects prevented to apply simple calibration curves. There is no doubt that the multivariate analysis is superior to univariate analysis. This has been proven by numerous researchers, for instance, the analysis of rocks [49], rare earth elements [38], glass [50], cerium oxide [51], alloy steel [52], liquid steel [53], soil [54, 55], soybean oil [56], PZT (Lead Zirconate Titanate) ceramics [57], Pb in navel orange [58], Marcellus Shale [59], tailing cores [60], geologically diverse samples [49], steel melt [61], slurry [62], iron ore [63] and pellets of plant materials [64].

PLS, is our best choice. But it should be pointed out that multivariate quantitative analyses

Method Advantage(s) Disadvantage(s) Other

Provides a complex model in which all coefficients are linear combinations of the original channels. Involves a complex optimization problem with no simple, closed-form representation.

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Arbitrarily chooses one covariate from a group of highly collinear covariates to use in the model and discards the rest.

Cannot be used for feature selection in situations when less data are available because it overwhelms the data with too

Higher-order polynomial kernels tend to overfit the training set and poorly predict the testing set in this application.

As above, polynomial kernels tend to overfit the training set and poorly predict the testing set in this application.

Tends to overfit the training data and is only as effective as the distance metric used

many model variables.

to compare samples.

Linear, uses all channels (not sparse)

99

Linear, sparse, eliminates noisy channels

Linear, sparse, eliminates noisy channels

May be linear or nonlinear; both use all channels

May be linear or nonlinear; either uses all channels

Nonlinear, uses all channels

CF-LIBS can overcome the influence of matrix effect, but the poor analysis accuracy has been the fatal shortcoming of CF-LIBS. This is mainly due to the fact that the laser-induced plasma is a very complex object and its realistic description is not attainable with simple mathematical models [88]. A number of researchers have made some modifications to the CF-LIBS algorithm, such as self-absorption [89, 90]. In recent years, several research groups [91–94] began using standard samples to improve the accuracy of the nonstandard analysis. Cavalcanti et al. [92] presented and used one-point-calibration CF-LIBS to analyze a set of copper-based samples. The results show that the new method achieves similar or even higher accuracy than the

This work was supported by the National Natural Science Foundation of China (Grant nos. 11075184 and 61505223) and the Knowledge Innovation Program of the Chinese Academy of

present a high risk of overfitting.

PLS Used when X has many collinear features and when p > > N. Provides a stable multivariate model that can account for all

LASSO Provides an interpretable model, selects subset of predictors with the strongest effects on the response variable. Can be used for feature selection when less data are

PCR Decorrelates the data and reduces its

SVR Performs well with a linear kernel. Can be

kNN Requires no model training other than

Table 5. Comparison of various regression methods.

dimensionality"

kernel.

data sets.

Performs well in the p > > N case. Provides an interpretable model that is more stable than the lasso. Useful for feature selection.

dimensionality, combating the "curse of

either linear or nonlinear depending on the

choosing the number of neighbors, reducing run time and making it scale well to large

oxides (PLS-2).

available.

Elastic net

calibration curve.

Acknowledgements

Sciences (Grant no. Y03RC21124).

Many multivariate analysis methods have been applied to the quantitative analysis of LIBS, especially chemometric. Generally, the most common chemometric technique applied to concentration measurement by LIBS is PLS. It has been applied to many fields of analysis, such as soil [55, 65, 66], steel [67–69], glass [50], rock [70], iron ore [63] and coal [71, 72]. The rest of the analysis methods are PCR [50, 73, 74], LASSO [75, 76], kNN [77], ANN [78–81], SVM [82, 83] and so on. PLS has been implemented either to calculate the concentrations of a single element (PLS-1) or to simultaneously calculate the concentrations of more than one element (PLS-2). In addition to PLS, other linear (MLR [84, 85], PCR [50, 73] and LASSO [75–77]) and nonlinear regression methods (ANN [86, 87]) have been applied to LIBS quantitative analysis. In order to discern the most effective models for interpreting chemical abundances from LIBS spectra of geological samples, Boucher et al. [77] had studied nine kinds of linear and nonlinear regression methods. The advantages and disadvantages of various methods are introduced, as shown in Table 5. The final results show that nonlinear methods tend to overfit the data and predict less accurately, while the linear methods proved to be more generalizable with better predictive performance. The performance of different models for different oxides is different. At present, multivariate analysis, especially


Table 5. Comparison of various regression methods.

effect, Ciucci et al. [48] proposed the calibration-free laser-induced breakdown spectroscopy (CF-LIBS) approach which takes the matrix into account as a part of the analytical problem. In local thermodynamic equilibrium (LTE), excited levels are populated according to the Boltzmann distribution and ionization states are populated according to the Saha-Boltzmann equilibrium equation. Each spectral line is represented as a point in a Boltzmann plane where the slope and intercept correspond to the plasma temperature and the concentration of the

Ciucci et al. [48] proposed CF-LIBS for the first time and used it for quantitative analysis of the composition of metallic alloys and quantitative determination of the composition of the atmosphere. CF-LIBS has been applied to many samples, such as aluminum alloys, steel and iron alloys, precious alloys for jewelry, copper alloys, archeological copper artifacts, glasses, pigments on roman frescoes and on parchments, soils and rocks, meteorites, coral skeletons and

LIBS is an analytical technique that can inspire all the elements in the sample. Univariate analysis uses only partial spectral information and suffers from the strong effects of plasma instability. More importantly, strong matrix effects prevented to apply simple calibration curves. There is no doubt that the multivariate analysis is superior to univariate analysis. This has been proven by numerous researchers, for instance, the analysis of rocks [49], rare earth elements [38], glass [50], cerium oxide [51], alloy steel [52], liquid steel [53], soil [54, 55], soybean oil [56], PZT (Lead Zirconate Titanate) ceramics [57], Pb in navel orange [58], Marcellus Shale [59], tailing cores [60], geologically diverse samples [49], steel melt [61], slurry [62], iron ore [63] and pellets of

Many multivariate analysis methods have been applied to the quantitative analysis of LIBS, especially chemometric. Generally, the most common chemometric technique applied to concentration measurement by LIBS is PLS. It has been applied to many fields of analysis, such as soil [55, 65, 66], steel [67–69], glass [50], rock [70], iron ore [63] and coal [71, 72]. The rest of the analysis methods are PCR [50, 73, 74], LASSO [75, 76], kNN [77], ANN [78–81], SVM [82, 83] and so on. PLS has been implemented either to calculate the concentrations of a single element (PLS-1) or to simultaneously calculate the concentrations of more than one element (PLS-2). In addition to PLS, other linear (MLR [84, 85], PCR [50, 73] and LASSO [75–77]) and nonlinear regression methods (ANN [86, 87]) have been applied to LIBS quantitative analysis. In order to discern the most effective models for interpreting chemical abundances from LIBS spectra of geological samples, Boucher et al. [77] had studied nine kinds of linear and nonlinear regression methods. The advantages and disadvantages of various methods are introduced, as shown in Table 5. The final results show that nonlinear methods tend to overfit the data and predict less accurately, while the linear methods proved to be more generalizable with better predictive performance. The performance of different models for different oxides is different. At present, multivariate analysis, especially

corresponding element, respectively (Figure 7).

human hair. However, the accuracy of CF-LIBS is still not high.

98 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

4. The comparison of calibration methods

plant materials [64].

PLS, is our best choice. But it should be pointed out that multivariate quantitative analyses present a high risk of overfitting.

CF-LIBS can overcome the influence of matrix effect, but the poor analysis accuracy has been the fatal shortcoming of CF-LIBS. This is mainly due to the fact that the laser-induced plasma is a very complex object and its realistic description is not attainable with simple mathematical models [88]. A number of researchers have made some modifications to the CF-LIBS algorithm, such as self-absorption [89, 90]. In recent years, several research groups [91–94] began using standard samples to improve the accuracy of the nonstandard analysis. Cavalcanti et al. [92] presented and used one-point-calibration CF-LIBS to analyze a set of copper-based samples. The results show that the new method achieves similar or even higher accuracy than the calibration curve.

### Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant nos. 11075184 and 61505223) and the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant no. Y03RC21124).

### Author details

Hongbo Fu1,2, Junwei Jia1,3, Huadong Wang1,3, Zhibo Ni1 and Fengzhong Dong1,2,3\*

\*Address all correspondence to: fzdong@aiofm.ac.cn

1 Anhui Provincial Key Laboratory of Photonic Devices and Materials, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, China

2 Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, China

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065201

3 University of Science and Technology of China, Hefei, China

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Author details

References

Hongbo Fu1,2, Junwei Jia1,3, Huadong Wang1,3, Zhibo Ni1 and Fengzhong Dong1,2,3\*

Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, China

1 Anhui Provincial Key Laboratory of Photonic Devices and Materials, Anhui Institute of

2 Key Laboratory of Environmental Optics and Technology, Anhui Institute of Optics and Fine

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\*Address all correspondence to: fzdong@aiofm.ac.cn

Mechanics, Chinese Academy of Sciences, Hefei, China

3 University of Science and Technology of China, Hefei, China

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**Chapter 6**

**Provisional chapter**

**Linearity of Calibration Curves for Analytical Methods:**

Calibration curve is a regression model used to predict the unknown concentrations of analytes of interest based on the response of the instrument to the known standards. Some statistical analyses are required to choose the best model fitting to the experimental data and also evaluate the linearity and homoscedasticity of the calibration curve. Using an internal standard corrects for the loss of analyte during sample preparation and analysis provided that it is selected appropriately. After the best regression model is selected, the analytical method needs to be validated using quality control (QC) samples prepared and stored in the same temperature as intended for the study samples. Most of the international guidelines require that the parameters, including linearity, specificity, selectivity, accuracy, precision, lower limit of quantification (LLOQ), matrix effect and stability, be assessed during validation. Despite the highly regulated area, some challenges still exist regarding the validation of some analytical methods including methods when no analyte-free matrix is available.

