Bayesian analysis and classification of two enzyme-linked immunosorbent assay tests without a gold standard

Reconciling two quantitative enzyme-linked immunosorbent assay tests for an antibody to an RNA virus, in a situation without a gold standard and where false negatives may occur, is the motivation for this work. False negatives occur when access of the antibody to the binding site is blocked. On the basis of the mechanism of the assay, a mixture of four bivariate normal distributions is proposed with the mixture probabilities depending on a two-stage latent variable model including the prevalence of the antibody in the population and the probabilities of blocking on each test. There is prior information on the prevalence of the antibody, and also on the probability of false negatives, and so a Bayesian analysis is used. The dependence between the two tests is modeled to be consistent with the biological mechanism. Bayesian decision theory is utilized for classification.The proposed method is applied to the motivating data set to classify the data into two groups: those with and those without the antibody. Simulation studies describe the properties of the estimation and the classification. Sensitivity to the choice of the prior distribution is also addressed by simulation. The same model with two levels of latent variables is applicable in other testing procedures such as quantitative polymerase chain reaction tests, where false negatives occur when there is a mutation in the primer sequence.