A model for evaluating sensitivity and specificity for correlated diagnostic tests in efficacy studies with an imperfect reference test

The purpose of a diagnostic efficacy study is to evaluate and compare the sensitivities and specificities of several diagnostic tests. Usually the diagnostic tests are correlated conditional on disease status, and the reference test is subject to error. In the Chlamydia trachomatis study, five screening tests far detecting chlamydia in endocervical specimens were compared. The five tests are correlated, and the reference test (the cell culture test) has less than 100% sensitivity. The conventional method ignores both the correlations between the tests and the misclassification of the reference test and thus cannot provide a valid analysis. We propose a model to evaluate and compare the sensitivities and specificities of correlated diagnostic tests when there is either an imperfect reference test or even no reference test. The model also can estimate the effects of covariates. It is a generalized linear mixed model with two unobserved variables, one continuous and one dichotomous. We use a hybrid algorithm, which consists of the EM algorithm and the Newton-Raphson method, for obtaining its maximum likelihood estimation. Methods fur model checking and for estimating and comparing both subject-specific and population-averaged sensitivities and specificities are given.