**Keywords:** analytical method, calibration, linearity, regression analysis, validation

Calibration curve in bioanalytical method is a linear relationship between concentration (independent variable) and response (dependent variable) using a least squares method. This relationship is built to predict the unknown concentrations of the analyte in a complicated matrix. The unknown samples can be from a wide range of sources: food and agricultural, pharmaceutical formulations, forensic and the clinical pharmacology studies. This chapter is more focused on the bioanalytical methods in which an analyte is measured in blood, plasma, urine or other biological matrices. However, the main concepts are applicable to the other analytical approaches.

**Linearity of Calibration Curves for Analytical Methods:** 

DOI: 10.5772/intechopen.72932

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

**A Review of Criteria for Assessment of Method**

**A Review of Criteria for Assessment of Method** 

Seyed Mojtaba Moosavi and Sussan Ghassabian

Seyed Mojtaba Moosavi and Sussan Ghassabian

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72932

**Reliability**

**Abstract**

**1. Introduction**

**Reliability**

**Provisional chapter**

### **Linearity of Calibration Curves for Analytical Methods: A Review of Criteria for Assessment of Method Reliability A Review of Criteria for Assessment of Method Reliability**

**Linearity of Calibration Curves for Analytical Methods:** 

DOI: 10.5772/intechopen.72932

Seyed Mojtaba Moosavi and Sussan Ghassabian Seyed Mojtaba Moosavi and Sussan Ghassabian Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72932

#### **Abstract**

Calibration curve is a regression model used to predict the unknown concentrations of analytes of interest based on the response of the instrument to the known standards. Some statistical analyses are required to choose the best model fitting to the experimental data and also evaluate the linearity and homoscedasticity of the calibration curve. Using an internal standard corrects for the loss of analyte during sample preparation and analysis provided that it is selected appropriately. After the best regression model is selected, the analytical method needs to be validated using quality control (QC) samples prepared and stored in the same temperature as intended for the study samples. Most of the international guidelines require that the parameters, including linearity, specificity, selectivity, accuracy, precision, lower limit of quantification (LLOQ), matrix effect and stability, be assessed during validation. Despite the highly regulated area, some challenges still exist regarding the validation of some analytical methods including methods when no analyte-free matrix is available.

**Keywords:** analytical method, calibration, linearity, regression analysis, validation

### **1. Introduction**

Calibration curve in bioanalytical method is a linear relationship between concentration (independent variable) and response (dependent variable) using a least squares method. This relationship is built to predict the unknown concentrations of the analyte in a complicated matrix. The unknown samples can be from a wide range of sources: food and agricultural, pharmaceutical formulations, forensic and the clinical pharmacology studies. This chapter is more focused on the bioanalytical methods in which an analyte is measured in blood, plasma, urine or other biological matrices. However, the main concepts are applicable to the other analytical approaches.

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

The quality of a bioanalytical method is highly dependent on the linearity of the calibration curve [1]. A linear calibration curve is a positive indication of assay performance in a validated analytical range. Other characteristics of the calibration curve, including regression model, slope of the line, weighting and correlation coefficient, need to be carefully evaluated. In the following sections, each of those parameters is explained, and few practical examples have been used to further discuss the concepts.

After the calibration model is chosen, it is required to demonstrate that all future measurements will be close to the true values of the content of the analyte in the sample. This will be achieved during validation of the analytical method. There are international guidelines for the validation of the analytical methods, which need to be followed closely in order to have more consistent data throughout different laboratories and increase the chance of their acceptability by the regulatory authorities.

### **2. Aims**

The aim of this chapter is to discuss different aspects of linearity and relevant assumption as a practical guide to develop a robust analytical method in order to predict true concentrations of the analytes in samples.

this assumption, the estimated parameters using the model cannot be used, and the model needs to be modified, e.g. using a non-linear model which requires more standard concentrations compared with having a linear relationship between concentrations and instrument response. A linear regression model between calculated standard points and the nominal ones used to evaluate the quality of the fit should have a unit slope and a zero intercept. In case of linear calibration method, the slope should be statistically different from 0, the intercept should not be statistically different from 0 and the regression coefficient should not be statistically different from 1. In case of having a significant non-zero intercept, the accuracy of

**Figure 1.** Linear regression model in which the differences between observed and predicted values (residuals) have been

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A standard 0 must be included in the calibration curve because the instrumental signal is subjected to the same kind of error for all points. The signal for the standard zero should not be subtracted from the response values for other standards before calculating the equation of the regression line because it can cause imprecision during the determination of the concentration

If one of the standard points deviates greatly from the calibration curve (outlier), it can be removed from the equation provided that six non-zero standards remain after removing the outlier and inclusion of that point can cause the loss of sensitivity or it clearly biases the quality control (QC) results, and the back-calculated standard concentrations deviate from its nominal value. The poor chromatography can also be considered as a justification for remov-

In order to verify the accuracy and precision of the analytical method during the period of sample analysis, quality control (QC) samples are prepared and stored frozen at the same temperature as is intended for the storage of the study samples. The calibration curve standards are prepared by spiking the reference standard solutions to the matrix (e.g. plasma or

urine) either freshly or by freezing and storage with QC samples [4].

the method must be demonstrated [2].

shown.

values for unknown samples [3].

ing the outlier standard [4].

### **3. Calibration curve: definitions and characteristics**

#### **3.1. Regression analysis**

Regression analysis is a deterministic model, which allows predicting of the values for a dependent variable (Y) when an independent variable (X) is known. The model determines the kind of relationship between X and Y. The experimental values rarely fit the mathematical model, and there are differences between the observed and the predicted values provided by the model, which are called residuals (**Figure 1**). The sum of squared residuals needs to be minimised to have the best estimate of the model parameters, and it can be done using the "method of least squares." The simplest regression model is the linear one in which the relationship between X (known without error) and Y (known with error) is a straight line, Y = a + bX, where a is the y-intercept and b is the slope of the line [1].

The relationship between an instrument response and the known concentrations of an analyte (standards), which is used as the calibration curve can be explained by a similar regression model. To have a robust calibration line (or curve), a series of replicates of each standard (at least three replicates of 6–8 expected range of concentration values) are recommended. The assumption for this model is that the measurement error is the same and normally distributed for each sample. If this assumption is not applicable, an extended or weighted least squares analysis will be required. The assumption regarding the measurement error must be verified to validate the results found. The distribution properties of the residuals are expected to be normal and centred on zero (Kolmogorov–Smirnov test). If the results found cannot support

Linearity of Calibration Curves for Analytical Methods: A Review of Criteria for Assessment… http://dx.doi.org/10.5772/intechopen.72932 111

The quality of a bioanalytical method is highly dependent on the linearity of the calibration curve [1]. A linear calibration curve is a positive indication of assay performance in a validated analytical range. Other characteristics of the calibration curve, including regression model, slope of the line, weighting and correlation coefficient, need to be carefully evaluated. In the following sections, each of those parameters is explained, and few practical examples

After the calibration model is chosen, it is required to demonstrate that all future measurements will be close to the true values of the content of the analyte in the sample. This will be achieved during validation of the analytical method. There are international guidelines for the validation of the analytical methods, which need to be followed closely in order to have more consistent data throughout different laboratories and increase the chance of their

The aim of this chapter is to discuss different aspects of linearity and relevant assumption as a practical guide to develop a robust analytical method in order to predict true concentrations

Regression analysis is a deterministic model, which allows predicting of the values for a dependent variable (Y) when an independent variable (X) is known. The model determines the kind of relationship between X and Y. The experimental values rarely fit the mathematical model, and there are differences between the observed and the predicted values provided by the model, which are called residuals (**Figure 1**). The sum of squared residuals needs to be minimised to have the best estimate of the model parameters, and it can be done using the "method of least squares." The simplest regression model is the linear one in which the relationship between X (known without error) and Y (known with error) is a straight line,

The relationship between an instrument response and the known concentrations of an analyte (standards), which is used as the calibration curve can be explained by a similar regression model. To have a robust calibration line (or curve), a series of replicates of each standard (at least three replicates of 6–8 expected range of concentration values) are recommended. The assumption for this model is that the measurement error is the same and normally distributed for each sample. If this assumption is not applicable, an extended or weighted least squares analysis will be required. The assumption regarding the measurement error must be verified to validate the results found. The distribution properties of the residuals are expected to be normal and centred on zero (Kolmogorov–Smirnov test). If the results found cannot support

have been used to further discuss the concepts.

110 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

acceptability by the regulatory authorities.

**3. Calibration curve: definitions and characteristics**

Y = a + bX, where a is the y-intercept and b is the slope of the line [1].

**2. Aims**

of the analytes in samples.

**3.1. Regression analysis**

**Figure 1.** Linear regression model in which the differences between observed and predicted values (residuals) have been shown.

this assumption, the estimated parameters using the model cannot be used, and the model needs to be modified, e.g. using a non-linear model which requires more standard concentrations compared with having a linear relationship between concentrations and instrument response. A linear regression model between calculated standard points and the nominal ones used to evaluate the quality of the fit should have a unit slope and a zero intercept. In case of linear calibration method, the slope should be statistically different from 0, the intercept should not be statistically different from 0 and the regression coefficient should not be statistically different from 1. In case of having a significant non-zero intercept, the accuracy of the method must be demonstrated [2].

A standard 0 must be included in the calibration curve because the instrumental signal is subjected to the same kind of error for all points. The signal for the standard zero should not be subtracted from the response values for other standards before calculating the equation of the regression line because it can cause imprecision during the determination of the concentration values for unknown samples [3].

