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Use of Coefficient of Variation in Assessing Variability of Quantitative Assays

Use of Coefficient of Variation in Assessing Variability of Quantitative Assays,10.1128/CDLI.9.6.1235-1239.2002,Clinical and Vaccine Immunology,George

Use of Coefficient of Variation in Assessing Variability of Quantitative Assays   (Citations: 25)
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We have derived the mathematical relationship between the coefficient of variation associated with repeated measurements from quantitative assays and the expected fraction of pairs of those measurements that differ by at least some given factor, i.e., the expected frequency of disparate results that are due to assay variability rather than true differences. Knowledge of this frequency helps determine what magnitudes of differences can be expected by chance alone when the particular coefficient of variation is in effect. This frequency is an operational index of variability in the sense that it indicates the probability of observing a particular disparity between two measurements under the assumption that they measure the same quantity. Thus the frequency or probability becomes the basis for assessing if an assay is sufficiently precise. This assessment also provides a standard for determining if two assay results for the same subject, separated by an intervention such as vaccination or infection, differ by more than expected from the variation of the assay, thus indicating an intervention effect. Data from an international collaborative study are used to illustrate the application of this proposed interpretation of the coefficient of variation, and they also provide support for the assumptions used in the mathematical derivation. Although assay variability is well recognized as pertinent to the interpretation of quantitative bioassays such as the en- zyme-linked immunosorbent assay (ELISA), few tools that link assay precision with interpretation of results are readily avail- able. In our investigations, we have expanded on previous studies that evaluated the relationship between assay precision and the capabilities and limitations of a given assay system. In this article we develop a simple procedure to determine the probability that an assay will accurately discern whether two samples have the same analyte concentration or not based on a knowledge of the assay variability as measured by the coef- ficient of variation (CV). In many laboratories, the variability of the ELISA and other methods of chemical assay that produce continuous-type val- ues is summarized not by the standard deviation (SD) but by the CV, which is defined as the SD divided by the mean, with the result often reported as a percentage. The main appeal of the CV is that the SDs of such assays generally increase or decrease proportionally as the mean increases or decreases, so that division by the mean removes it as a factor in the variabil- ity. The CV is therefore a standardization of the SD that allows comparison of variability estimates regardless of the magni- tude of analyte concentration, at least throughout most of the working range of the assay. In serological assays a twofold difference in measurements of the same sample has been widely regarded as the upper limit on acceptable variability, and the frequency of such differences among pairs of repeated measurements has been proposed as an apt index for assay variability (5). Wood (4) showed the mathematical relationship between that frequency and the size of the SD of repeated assay measurements, under the assump- tion that the logarithm of measurements is normally distrib- uted. The tables he provided indicate how small an SD of the log measurements must be in order to ensure that only some predetermined fraction of pairs of measurements differ by a factor of two or more. Wood's formulation was a valuable link between the precision of titration assays and an operational assessment of assay performance. As expressed above, in the context of serum assays and other applications the CV may be preferred over SD as a measure of precision, but there is no published formulation that links the CV to assay performance in a manner analogous to Wood's treatment of the SD in the log scale. Such a formulation would be even more useful if it were to generalize from twofold to k-fold disparities in replicate measurements (where k can be any number greater than one and arbitrarily close to one). This generalization would take advantage of the fact that ELISAs and other assays with continuous scales are capable of mea- suring a continuous range of differences in samples, unlike classic titration assays utilizing step-wise, usually twofold, serial dilutions. The intent of this article is to introduce the mathe- matical relationship between the CV and the frequency of k-fold or more-disparate assay values when the same sample is subjected to repeated measurements. We also demonstrate how this relationship can be used to address practical problems in a clinical laboratory.
Journal: Clinical and Vaccine Immunology - CLIN VACCINE IMMUNOL , vol. 9, no. 6, pp. 1235-1239, 2002
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