Linearity evaluation of analytical methods that count particles

Linearity evaluation of an analytical method is important for both manufacturers of diagnostic devices and laboratory users. Some of the statistical assumptions for estimation and testing in linear regression are violated in analytical methods that count particles per unit of volume or/and time, leading to potential erroneous evaluation of linearity. The objective of this paper is to provide an approach for evaluating linearity in these cases. The number of counts for each concentration level has a Poisson probability distribution that is linear, second-, or higher-order polynomial function of the concentration. Maximum likelihood approach is used to estimate the parameters of the models. Deviance of a particular model and the likelihood ratio test are used to test for linearity. An evaluation of linearity of an analytical method in multiple experiments is also described. No particular changes to the standard testing protocols and data collections are necessary. There are several statistical software packages that can perform the calculations. Formulas and SAS codes presented in this article can also assist in estimation and statistical testing.