If one of the standard points deviates greatly from the calibration curve (outlier), it can be removed from the equation provided that six non-zero standards remain after removing the outlier and inclusion of that point can cause the loss of sensitivity or it clearly biases the quality control (QC) results, and the back-calculated standard concentrations deviate from its nominal value. The poor chromatography can also be considered as a justification for removing the outlier standard [4].

In order to verify the accuracy and precision of the analytical method during the period of sample analysis, quality control (QC) samples are prepared and stored frozen at the same temperature as is intended for the storage of the study samples. The calibration curve standards are prepared by spiking the reference standard solutions to the matrix (e.g. plasma or urine) either freshly or by freezing and storage with QC samples [4].

#### **3.2. Weighting in linear regression**

When the range in x-values is large, e.g. more than one order of magnitude, the variance of each data point might be quite different. However, the simple least squares method considers that all the y-values have equal variances. Larger deviations at larger concentrations tend to influence the regression line more than smaller deviations associated with smaller concentrations (heteroscedasticity) leading to the inaccuracy in the lower end of the calibration range (see the practical example 1). A simple and effective way to counteract this situation is to use weighted least squares linear regression (WLSLR) [1]. WLSLR is able to reduce the lower limit of quantification (LLOQ) and enables a broader linear calibration range with higher accuracy and precision especially for bioanalytical methods.

linearity. The residuals are expected to be normally distributed for a linear model, so a plot of them on a normal probability graph may be useful. Any curvature suggests a lack of fit (LOF) due to a non-linear effect. A segmented pattern indicates heteroscedasticity in data, so

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A clear curved relationship between concentration and response may also have an r value close to one. Two statistical tests, including the lack-of-fit and Mandel's fitting tests, are suitable for the validation of the linear calibration model (practical example 2 [8]). A straight-line model with r close to 1, but with a lack of fit, can produce significantly less accurate results than its curvilinear alternative. A straight-line calibration curve should always be preferred over curvilinear or non-linear calibration models if equivalent results can be obtained and is easier to

Slope of the calibration curve can be used to estimate the detection limit of the assay [9]. Three times the standard deviation value of the response corresponding to the blank according to Eq. (1), obtained for seven determinations, divided by the slope of the calibration line (note that we are calculating the standard deviation of the concentration corresponding to the blank equation, and again the imprecision of the value of the slope is not taken into account) [3]:

LOD = 3.3 × (SY/a). (1)

SY denotes the SD of responses, Y, for blanks or around expected LOD (limit of detection) and "a" for the slope of a linear calibration line. If the calibration curve is linear, "a" is constant, and the estimation of LOD is easy to calculate. However, when the calibration curve is not linear, e.g. in enzyme-linked immunosorbent assay (ELISA), the definition needs to be modified. In the case of ELISA, when there is a semilogarithmic calibration curve over a wide range of concentrations, the detection limit is calculated using a differential coefficient which is

It is assumed that a validated analytical method should have constant slope over the period of sample analysis. Variation in the slope might be due to the laboratory errors during sample preparations, change in the internal standard (IS) of working solution concentrations between preparations, instrument variations such as changes in mass spectrum (MS) calibrations, MS signal cross contributions between analyte and IS and matrix effect (ME) [10]. Although there is no criteria in the international guidelines to report the slope, monitoring the slope can pro-

ME can also affect the slope of the calibration curve. Coeluting of the matrix components escaped during extraction may reduce the signal intensity and affect the accuracy and precision of the MS-based assays. The phenomenon is called ion suppression, and it has been shown that the electrospray ionisation responses of organic bases decrease with an increase in concentrations of other organic bases present in the matrix. The ME is especially dependent on the degree of sample clean-up and chromatographic separation of the analyte. When developing high-throughput assays using a short run time, a careful assessment of the ME

vide valuable information regarding the quality of the sample analysis.

weighted regression model should be used to find the straight line for calibration [7].

**3.4. Slope of the curve and application in matrix effect and detection limit**

implement [8].

obtained using a computer programme [9].

and ion suppression is necessary [11].

Two most commonly used regression models, particularly for liquid chromatography tandem mass spectrometry (LC-MS/MS) calibration curves, are linear and quadratic regression models using non-weighted or weighted least squares regression algorithm. To select the type of calibration curve and weighting, "Test and Fit" strategy is widely used due to its simplicity and lack of statistical analysis and causes inaccuracy in the regression model based on the limited set of test results. The Food and Drug Administration (FDA) guideline suggests that "the simplest model that adequately describes the concentration-response relationship should be used and selection of weighting and use of a complex regression equation should be justified" [5]. However, other experts suggested that a weighting should be used if homoscedasticity was not met for the analytical data. By neglecting the weighting for analysing data with heteroscedastic distribution, a precision loss as big as one order of magnitude in the low concentration region of the calibration curve could happen [4].

For most immunoassay methods, the response is a non-linear function of the analyte concentration, and the standard deviations (SD) of the calculated concentrations are not a constant function of the mean response; therefore, a weighted, non-linear least squares method is generally recommended for fitting dose-response data. The nonevidence-based weights (e.g. 1/Y or 1/X) are not recommended without assessment of the response-error relationship. A reference model for immunoassay data employs the four-parameter logistic (4PL) equation to fit the concentration-response relationship and a power-of-the-mean (POM) equation to fit the response-error relationship [6].

#### **3.3. Correlation coefficient**

Linearity of the calibration curve is usually expressed through the coefficient of correlation, r, or coefficient of determination, r<sup>2</sup> . A correlation coefficient close to unity (r = 1) is considered by some authors' sufficient evidence to conclude that the calibration curve is linear. However, r is not an appropriate measure for the linearity. The FDA guidance for validation of analytical procedures [5] recommends that the r should be submitted when evaluating a linear relationship and that the linearity should be evaluated by appropriate statistical methods, e.g. analysis of variance (ANOVA). This guidance does not suggest that the numerical value of r can be used as a degree of deviation from linearity.

Other mathematical measures, including slope standard relative deviation or goodness of fit, can be used to evaluate the linearity [3]. Using residual plots is a simple way to check the linearity. The residuals are expected to be normally distributed for a linear model, so a plot of them on a normal probability graph may be useful. Any curvature suggests a lack of fit (LOF) due to a non-linear effect. A segmented pattern indicates heteroscedasticity in data, so weighted regression model should be used to find the straight line for calibration [7].

A clear curved relationship between concentration and response may also have an r value close to one. Two statistical tests, including the lack-of-fit and Mandel's fitting tests, are suitable for the validation of the linear calibration model (practical example 2 [8]). A straight-line model with r close to 1, but with a lack of fit, can produce significantly less accurate results than its curvilinear alternative. A straight-line calibration curve should always be preferred over curvilinear or non-linear calibration models if equivalent results can be obtained and is easier to implement [8].

#### **3.4. Slope of the curve and application in matrix effect and detection limit**

**3.2. Weighting in linear regression**

response-error relationship [6].

or coefficient of determination, r<sup>2</sup>

can be used as a degree of deviation from linearity.

**3.3. Correlation coefficient**

and precision especially for bioanalytical methods.

112 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

When the range in x-values is large, e.g. more than one order of magnitude, the variance of each data point might be quite different. However, the simple least squares method considers that all the y-values have equal variances. Larger deviations at larger concentrations tend to influence the regression line more than smaller deviations associated with smaller concentrations (heteroscedasticity) leading to the inaccuracy in the lower end of the calibration range (see the practical example 1). A simple and effective way to counteract this situation is to use weighted least squares linear regression (WLSLR) [1]. WLSLR is able to reduce the lower limit of quantification (LLOQ) and enables a broader linear calibration range with higher accuracy

Two most commonly used regression models, particularly for liquid chromatography tandem mass spectrometry (LC-MS/MS) calibration curves, are linear and quadratic regression models using non-weighted or weighted least squares regression algorithm. To select the type of calibration curve and weighting, "Test and Fit" strategy is widely used due to its simplicity and lack of statistical analysis and causes inaccuracy in the regression model based on the limited set of test results. The Food and Drug Administration (FDA) guideline suggests that "the simplest model that adequately describes the concentration-response relationship should be used and selection of weighting and use of a complex regression equation should be justified" [5]. However, other experts suggested that a weighting should be used if homoscedasticity was not met for the analytical data. By neglecting the weighting for analysing data with heteroscedastic distribution, a precision loss as big as one order of magnitude in the low concentration region of the calibration curve could happen [4].

For most immunoassay methods, the response is a non-linear function of the analyte concentration, and the standard deviations (SD) of the calculated concentrations are not a constant function of the mean response; therefore, a weighted, non-linear least squares method is generally recommended for fitting dose-response data. The nonevidence-based weights (e.g. 1/Y or 1/X) are not recommended without assessment of the response-error relationship. A reference model for immunoassay data employs the four-parameter logistic (4PL) equation to fit the concentration-response relationship and a power-of-the-mean (POM) equation to fit the

Linearity of the calibration curve is usually expressed through the coefficient of correlation, r,

by some authors' sufficient evidence to conclude that the calibration curve is linear. However, r is not an appropriate measure for the linearity. The FDA guidance for validation of analytical procedures [5] recommends that the r should be submitted when evaluating a linear relationship and that the linearity should be evaluated by appropriate statistical methods, e.g. analysis of variance (ANOVA). This guidance does not suggest that the numerical value of r

Other mathematical measures, including slope standard relative deviation or goodness of fit, can be used to evaluate the linearity [3]. Using residual plots is a simple way to check the

. A correlation coefficient close to unity (r = 1) is considered

Slope of the calibration curve can be used to estimate the detection limit of the assay [9]. Three times the standard deviation value of the response corresponding to the blank according to Eq. (1), obtained for seven determinations, divided by the slope of the calibration line (note that we are calculating the standard deviation of the concentration corresponding to the blank equation, and again the imprecision of the value of the slope is not taken into account) [3]:

$$\text{LOD} = \text{3.3} \times \text{(S}\_{\text{y}}/\text{a)}.\tag{1}$$

SY denotes the SD of responses, Y, for blanks or around expected LOD (limit of detection) and "a" for the slope of a linear calibration line. If the calibration curve is linear, "a" is constant, and the estimation of LOD is easy to calculate. However, when the calibration curve is not linear, e.g. in enzyme-linked immunosorbent assay (ELISA), the definition needs to be modified. In the case of ELISA, when there is a semilogarithmic calibration curve over a wide range of concentrations, the detection limit is calculated using a differential coefficient which is obtained using a computer programme [9].

