Preface

**Section 3 Validation Approaches 129**

**VI** Contents

Thomas Layloff

Chapter 7 **Validation of Analytical Methods 131** Tentu Nageswara Rao

Chapter 8 **Method Validation Approaches for Pharmaceutical**

**Chromatographic (HPTLC) Techniques 143**

**Assessments – Highlights with High Performance Thin Layer**

David Jenkins, Cherif Diallo, Ed Bethea, Eliangiringa Kaale and

Ask any analytical chemist what constitutes the most important aspect of any quantitative ana‐ lytical determination, and the most frequent response one might receive is "calibration" and per‐ haps even "calibration and validation." One might ask: "Why would this be so?" If one mulls over this matter for a moment, the answer might become apparent. Consider any analytical in‐ strument, e.g., a UV-visible spectrophotometer, and the absorbance response produced as radia‐ tion from the spectrophotometer's source lamp passes through the solution of absorbing analyte and is absorbed to a particular degree. At face value, that absorbance has no meaning at all *un‐ less* that signal is referenced to a *known* amount of the absorbing analyte present in the measured solution. Now, the absorbance does have meaning, as it can be expressed as a number of absorb‐ ance units per unit amount of the sought-after analyte and may potentially be used for determi‐ nation of analyte concentration in an unknown solution or other types of sample. This referencing process is known as *calibration*.

The calibration process establishes a relationship between analyte signal and analyte concentra‐ tion that is useful for quantitation of a sought-after analyte in a sample, using a given analytical method. A typical approach is to measure the signals produced by a series of calibration *stand‐ ards* of known analyte concentrations that cover a particular range of concentration and then re‐ gress the blank-corrected signals (response variable) on the standard concentrations (predictor variable) to obtain the equation (i.e., calibration curve) that best fits the experimental calibration data and yields predicted values of the response variable. This type of approach to calibration is termed *univariate* (one response variable, one or more predictor variables) calibration and can also hold for the opposite arrangement—a response variable of concentration regressed on a pre‐ dictor variable of signal. Also, included under the umbrella of univariate calibration methods is multiple linear regression (MLR), comprised of one response variable (usually concentration) re‐ gressed into two or more predictor variables (usually signal). Another broad class of calibration model, known as *multivariate* (two or more response and predictor variables each) calibration, involves the use of data arrays for the response and predictor variables, with the response ma‐ trix regressed on the predictor matrix, using the principles of linear algebra and statistics. Most multivariate calibrations are designed so that the response matrix is the array of concentration vectors for the calibration standards containing the sought-after analytes and the predictor ma‐ trix is the array of signal vectors for, e.g., spectra or chromatograms of the calibration standards at, e.g., particular wavelengths/frequencies or response times.

The *validation* process is equally important, as it verifies the signal-versus-concentration relation‐ ship acquired from the calibration samples via analysis of another, separate set of samples with known concentrations of analyte. A set of predicted analyte concentrations for the validation samples are then obtained using the calibration relationship for the method employed. The known and predicted concentrations of the validation samples are compared, and the *residuals* (errors or differences between known and predicted concentration) are analyzed statistically, e.g., by standard deviation and bias, to evaluate the accuracy and precision (i.e., the reliability), respectively, of the calibration system and, ultimately, the analytical method used for analyte quantitation. Other validation parameters assess the goodness of fit of the experimental calibra‐ tion data to the values predicted by the calibration curve and also yield the limits of analyte con‐ centration detectable by the analytical method utilized as well as the sensitivity of the method.

The focus of this book is on the roles of calibration and validation in the utilization of these tech‐ niques and their associated methods for analyte quantitation in samples. A number of ap‐ proaches to calibration and validation of analytical methods will be presented in a series of selected research papers and reviews dealing with such topics as the use of the internal standard method for calibration and quantitation of proteins in biological matrices by LC-MS/MS, using a variety of data preprocessing methods and a DoE (Design of Experiments) chemometric ap‐ proach to the development of calibration models for vibrational spectroscopic methods, employ‐ ing DoE in conjunction with such chemometric methods as partial least squares (PLS), principal component analysis (PCA), and parallel factor analysis (PFA) for application to pharmaceutical analysis, and application of a variety of univariate and multivariate regression methods to the development of calibration models for laser-induced breakdown spectroscopy (LIBS).

This book seeks to introduce the reader to current methodologies in analytical calibration and validation. This collection of contributed research articles and reviews addresses current devel‐ opments in the calibration of analytical methods and techniques and their subsequent validation. Section 1, "Introduction," contains an Introductory Chapter, a broad overview of analytical cali‐ bration and validation, and a brief synopsis of the following chapters. Section 2, "Calibration Approaches," presents five chapters covering calibration schemes for some modern analytical methods and techniques. The last chapter in this section provides a segue into Section 3, "Valida‐ tion Approaches," which contains two chapters on validation procedures and parameters. This book is a valuable source of scientific information for anyone interested in analytical calibration and validation.

I am most grateful to Mr. Teo Kos, the initial Publishing Process Manager for this project, for all his efforts and support at the start of this book project and Mrs. Marina Dusevic who succeeded him for her supervision and organization of the publication of all materials; her assistance to me and the authors in the completion of our work in an easy, timely manner; and her helpful advice and guidance throughout the bulk of this project. I thank the authors for their excellent contribu‐ tions to this compendium of research articles and reviews on calibration and validation schemes for quantitative analysis. I express many thanks to the technical editor who prepared these manuscripts for publication by InTech Open Access Publisher. I thank my wife, Resa, who is also an analytical chemist, for her advice, support, and encouragement; the University of Pitts‐ burgh at Greensburg for their support; my secretary, Mrs. Valerie Kubenko, for her encourage‐ ment and assistance with this project as well as with my administrative and academic duties during my work on this book; and finally—and perhaps most importantly—my colleague, fel‐ low administrator, and our campus statistician, Dr. Dean Nelson, for his support, encourage‐ ment, and helpful advice on statistics. Lastly, I am honored to complete this book project on the occasion of my 61st birthday—a nice "present" for the one who is embracing his later years with enthusiasm and has no intention of ceasing his work on analytical data treatment.

> **Mark T. Stauffer, PhD** University of Pittsburgh, Greensburg Greensburg, Pennsylvania United States of America

**Section 1**

**Introduction**

**Section 1**
