Use of Coefficient of Variation in Assessing Variability of Quantitative Assays

Abstract

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.