It is assumed that a validated analytical method should have constant slope over the period of sample analysis. Variation in the slope might be due to the laboratory errors during sample preparations, change in the internal standard (IS) of working solution concentrations between preparations, instrument variations such as changes in mass spectrum (MS) calibrations, MS signal cross contributions between analyte and IS and matrix effect (ME) [10]. Although there is no criteria in the international guidelines to report the slope, monitoring the slope can provide valuable information regarding the quality of the sample analysis.

ME can also affect the slope of the calibration curve. Coeluting of the matrix components escaped during extraction may reduce the signal intensity and affect the accuracy and precision of the MS-based assays. The phenomenon is called ion suppression, and it has been shown that the electrospray ionisation responses of organic bases decrease with an increase in concentrations of other organic bases present in the matrix. The ME is especially dependent on the degree of sample clean-up and chromatographic separation of the analyte. When developing high-throughput assays using a short run time, a careful assessment of the ME and ion suppression is necessary [11].

#### **3.5. Internal standard (IS)**

IS is a chemical substance that is added in equal amounts to all samples, and it changes the way that calibration curve is prepared. Instead of analyte response, the ratio of the analyte to the IS signal versus the analyte concentration is plotted. The benefits of adding the IS are to correct or compensate analyte losses during sample preparation including transfer loss, adsorption loss, evaporation loss and variation in injection volume and in MS response due to ion suppression or enhancement (ME).

the analyte is used as its own IS. In this method, after the injection of the sample containing the analyte of interest, a standard solution is also injected, which result in two peaks for the analyte, one from the sample and the other from the standard solution with constant concentration (an echo peak). By using their response ratio for quantitation, the ME might be compensated for because the two peaks are affected by the coeluted matrix components

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There is no general rule for choosing the IS concentrations. However, the accuracy and precision of the method may be affected if an inappropriate IS concentration is used. As shown in practical example 3, reducing the concentration of IS can lead to the increasingly non-linear calibration curve due to chemical impurity in the reference standard or because of isotope interferences.

When choosing the IS and its concentration, the magnitude of the cross signal contribution between the analyte and IS should be considered. The IS interference signal due to its impurity or isotope interferences should be equal or less than 20% of the LLOQ response and 5% of the IS response for IS-to-analyte and analyte-to-IS contributions, respectively [14]. The minimum IS concentration required (CIS-Min) and the maximum IS concentration allowed

CIS-Min = m × ULOQ/5. (2)

CIS-Max = 20 × LLOQ/n. (3)

where m and n represent the % of cross signal contributions from analyte to IS and IS to analyte, respectively. As an example, if the cross signal contribution from analyte to IS is 2.5%, the minimum IS concentration calculated accordingly is 50% of the ULOQ. A high IS concentration might be useful in reducing a systemic error in the analysis of unknown samples. If the IS

In some cases, the analyte signal might be suppressed by the coeluting IS signal, and therefore the IS concentration must be kept low to maintain a low detection limit. However, it might be

IS should be added as early as possible to compensate for the variabilities during sample preparation and analysis; however, if the IS structure is not very close to the analyte, it can be used to reduce the variabilities due to the ion suppression or enhancement only and not

For making calibrators and QCs, an analyte-free matrix is required. The presence of unknown amount of the analyte in the matrix makes the quantification difficult, and different approaches have been used to overcome the problem including using stripped matrices (filtration on activated charcoal-dextran or dialysis), substitute matrices (e.g. neat solutions, artificial matrices, human serum albumin or 0.9% sodium chloride) or diluted matrices. If the actual matrix is used, various methods are followed including, background subtraction, or the standard addi-

coelutes more closely to the analyte, it will be more effective in minimising ME.

required to increase the IS concentration when the analyte suppresses the IS signal.

similarly [13].

sample extraction [13].

tion method [3, 15].

(CIS-Max) can be calculated using Eqs. (2 and 3):

**3.6. Linearity when no analyte-free matrix exists**

The IS must have similar physicochemical properties and show similar behaviour to the analyte when extracted or run through the analytical column or detection in the analytical system. An external standard also behaves similarly with the analyte, but it is run alone at different concentrations, so a standard curve can be generated. External standards do not correct for losses that may occur during preparation of the sample. Using IS is usually more effective due to lower measurement uncertainty and therefore is more common in analytical chemistry [12].

Two common types of ISs are used: structural analogues and stable isotope-labelled (SIL) ISs or isotope dilution mass spectrometry (IDMS). SIL ISs are more effective. To reduce the interferences between IS and analyte, SIL IS molecular weight is preferred to be ideally 4 or 5 Da higher than that of the analyte. Labelled SIL ISs with 13C and/or 15N are usually superior to those labelled with deuterium (2H, D or d) in terms of performance; however, the synthesis of deuterated ISs is easier and cheaper. The location of stable isotope atoms should be in a way that deuterium-hydrogen exchange is minimised during sample preparation.

A structural analogue of the analyte can be used if SIL ISs are not available or expensive. In this case, the IS should preferably have key structure and functionalities (e.g. –COOH, –SO<sup>2</sup> , NH2 , halogen and heteroatoms) of the analyte with difference only being C–H moieties (length and/or position). Modifications in key chemical structure and/or functionalities cause significant differences in ionisation pattern and even extraction recovery. The IS should not be similar or converted to any in vivo biotransformed products of the analyte (e.g. hydroxylated or N-dealkylation metabolites). An appropriate structural analogue IS can be selected from the same therapeutic class as the analyte or by key chemical structure and preferably a compound that is not very commonly prescribed because those compounds may be present in pooled blank plasmas used for preparation of the calibrators and QCs. Other parameters for choosing a right structure analogue IS are physicochemical properties, such as log D (hydrophobicity), pKa and water solubility. For selection of the IS, it may be difficult to have a compound to track the analyte of interest in all the three distinctive stages of LC-MS bioanalysis, sample preparation (extraction), chromatographic separation and mass spectrometric detection. The IS should be chosen depending on which step is more critical. For example, when the extracts of samples contain coeluting matrix components that cause ion suppression, then tracking the analyte during MS detection to avoid or minimise ME becomes more important. The choice of IS is also depending on the extraction method. Tracking an analyte during a simple protein precipitation procedure would be less stringent than that for liquid-liquid extraction (LLE) or solid-phase extraction (SPE) method [13].

It is possible to develop an assay without using any IS, for example, in early drug discovery stage or when clean extracts are used. In this case, ECHO peak technique can be used where the analyte is used as its own IS. In this method, after the injection of the sample containing the analyte of interest, a standard solution is also injected, which result in two peaks for the analyte, one from the sample and the other from the standard solution with constant concentration (an echo peak). By using their response ratio for quantitation, the ME might be compensated for because the two peaks are affected by the coeluted matrix components similarly [13].

There is no general rule for choosing the IS concentrations. However, the accuracy and precision of the method may be affected if an inappropriate IS concentration is used. As shown in practical example 3, reducing the concentration of IS can lead to the increasingly non-linear calibration curve due to chemical impurity in the reference standard or because of isotope interferences.

When choosing the IS and its concentration, the magnitude of the cross signal contribution between the analyte and IS should be considered. The IS interference signal due to its impurity or isotope interferences should be equal or less than 20% of the LLOQ response and 5% of the IS response for IS-to-analyte and analyte-to-IS contributions, respectively [14]. The minimum IS concentration required (CIS-Min) and the maximum IS concentration allowed (CIS-Max) can be calculated using Eqs. (2 and 3):

$$\text{CIS-Min} = \text{m} \times \text{ULOQ/5.} \tag{2}$$

$$\text{CIS-Max} = \text{20} \times \text{LLOQ/n.} \tag{3}$$

where m and n represent the % of cross signal contributions from analyte to IS and IS to analyte, respectively. As an example, if the cross signal contribution from analyte to IS is 2.5%, the minimum IS concentration calculated accordingly is 50% of the ULOQ. A high IS concentration might be useful in reducing a systemic error in the analysis of unknown samples. If the IS coelutes more closely to the analyte, it will be more effective in minimising ME.

In some cases, the analyte signal might be suppressed by the coeluting IS signal, and therefore the IS concentration must be kept low to maintain a low detection limit. However, it might be required to increase the IS concentration when the analyte suppresses the IS signal.

IS should be added as early as possible to compensate for the variabilities during sample preparation and analysis; however, if the IS structure is not very close to the analyte, it can be used to reduce the variabilities due to the ion suppression or enhancement only and not sample extraction [13].

#### **3.6. Linearity when no analyte-free matrix exists**

**3.5. Internal standard (IS)**

–SO<sup>2</sup>

, NH2

ion suppression or enhancement (ME).

