2. Systematic error detection using quality control experiments

Simply stated, the aim of quality control experiments is to determine the performance of the laboratory tests with measuring of known samples or references, that is, samples in which the true value of the analyte being tested is known. These methods are mainly set up to detect random error and check instrument precision. However, the same results can be used to detect bias and systematic error [7].

The laboratories can use certified reference materials to measure and identify systematic error. If the reference sample is measured with each analytical run, you would expect the results of the reference sample measurements to show a random distribution around the true value, yet if the results are consistently lower or higher than the reference value then you would suspect that a bias exists [2, 8].

For systematic error measurement, a method comparison method is needed to identify systematic error. Any systematic error found needs to be corrected using a recovery experiment and calibration.

#### 2.1. Levey-Jennings plots

proximity of the test results to the true value. Precision measures reliability and reproducibility. These metrics are complementary and a good clinical test needs to be both accurate and precise [2]. Some have suggested that trueness should be used to refer to the agreement of the measure-

Accuracy and precision are related to a concept called measurement error: every measurement is associated with a degree of error or uncertainty. The goal in laboratory medicine is to minimize the measurement error so that it does not adversely affect the clinical decision-making process. Measurement error can never be truly nullified, but it can be decreased to a scale that is

Measurement errors can be random, i.e. they can be unpredictable. All measurements have random error. Random errors are due to unpredictable variations in sample, instrument, measurement process or analysis and it can be said to follow a Gaussian distribution, i.e. random error follows randomness and chance and thus laws of probability apply to random error. As the instruments get more precise the Gaussian distribution of the random error gets narrower and the random error decreases. At the same time, if we repeat an experiment or test multiple times we can average out random error from our measurements. i.e. the mean of multiple repeated measurements gets closer to the true value as the number of repeats increases. This forms the basis of reporting confidence intervals for measurements [2, 4].

Bias or systematic error is a form of measurement error that skews the results to one side. Repeating the measurements cannot eliminate bias. In other words, bias is a non-zero error which will consistently affect the results and can show a problem with the measurement process often requiring corrective action. The corrective action can be in form of calibration by introducing a correction factor or by changing components of measurement. Systematic error can be short-term or long-term, with very short-term systematic error often manifesting

Systematic error and random error have a cumulative effect on the measurement results (Figure 1). Thus, measurement error is often considered as total error with both bias and random error contributing. Laboratories often have limits for total error, bias and random

Figure 1. This figure depicts the cumulative effect of systematic error and random error. The X-axis represents the value

determined and the Y-axis plots the frequency of occurrence of each value.

as random error.

50 Quality Control in Laboratory

ment to the true value and accuracy to encompass both trueness and precision.

acceptable by clinicians, laboratory directors and laboratory regulatory agencies [2, 3].

The first step in identification of systematic error is to visually inspect the quality control process. Levey-Jennings plot shows the fluctuation of reference sample measurements around the mean against time. The chart's reference lines include control limits, 2 standard deviation lines, 1 standard deviation lines and the mean reference line.

The mean, standard deviation and the control limits are calculated by a replication study where the certified reference material is repeatedly measured. The repeated measurements allow for calculation of mean and standard deviation of the control sample levels. The trial limits are mean 3 standard deviations. The next step is to eliminate the replication study results that are beyond the 3 standard deviations. Then the mean and standard deviation are recalculated and the trial limits are again set. Again, results beyond the trial limits are excluded. The process continues until all the remaining results are within the trial limits. These final trial limits, mean and standard deviation are set as the reference measures for that reference sample.

The number of replication studies to perform can be calculated based on the number of acceptable failures. The sample size calculation is based on set levels of confidence and reliability. Confidence (accuracy) is the difference between 1 and type I error rate. Reliability is the degree of precision. For a failure rate of 0 (i.e. we are not allowing any incorrect results), the equation can be stated as:

$$n = \frac{\ln\left(1 - \text{confidence}\right)}{\ln\left(reliability\right)}\tag{1}$$

concerned with identification of random error and within runs error detection [2, 7]. Other Westgard rules are focused on identification of systematic error and between runs error detec-

Systematic Error Detection in Laboratory Medicine http://dx.doi.org/10.5772/intechopen.72311 53

• 22S rule: The QC results are considered to have failed and a bias is present if two consecutive control values fall between the 3 standard deviations and 2 standard deviation limits

• 41S rule: The QC results is considered to have failed and a bias is present if four consecutive control values fall on the same side of the mean reference line and are at least one

• 10x rule: The QC results are considered to have failed and a bias is present if 10 consecu-

Method comparison is used for initial assay validation as well as for studying accuracy of a test. The aim of method comparison is to establish whether the assay measures what it is supposed to measure and how accurately it measures it. The findings of method comparison also allow for correction of the results if a bias is found (i.e. calibration). The principal for method comparison is that a gold standard or a standard reference material exists where in the amount of analyte in the sample is exactly known (or known with a high degree of accuracy). We can use this reference standard as a comparator against the performance of our assay and determine the degree of bias that exists in our measurements. This essentially means that we are measuring the relative

Ideally, identification of a bias should lead to a search for the source of the bias and systematic error, and attempts should be made to rectify the cause of the observed bias. However, there are instances in which no fault or solvable problem is identified; in these instances, if the assay has enough precision and stability as well as clinical merit then we can use the findings of

Bias can take two general forms: constant bias and proportional bias. The constant bias is a difference between the observed measurement and the expected measurement that is constant throughout the range of the observations. Constant bias (β0) is represented in regression statistics

Figure 3. Examples of systematic error in Levey-Jennings plot: A. An example of 2-2S rule, B. An example of 4-1S rule, C.

tive control values fall on the same side of the mean reference line.

tion. In this chapter we will focus on the latter rules.

on the same side of the means reference line.

standard deviation away from the mean.

performance of our assay against the reference standard.

method comparison to adjust for the observed bias.

These rules are shown in Figure 3.

2.3. Method comparison

An example of 10x rule.

The confidence level is often set at 0.95 and reliability at 0.90 or 0.80. If we allow failure events, then the calculation of the sample size is based on the following equation:

$$(1 - \text{Confidence} = \sum\_{i=1}^{f} \binom{n}{i} (1 - \text{Reliability})^i \text{Reliability}^{n-i} \tag{2}$$

where f is the failure rate and n is the sample size.

In a Levey-Jennings plot the X-axis represents time and Y-axis represents the measured value. Reference lines are drawn parallel to the X-axis corresponding to mean, mean �1 standard deviations, mean �2 standard deviations, and mean �3 standard deviations. The next step is to plot measured values of the reference material for each run on the plot (Figure 2).

#### 2.2. Westgard rules

Westgard rules are a set of guidelines set by Dr. James Westgard for identification of random and systematic error in laboratory quality control experiments. They are based on repeated measurements of at least two reference samples with each analytical run. Some of the Westgard rules are

Figure 2. An example of a Levey-Jennings plot. X-axis plots the time of measurement (e.g. day) and the Y-axis plot the measurement value for that unit of time. The lines denoting the mean value and 1, 2 and 3 standard deviations from the mean are explained in the figure.

concerned with identification of random error and within runs error detection [2, 7]. Other Westgard rules are focused on identification of systematic error and between runs error detection. In this chapter we will focus on the latter rules.


These rules are shown in Figure 3.