114 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

IS is a chemical substance that is added in equal amounts to all samples, and it changes the way that calibration curve is prepared. Instead of analyte response, the ratio of the analyte to the IS signal versus the analyte concentration is plotted. The benefits of adding the IS are to correct or compensate analyte losses during sample preparation including transfer loss, adsorption loss, evaporation loss and variation in injection volume and in MS response due to

The IS must have similar physicochemical properties and show similar behaviour to the analyte when extracted or run through the analytical column or detection in the analytical system. An external standard also behaves similarly with the analyte, but it is run alone at different concentrations, so a standard curve can be generated. External standards do not correct for losses that may occur during preparation of the sample. Using IS is usually more effective due to lower measurement uncertainty and therefore is more common in analytical chemistry [12]. Two common types of ISs are used: structural analogues and stable isotope-labelled (SIL) ISs or isotope dilution mass spectrometry (IDMS). SIL ISs are more effective. To reduce the interferences between IS and analyte, SIL IS molecular weight is preferred to be ideally 4 or 5 Da higher than that of the analyte. Labelled SIL ISs with 13C and/or 15N are usually superior to those labelled with deuterium (2H, D or d) in terms of performance; however, the synthesis of deuterated ISs is easier and cheaper. The location of stable isotope atoms should be in a way

A structural analogue of the analyte can be used if SIL ISs are not available or expensive. In this case, the IS should preferably have key structure and functionalities (e.g. –COOH,

(length and/or position). Modifications in key chemical structure and/or functionalities cause significant differences in ionisation pattern and even extraction recovery. The IS should not be similar or converted to any in vivo biotransformed products of the analyte (e.g. hydroxylated or N-dealkylation metabolites). An appropriate structural analogue IS can be selected from the same therapeutic class as the analyte or by key chemical structure and preferably a compound that is not very commonly prescribed because those compounds may be present in pooled blank plasmas used for preparation of the calibrators and QCs. Other parameters for choosing a right structure analogue IS are physicochemical properties, such as log D (hydrophobicity), pKa and water solubility. For selection of the IS, it may be difficult to have a compound to track the analyte of interest in all the three distinctive stages of LC-MS bioanalysis, sample preparation (extraction), chromatographic separation and mass spectrometric detection. The IS should be chosen depending on which step is more critical. For example, when the extracts of samples contain coeluting matrix components that cause ion suppression, then tracking the analyte during MS detection to avoid or minimise ME becomes more important. The choice of IS is also depending on the extraction method. Tracking an analyte during a simple protein precipitation procedure would be less stringent than that for liquid-liquid

It is possible to develop an assay without using any IS, for example, in early drug discovery stage or when clean extracts are used. In this case, ECHO peak technique can be used where

, halogen and heteroatoms) of the analyte with difference only being C–H moieties

that deuterium-hydrogen exchange is minimised during sample preparation.

extraction (LLE) or solid-phase extraction (SPE) method [13].

For making calibrators and QCs, an analyte-free matrix is required. The presence of unknown amount of the analyte in the matrix makes the quantification difficult, and different approaches have been used to overcome the problem including using stripped matrices (filtration on activated charcoal-dextran or dialysis), substitute matrices (e.g. neat solutions, artificial matrices, human serum albumin or 0.9% sodium chloride) or diluted matrices. If the actual matrix is used, various methods are followed including, background subtraction, or the standard addition method [3, 15].

One of the approaches for validation of the assay is to determine the accuracy throughout the validation step, using the biological matrix containing the endogenous compound to prepare the standard curves and all pools of six or more assays of each QC sample [3]. The amount of the analyte in the matrix (Cbasal) can be computed using a calibration curve in the substitute matrix, and the concentration of the analyte in the QC can be calculated by subtracting the Cbasal from the calculated one as follows, Creal = Cfound – Cbasal, in which Cfound is the concentration of the analyte in the QCs calculated against a calibration curve in the substitute matrix and Creal is the corrected concentration [3]. When using this approach, the LLOQ of the method cannot be smaller than the endogenous concentrations of the analyte in the matrix, and therefore a lot of blank matrices need to be screened to find the suitable one.

spiking the analyte. Some analytes, e.g. homocysteine, cannot be removed by the charcoal and also the composition of the matrix may change or cause batch-to-batch variation after adding the charcoal leading to the altered analyte recovery and ME. Some light-sensitive analytes can be decomposed by heat or exposing to the light and therefore removed from the matrix.

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In the standard addition method, every study sample is divided into aliquots of equal volumes, and the aliquots are spiked with known and varying amounts of the analyte to build the calibration curve. The sample concentration is then calculated as the negative x-intercept of the calibration line. This method is very accurate because it allows direct quantitation of endogenous analytes without manual subtraction of background peak areas. The disadvantage of the method is that it requires a large amount of sample and is very time-consuming and labour intensive. Examples of using this method when the analyte-free matrices are not available include measuring abscisic acid, a phytohormone from plant leaves and the emission of polycyclic aromatic hydrocarbons from petroleum refineries. Standard addition can also be used when some matrix components produce MS signals that interfere with the analytes of interest. We have used this method by some modifications to measure homocysteine and pyridoxal 5-phosphate in samples of human serum and whole blood, respectively [16, 17]. The matrix was first spiked with different concentrations of the analytes, and the endogenous concentrations of the analytes were estimated using the negative x-intercept of the calibration line. Then, the endogenous concentrations were added to the spiked concentrations, and new calibration curves with real concentrations were constructed (practical example 4). QCs were prepared in both actual and surrogate matrices, and the sample volume reduced to only 20 μL to

All the developed analytical methods need to be validated to make sure that each measurement of the content of the analyte in the sample in routine analysis is close to the true values [7]. There are international guidelines for validation of the analytical methods including FDA [6], European Medicines Agency (EMA) [14], International Union of the Pure and Applied Chemistry (IUPAC) [18] and Association of Official Analytical Chemists (AOAC) International. The major parameters need to be validated including linearity, accuracy, preci-

Selectivity is the ability of a method to determine a particular analyte in a complex matrix without interference from other ingredients of the matrix. Specificity, however, is the ultimate in selectivity, and it means that no interference is expected to occur, but these two terms are used interchangeably in the literature. If a method has specificity for an analyte, it means that either you have it or you do not. Selectivity can be graded as low, high, partial, good or bad,

sion, specificity, selectivity, sensitivity, ME and stability testing.

but the selectivity refers to 100% selectivity (or 0% interference) [19].

*3.6.3. Method of standard addition*

minimise the matrix effect.

*3.7.1. Selectivity and specificity*

**3.7. Validation**

Alternatively, the endogenous concentration of the analyte in the matrix can be subtracted from the added concentrations and uses the subtracted concentrations to build the calibration curve. Using the actual biological matrix for making the calibrators and QCs reduces the recovery and matrix effects between samples and calibrators. Again, the limitation of this method is that the increase in background peak area after spiking with standards has to be at least 15–20% of the background peak area, and the LLOQ is limited by the endogenous background concentration even if much lower concentrations can be detected by the method. Another difficulty is when multiple analytes with different endogenous compounds need to be quantified [15].

Alternatively, the background concentration in the blank matrices can be lowered by dilution of the blank matrices before spiking with standards. However, by diluting the matrix, the composition of the matrices in the study samples versus calibration curve is different leading to different recoveries of the analytes. Therefore, the extraction recoveries of analytes between the matrix and diluted matrix should be determined before using this method [15].

#### *3.6.1. Surrogate matrices*

Surrogate matrices can vary widely from a simplest form, mobile-phase solvents (neat) or pure water to a synthetic polymer-based solution. Some biological matrices, e.g. cerebrospinal fluid or tears, are difficult to obtain. The surrogate matrix should simulate the authentic matrix in terms of composition, salt content, analyte solubility, recovery and ME. For example, phosphate-buffered saline (PBS) or bovine serum albumin (BSA) in PBS (20–80 g/L) has the similar protein and ionic strength as human plasma.

To use neat solutions as surrogate matrices, extraction recovery and ME are required to be com parable with the original matrix. For example, thromboxane B2 and 12(S)-hydroxyeicosatetraenoic acid were quantified in human serum using mixture of water/methanol/acetonitrile (80:10:10, v/v/v) as a surrogate matrix, and the ME and recoveries of the analytes were demonstrated to be comparable.

#### *3.6.2. Stripped matrices*

Biological matrices can be stripped from particular endogenous components to generate analyte-free surrogate matrices. Adding activated charcoal, for example, can adsorb and remove the analyte from the matrix, but the charcoal must effectively remove from the matrix before spiking the analyte. Some analytes, e.g. homocysteine, cannot be removed by the charcoal and also the composition of the matrix may change or cause batch-to-batch variation after adding the charcoal leading to the altered analyte recovery and ME. Some light-sensitive analytes can be decomposed by heat or exposing to the light and therefore removed from the matrix.

#### *3.6.3. Method of standard addition*

One of the approaches for validation of the assay is to determine the accuracy throughout the validation step, using the biological matrix containing the endogenous compound to prepare the standard curves and all pools of six or more assays of each QC sample [3]. The amount of the analyte in the matrix (Cbasal) can be computed using a calibration curve in the substitute matrix, and the concentration of the analyte in the QC can be calculated by subtracting the Cbasal from the calculated one as follows, Creal = Cfound – Cbasal, in which Cfound is the concentration of the analyte in the QCs calculated against a calibration curve in the substitute matrix and Creal is the corrected concentration [3]. When using this approach, the LLOQ of the method cannot be smaller than the endogenous concentrations of the analyte in the matrix, and there-

Alternatively, the endogenous concentration of the analyte in the matrix can be subtracted from the added concentrations and uses the subtracted concentrations to build the calibration curve. Using the actual biological matrix for making the calibrators and QCs reduces the recovery and matrix effects between samples and calibrators. Again, the limitation of this method is that the increase in background peak area after spiking with standards has to be at least 15–20% of the background peak area, and the LLOQ is limited by the endogenous background concentration even if much lower concentrations can be detected by the method. Another difficulty is when

Alternatively, the background concentration in the blank matrices can be lowered by dilution of the blank matrices before spiking with standards. However, by diluting the matrix, the composition of the matrices in the study samples versus calibration curve is different leading to different recoveries of the analytes. Therefore, the extraction recoveries of analytes between

Surrogate matrices can vary widely from a simplest form, mobile-phase solvents (neat) or pure water to a synthetic polymer-based solution. Some biological matrices, e.g. cerebrospinal fluid or tears, are difficult to obtain. The surrogate matrix should simulate the authentic matrix in terms of composition, salt content, analyte solubility, recovery and ME. For example, phosphate-buffered saline (PBS) or bovine serum albumin (BSA) in PBS (20–80 g/L) has

To use neat solutions as surrogate matrices, extraction recovery and ME are required to be com parable with the original matrix. For example, thromboxane B2 and 12(S)-hydroxyeicosatetraenoic acid were quantified in human serum using mixture of water/methanol/acetonitrile (80:10:10, v/v/v) as a surrogate matrix, and the ME and recoveries of the analytes were dem-

Biological matrices can be stripped from particular endogenous components to generate analyte-free surrogate matrices. Adding activated charcoal, for example, can adsorb and remove the analyte from the matrix, but the charcoal must effectively remove from the matrix before

multiple analytes with different endogenous compounds need to be quantified [15].

the matrix and diluted matrix should be determined before using this method [15].

the similar protein and ionic strength as human plasma.

*3.6.1. Surrogate matrices*

onstrated to be comparable.

*3.6.2. Stripped matrices*

fore a lot of blank matrices need to be screened to find the suitable one.

116 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

In the standard addition method, every study sample is divided into aliquots of equal volumes, and the aliquots are spiked with known and varying amounts of the analyte to build the calibration curve. The sample concentration is then calculated as the negative x-intercept of the calibration line. This method is very accurate because it allows direct quantitation of endogenous analytes without manual subtraction of background peak areas. The disadvantage of the method is that it requires a large amount of sample and is very time-consuming and labour intensive. Examples of using this method when the analyte-free matrices are not available include measuring abscisic acid, a phytohormone from plant leaves and the emission of polycyclic aromatic hydrocarbons from petroleum refineries. Standard addition can also be used when some matrix components produce MS signals that interfere with the analytes of interest.

We have used this method by some modifications to measure homocysteine and pyridoxal 5-phosphate in samples of human serum and whole blood, respectively [16, 17]. The matrix was first spiked with different concentrations of the analytes, and the endogenous concentrations of the analytes were estimated using the negative x-intercept of the calibration line. Then, the endogenous concentrations were added to the spiked concentrations, and new calibration curves with real concentrations were constructed (practical example 4). QCs were prepared in both actual and surrogate matrices, and the sample volume reduced to only 20 μL to minimise the matrix effect.

#### **3.7. Validation**

All the developed analytical methods need to be validated to make sure that each measurement of the content of the analyte in the sample in routine analysis is close to the true values [7]. There are international guidelines for validation of the analytical methods including FDA [6], European Medicines Agency (EMA) [14], International Union of the Pure and Applied Chemistry (IUPAC) [18] and Association of Official Analytical Chemists (AOAC) International. The major parameters need to be validated including linearity, accuracy, precision, specificity, selectivity, sensitivity, ME and stability testing.

#### *3.7.1. Selectivity and specificity*

Selectivity is the ability of a method to determine a particular analyte in a complex matrix without interference from other ingredients of the matrix. Specificity, however, is the ultimate in selectivity, and it means that no interference is expected to occur, but these two terms are used interchangeably in the literature. If a method has specificity for an analyte, it means that either you have it or you do not. Selectivity can be graded as low, high, partial, good or bad, but the selectivity refers to 100% selectivity (or 0% interference) [19].

Selectivity can be calculated by comparing the chromatograms obtained after injection of a blank sample with and without the analyte or analytical solutions and with and without the matrix components.

chemicals and in high-performance liquid chromatography (HPLC) are repeatability of peak area, dilutions factors, reference materials and sampling. Sampling, calibration and repeat-

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The LOD is generally defined as the lowest amount of an analyte in a sample that can be detected by a particular analytical method. LOD is usually evaluated using the calculation of the signal/noise relationship considering the assumption that data normality, homoscedasticity and independency of residuals are met. The signal-to-noise ratio is determined by comparing the analytical signals at known low concentrations compared with those of blank sample up to a concentration that produces a signal equivalent to three times the standard deviation of the blank sample [19]. Determination of the LOD is not necessary during the validation,

On the other hand, the lowest concentration of an analyte in a sample, which can be reliably quantified is defined as the LLOQ. The analyte signal at the LLOQ level should be at least five times the signal of blank sample and the accuracy and precision within 20% of the nominal concentrations. The LLOQ should be selected based on the expected concentrations in the study. For example, for bioequivalence studies the LLOQ should not be higher than 5% of the

ME measurement is necessary for validation when the analytical method uses mass spectrometry as the detector due to the ion suppression or induction caused by the matrix components. The ME evaluation required spiking the analyte (at low and high concentrations) in six lots of matrix obtained from individual donors. First, the ratio of the peak area in the presence of matrix to the peak area in the absence of the matrix is calculated to achieve the matrix factor (MF), followed by the calculation of the IS normalised MF by dividing the MF of the analyte of interests by the MF of the IS. The CV of the IS-normalised MF is calculated from the six lots of the matrix and should be ≤15% (practical example 5). In some cases that this method is not practical (e.g. online sample preparation), the variability of the response should be assessed by analysing at least six lots of matrix spiked at low and high levels. The overall CV should not be greater than 15%. The ME is also recommended to be tested in haemolysed, hyperlipidaemic matrices or plasma collected from renally or hepatically impaired patients depending

Stability testing must be planned based on the conditions applied to the samples during processing. The stability is tested using spiked concentrations of the analyte to the matrix at low and high QC levels (six replicates at two levels are generally sufficient). Short-term stability at room temperature (2–8 h depending on the latest period of time required for sample processing), long-term stability at storage temperature (e.g. at −20°C or −80°C), freeze and

ability were the most significant sources, which affect combined uncertainty [20].

because the assay may have high variability in that level.

maximum concentration of the analyte in the samples (Cmax) [14].

*3.7.5. LOD and LLOQ*

*3.7.6. Matrix effect (ME)*

*3.7.7. Stability*

on the target population of the study [14].

#### *3.7.2. Accuracy*

Accuracy (or trueness or bias) is the most important aspect of validation and should be addressed in any analytical method. Accuracy shows the extent of agreement between the experimental value (calculated from replicate measurements) and the nominal (reference) values. Accuracy is a measurement of the systematic errors affecting the method. To estimate the accuracy of a method, the analyte is measured in comparison with a reference material or by spiking known amount of analyte in the blank matrix (QC samples) and calculating the percentage of recovery from the matrix. It can also be estimated using the comparison of the results from the method by a reference method [19].

The guideline for validation of analytical methods by the EMA [14] recommends checking the accuracy within run and between runs by analysing a minimum of five samples per four QC levels (LLOQ, low, medium and high) as a representative of the whole analytical range in at least two different days. The accuracy needs to be reported as the percentage of the nominal concentrations and the mean concentration should be within 15% of the nominal values for all QC levels, except LLOQ, which should be within 20% of the nominal values [14].

#### *3.7.3. Precision*

The term precision is defined as the closeness of repeated individual measurements of an analyte under specified conditions. This term is demonstrating the repeatability and reproducibility of the method and expressed as the coefficient of variation (CV). Precision should be measured for LLOQ, low, medium and high QC samples in the same run that accuracy is testing. The acceptance criteria are also similar to the accuracy evaluation [14, 19].

#### *3.7.4. Uncertainty*

To make sure that a method is correctly fit for the purpose of measurement, "uncertainty" of the method is required to be evaluated [7].

A detailed list of all possible sources of uncertainty needs to be prepared. A preliminary study may identify the most significant sources of uncertainty. Typically, the two sources of uncertainties are Type A or random error and Type B or systematic error. Random error is caused by unpredictable variations and gives rise to variations in repeated observations. The random error can generally be minimised by increasing the number of observations. Systematic error, however, is a type of errors, which remain constant, or its variation is predictable and therefore independent of the number of observations. The result should be corrected for all recognised significant systematic errors. The steps involved in uncertainty estimation are identification of uncertainty sources, quantification of uncertainty components and calculation of combined and expanded uncertainty. The main sources of uncertainity are sampling, environmental conditions, method validation, instruments, weighting and dilutions, reference materials, chemicals and in high-performance liquid chromatography (HPLC) are repeatability of peak area, dilutions factors, reference materials and sampling. Sampling, calibration and repeatability were the most significant sources, which affect combined uncertainty [20].

#### *3.7.5. LOD and LLOQ*

Selectivity can be calculated by comparing the chromatograms obtained after injection of a blank sample with and without the analyte or analytical solutions and with and without the

Accuracy (or trueness or bias) is the most important aspect of validation and should be addressed in any analytical method. Accuracy shows the extent of agreement between the experimental value (calculated from replicate measurements) and the nominal (reference) values. Accuracy is a measurement of the systematic errors affecting the method. To estimate the accuracy of a method, the analyte is measured in comparison with a reference material or by spiking known amount of analyte in the blank matrix (QC samples) and calculating the percentage of recovery from the matrix. It can also be estimated using the comparison of the

The guideline for validation of analytical methods by the EMA [14] recommends checking the accuracy within run and between runs by analysing a minimum of five samples per four QC levels (LLOQ, low, medium and high) as a representative of the whole analytical range in at least two different days. The accuracy needs to be reported as the percentage of the nominal concentrations and the mean concentration should be within 15% of the nominal values for all

The term precision is defined as the closeness of repeated individual measurements of an analyte under specified conditions. This term is demonstrating the repeatability and reproducibility of the method and expressed as the coefficient of variation (CV). Precision should be measured for LLOQ, low, medium and high QC samples in the same run that accuracy is

To make sure that a method is correctly fit for the purpose of measurement, "uncertainty" of

A detailed list of all possible sources of uncertainty needs to be prepared. A preliminary study may identify the most significant sources of uncertainty. Typically, the two sources of uncertainties are Type A or random error and Type B or systematic error. Random error is caused by unpredictable variations and gives rise to variations in repeated observations. The random error can generally be minimised by increasing the number of observations. Systematic error, however, is a type of errors, which remain constant, or its variation is predictable and therefore independent of the number of observations. The result should be corrected for all recognised significant systematic errors. The steps involved in uncertainty estimation are identification of uncertainty sources, quantification of uncertainty components and calculation of combined and expanded uncertainty. The main sources of uncertainity are sampling, environmental conditions, method validation, instruments, weighting and dilutions, reference materials,

QC levels, except LLOQ, which should be within 20% of the nominal values [14].

testing. The acceptance criteria are also similar to the accuracy evaluation [14, 19].

matrix components.

results from the method by a reference method [19].

118 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

*3.7.2. Accuracy*

*3.7.3. Precision*

*3.7.4. Uncertainty*

the method is required to be evaluated [7].

The LOD is generally defined as the lowest amount of an analyte in a sample that can be detected by a particular analytical method. LOD is usually evaluated using the calculation of the signal/noise relationship considering the assumption that data normality, homoscedasticity and independency of residuals are met. The signal-to-noise ratio is determined by comparing the analytical signals at known low concentrations compared with those of blank sample up to a concentration that produces a signal equivalent to three times the standard deviation of the blank sample [19]. Determination of the LOD is not necessary during the validation, because the assay may have high variability in that level.

On the other hand, the lowest concentration of an analyte in a sample, which can be reliably quantified is defined as the LLOQ. The analyte signal at the LLOQ level should be at least five times the signal of blank sample and the accuracy and precision within 20% of the nominal concentrations. The LLOQ should be selected based on the expected concentrations in the study. For example, for bioequivalence studies the LLOQ should not be higher than 5% of the maximum concentration of the analyte in the samples (Cmax) [14].

#### *3.7.6. Matrix effect (ME)*

ME measurement is necessary for validation when the analytical method uses mass spectrometry as the detector due to the ion suppression or induction caused by the matrix components. The ME evaluation required spiking the analyte (at low and high concentrations) in six lots of matrix obtained from individual donors. First, the ratio of the peak area in the presence of matrix to the peak area in the absence of the matrix is calculated to achieve the matrix factor (MF), followed by the calculation of the IS normalised MF by dividing the MF of the analyte of interests by the MF of the IS. The CV of the IS-normalised MF is calculated from the six lots of the matrix and should be ≤15% (practical example 5). In some cases that this method is not practical (e.g. online sample preparation), the variability of the response should be assessed by analysing at least six lots of matrix spiked at low and high levels. The overall CV should not be greater than 15%. The ME is also recommended to be tested in haemolysed, hyperlipidaemic matrices or plasma collected from renally or hepatically impaired patients depending on the target population of the study [14].

#### *3.7.7. Stability*

Stability testing must be planned based on the conditions applied to the samples during processing. The stability is tested using spiked concentrations of the analyte to the matrix at low and high QC levels (six replicates at two levels are generally sufficient). Short-term stability at room temperature (2–8 h depending on the latest period of time required for sample processing), long-term stability at storage temperature (e.g. at −20°C or −80°C), freeze and thaw and stock solution stabilities are the most common tests. The stability of QC samples are analysed against a freshly prepared calibration curve, and the calculated concentrations should be within 15% of the nominal concentrations. The stability of processed samples in the autosampler temperature also determines how long samples can be stored in the autosampler without the analyte been degraded [14]. Any other variation during sample processing which can potentially affect the stability of the analyte of interest needs to be tested during validation.

### **4. Practical examples**

#### **4.1. Practical example 1: impact of weighting**

See **Table 1**.

#### **4.2. Practical example 2: linearity assessment**

In **Table 2,** it shows that the linear regression model (LRM) must systemically be rejected at the 95% confidence level (Fcrit,95% = 4.53) for lack-of-fit test and at 99% confidence level (Fcrit,99% = 10.56) for Mandel's fitting test. Thus, despite the fact that r and quality coefficient (QC) are greater than 0.997 and lower than 5%, respectively, the linearity of the calibration lines was rejected based on the F-tests. So, the r is not a good measure of the linearity assessment. Even with a QC value less than 3%, the LRM is rejected at the 95% confidence level (**Table 2**). Alternatively, the residual plots give useful information to validate the chosen regression model.

The residual plot can be used to check if the principle assumptions, i.e. normality of the residuals and homoscedasticity, are met when evaluating the goodness of fit of the regression model. The U-shaped residual plot usually shows that a curvilinear regression model is a better fit than an LRM. In order to correct the non-linearity, a quadratic curvilinear function (f(x) = a + bx + cx<sup>2</sup> ) can be chosen. The "lack of fit" tests for the quadratic regression model

(QRM) are summarised in **Table 2**. The test for lack of fit indicates that this QRM fits the calibration data at 99% confidence level in all cases except one. To check the suitability of the order of polynomial regression model, the significance of the second-order coefficient needs to be estimated. The P-value on the second-order coefficient, shown in **Table 2**, is systemically smaller than 1%, and therefore a lower order model should not be considered. Moreover, residual plots (**Figure 2**) were constructed for the QRM, and the residuals were randomly scattered within a horizontal band around the centre line. Therefore, the QRM was selected as the reference model. It is noted that an increase of the variance is observed at higher concentra-

**Table 2.** The F-value of the lack-of-fit (LOF) test and Mandel's fitting test is compared with the quality coefficient for

For the quadratic regression model, the F-value of the lack-of-fit test and the P-value for testing significance of the second-order coefficient for the quadratic regression model are represented. The significance value at the 95% confidence

level is underlined (reproduced from Van Loco et al. [8] with permission from Springer-Verlag).

**Linear regression model Quadratic regression model**

11.08 51.46 3.93 0.9982 0.63 0.0000 19.42 56.84 4.23 0.9978 1.58 0.0000 7.13 26.29 3.67 0.9985 0.94 0.0006 6.99 37.73 3.79 0.9984 0.18 0.0002 11.43 58.21 4.03 0.9981 0.31 0.0000 29.91 53.02 3.53 0.9986 4.08 0.0000 49.80 71.07 3.76 0.9984 5.69 0.0000 23.77 73.86 3.19 0.9989 1.66 0.0000 31.95 63.37 3.24 0.9988 3.55 0.0000 7.49 33.50 2.92 0.9991 0.54 0.0003 9.99 55.19 3.95 0.9983 0.15 0.0000 10.71 28.65 4.70 0.9975 1.89 0.0005 25.21 79.60 3.34 0.9987 1.62 0.0000 13.16 35.74 3.37 0.9987 1.93 0.0002

**LOF Mandel's test value QC (%) r LOF P-value on second-order coefficient**

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As a summary, in this example, a linear model with r > 0.997 and QC < 5% but with lack of fit (LOF) yielded predicted values for a mid-scale calibration standard that significantly differ from the nominal ones. The accuracy was overestimated, while the precision on the results

The role of IS concentration on the linearity of the calibration curve has been demonstrated by Tan et al. [13]. They presented a case in which decreasing concentration of the IS from 100%

tions [8].

several linear calibration lines of Cd.

was comparable in both LRM and QRM [8].

**4.3. Practical example 3: IS concentration and the linearity**


**Table 1.** Increasing the accuracy of the lower end of the calibration curve by applying the weighing.


For the quadratic regression model, the F-value of the lack-of-fit test and the P-value for testing significance of the second-order coefficient for the quadratic regression model are represented. The significance value at the 95% confidence level is underlined (reproduced from Van Loco et al. [8] with permission from Springer-Verlag).

**Table 2.** The F-value of the lack-of-fit (LOF) test and Mandel's fitting test is compared with the quality coefficient for several linear calibration lines of Cd.

(QRM) are summarised in **Table 2**. The test for lack of fit indicates that this QRM fits the calibration data at 99% confidence level in all cases except one. To check the suitability of the order of polynomial regression model, the significance of the second-order coefficient needs to be estimated. The P-value on the second-order coefficient, shown in **Table 2**, is systemically smaller than 1%, and therefore a lower order model should not be considered. Moreover, residual plots (**Figure 2**) were constructed for the QRM, and the residuals were randomly scattered within a horizontal band around the centre line. Therefore, the QRM was selected as the reference model. It is noted that an increase of the variance is observed at higher concentrations [8].

As a summary, in this example, a linear model with r > 0.997 and QC < 5% but with lack of fit (LOF) yielded predicted values for a mid-scale calibration standard that significantly differ from the nominal ones. The accuracy was overestimated, while the precision on the results was comparable in both LRM and QRM [8].

#### **4.3. Practical example 3: IS concentration and the linearity**

**Concentration (ng/mL) Area ratio Accuracy**

**4. Practical examples**

See **Table 1**.

(f(x) = a + bx + cx<sup>2</sup>

**4.1. Practical example 1: impact of weighting**

120 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

**4.2. Practical example 2: linearity assessment**

 0.002 0 0 0.006 125 92.3 0.019 104 94.1 37.5 0.400 98.5 94.1 0.836 101 99.3 3.320 98.5 98.9 5.290 97.8 98.5 6.890 102 103

residual plots give useful information to validate the chosen regression model.

**Table 1.** Increasing the accuracy of the lower end of the calibration curve by applying the weighing.

**(no weighting)**

) can be chosen. The "lack of fit" tests for the quadratic regression model

thaw and stock solution stabilities are the most common tests. The stability of QC samples are analysed against a freshly prepared calibration curve, and the calculated concentrations should be within 15% of the nominal concentrations. The stability of processed samples in the autosampler temperature also determines how long samples can be stored in the autosampler without the analyte been degraded [14]. Any other variation during sample processing which can potentially affect the stability of the analyte of interest needs to be tested during validation.

In **Table 2,** it shows that the linear regression model (LRM) must systemically be rejected at the 95% confidence level (Fcrit,95% = 4.53) for lack-of-fit test and at 99% confidence level (Fcrit,99% = 10.56) for Mandel's fitting test. Thus, despite the fact that r and quality coefficient (QC) are greater than 0.997 and lower than 5%, respectively, the linearity of the calibration lines was rejected based on the F-tests. So, the r is not a good measure of the linearity assessment. Even with a QC value less than 3%, the LRM is rejected at the 95% confidence level (**Table 2**). Alternatively, the

The residual plot can be used to check if the principle assumptions, i.e. normality of the residuals and homoscedasticity, are met when evaluating the goodness of fit of the regression model. The U-shaped residual plot usually shows that a curvilinear regression model is a better fit than an LRM. In order to correct the non-linearity, a quadratic curvilinear function

> **Accuracy (1/x weighting)**

> > The role of IS concentration on the linearity of the calibration curve has been demonstrated by Tan et al. [13]. They presented a case in which decreasing concentration of the IS from 100%

**Figure 2.** Plots of residuals for (a) the linear regression model (LRM) and (b) the quadratic regression model (QRM) versus predicted values (adopted from Van Loco et al. [8] with permission from Springer-Verlag).

to 5% ULOQ made the calibration curve non-linear. In that case, the cross-contribution from the analyte to the IS is equivalent to 5% of the concentration of the analyte. The cross-signal contribution from the analyte to the IS is either due to the isotope interference or chemical impurity in reference standard [13].

#### **4.4. Practical example 4: method of standard addition for homocysteine calibration curve**

**Table 3** shows the calculated calibration curve data for homocysteine standard solutions spiked into a pooled human serum.

To estimate the endogenous concentrations of homocysteine in the sample of pooled human serum, the negative x-intercept of the curve is calculated:


 x = \_\_\_\_\_\_\_ −0.262 0.000598 = 438 ng/mL. (4) Then, the nominated concentration is changed to the spiked + endogenous concentrations,

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Now, by comparing the detector response for the unknown samples with the second calibra-

**Table 5** is representing the analyte peak area spiked in six different lots of human plasma. The MF has been calculated by dividing the area of analyte (or IS) in each matrix to the average peak area of the analyte (or IS) in the pure solutions. The IS-normalised MF is the ratio of the MF for the

**Spiked + endogenous concentration (ng/mL) Calculated concentration (ng/mL)**

**Table 4.** Homocysteine calibration curve: The x-axis is representing the spiked + endogenous concentrations.

**Analyte of interest IS IS-normalised MF**

**Spiked Pure (mean of three replicates)**

**Peak area Matrix** 

and a new calibration is constructed (**Table 4**).

**4.5. Practical example 5: ME calculations**

Regression equation: y = 0.000598 x – 0.000762.

**three replicates)**

**Table 5.** Calculation of ME.

**Peak area Matrix** 

**factor**

**factor Spiked Pure (mean of** 

1,095,000 1,210,000 0.905 4,320,000 6,343,333 0.681 1.33 1,050,000 0.868 6,240,000 0.984 0.882 1,110,000 0.917 5,780,000 0.911 1.01 1,120,000 0.926 5,660,000 0.892 1.04 1,100,000 0.909 5,770,000 0.910 0.999 1,130,000 0.934 5,170,000 0.815 1.15 Mean 1.07 SD 0.154 CV% 14.4

tion curve, the unknown sample concentrations can be calculated.

 + 438 = 438 381.51 + 438 = 488 469.28 + 438 = 1038 1071.34 + 438 = 1538 1545.77 + 438 = 2038 2091.35 + 438 = 2538 2606.98 + 438 = 3038 3023.15 + 438 = 3538 3471.01

**Table 3.** Homocysteine calibration curve: the x-axis is representing the spiked concentrations.

Then, the nominated concentration is changed to the spiked + endogenous concentrations, and a new calibration is constructed (**Table 4**).

Now, by comparing the detector response for the unknown samples with the second calibration curve, the unknown sample concentrations can be calculated.

#### **4.5. Practical example 5: ME calculations**

**Table 5** is representing the analyte peak area spiked in six different lots of human plasma. The MF has been calculated by dividing the area of analyte (or IS) in each matrix to the average peak area of the analyte (or IS) in the pure solutions. The IS-normalised MF is the ratio of the MF for the


**Table 4.** Homocysteine calibration curve: The x-axis is representing the spiked + endogenous concentrations.


**Table 5.** Calculation of ME.

to 5% ULOQ made the calibration curve non-linear. In that case, the cross-contribution from the analyte to the IS is equivalent to 5% of the concentration of the analyte. The cross-signal contribution from the analyte to the IS is either due to the isotope interference or chemical

**Figure 2.** Plots of residuals for (a) the linear regression model (LRM) and (b) the quadratic regression model (QRM)

**Table 3** shows the calculated calibration curve data for homocysteine standard solutions

To estimate the endogenous concentrations of homocysteine in the sample of pooled human

0.000598 = 438 ng/mL. (4)

**4.4. Practical example 4: method of standard addition for homocysteine calibration** 

**Spiked concentrations (ng/mL) Calculated concentration (ng/mL)**

**Table 3.** Homocysteine calibration curve: the x-axis is representing the spiked concentrations.

versus predicted values (adopted from Van Loco et al. [8] with permission from Springer-Verlag).

122 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

impurity in reference standard [13].

spiked into a pooled human serum.

Regression equation: y = 0.000598 x + 0.262.

serum, the negative x-intercept of the curve is calculated:

0 N/A 50 30.87 600 632.76 1100 1107.05 1600 1652.48 2100 2167.02 2600 2584.02 3100 3031.75

x = \_\_\_\_\_\_\_ −0.262

**curve**

analyte to the MF for the IS. The CV% in this example was 14.4%, which is within the acceptance limit for the matrix effect by the EMA guideline for validation of bioanalytical methods [14].

HPLC High-performance liquid chromatography

IUPAC International Union of Pure and Applied Chemistry LC–MS/MS Liquid chromatography tandem mass spectrometry

Linearity of Calibration Curves for Analytical Methods: A Review of Criteria for Assessment…

http://dx.doi.org/10.5772/intechopen.72932

125

IDMS Isotope dilution mass spectrometry

IS Internal standard

LOD Limit of detection

LOF Lack of fit

ME Matrix effect MF Matrix factor

MS Mass spectrometry

POM Power of the mean

SD Standard deviation SD Standard deviation

SIL Stable isotope labelled SPE Solid-phase extraction

**Author details**

Seyed Mojtaba Moosavi1

ULOQ Upper limit of quantification

WLSLR Weighted least squares linear regression

\*Address all correspondence to: s.ghassabian@uq.edu.au 1 The University of Technology Sydney, Sydney, Australia

2 The University of Queensland, Brisbane, Australia

and Sussan Ghassabian2

\*

QC Quality control

PBS Phosphate buffer saline

QRM Quadratic regression model

LLE Liquid–liquid extraction

LRM Linear regression model

LLOQ Lower limit of quantification

### **5. Key results**


### **Abbreviations**



### **Author details**

analyte to the MF for the IS. The CV% in this example was 14.4%, which is within the acceptance limit for the matrix effect by the EMA guideline for validation of bioanalytical methods [14].

• Calibration curve is a regression model between an known concentration of an analyte and the response from an instrument enabling the estimation of the concentration of the analyte

• Weighted least squares linear regression (WLSLR) is necessary when the standard deviations across the standard range are not consistent. Weighting improves the sensitivity and

• Coefficient of correlation is not a suitable measure for the linearity of the calibration curve,

• Stable isotope-labelled compounds are the most preferable internal standards. However, carefully chosen structural analogues with similar functional groups and physicochemical

• The concentration of the internal standard may affect the linearity of the calibration curve due to the cross signal contribution between the analyte and the internal standards.

• When an analyte-free matrix does not exist, the amount of endogenous analyte in the matrix can be estimated using the negative x-intercept of the regression equation and adding this value to the spiked concentrations of the analyte to calculate the actual concentrations of each standard.

• During validation of an analytical method, selectivity, specificity, accuracy, precision, uncertainty, LLOQ, matrix effect and stability are the minimum criteria to be evaluated.

and the linearity should be evaluated using an appropriate statistical analysis.

properties can contribute to generation of comparable analytical methods.

**5. Key results**

**Abbreviations**

4PL Four-parameter logistic

ANOVA Analysis of variance

BSA Bovine serum albumin

CV Coefficient of variation

CIS-Max Maximum IS concentration CIS-Min Minimum IS concentration

EMA European Medicines Agency

FDA Food and Drug Administration

ELISA Enzyme-linked immunosorbent assay

in an unknown sample.

accuracy of the lower end of the calibration range.

124 Calibration and Validation of Analytical Methods - A Sampling of Current Approaches

Seyed Mojtaba Moosavi1 and Sussan Ghassabian2 \* \*Address all correspondence to: s.ghassabian@uq.edu.au 1 The University of Technology Sydney, Sydney, Australia 2 The University of Queensland, Brisbane, Australia

### **References**

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[15] Thakare R et al. Quantitative analysis of endogenous compounds. Journal of Pharmaceutical

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**Section 3**

**Validation Approaches**
