Modeling conditional dependence between diagnostic tests: a multiple latent variable model

Applications of latent class analysis in diagnostic test studies have assumed that all tests are measuring a common binary latent variable, the true disease status. In this article we describe a new approach that recognizes that tests based on different biological phenomena measure different latent variables, which in turn measure the latent true disease status. This allows for adjustment of conditional dependence between tests within disease categories. The model further allows for the inclusion of measured covariates and unmeasured random effects affecting test performance within latent classes. We describe a Bayesian approach for model estimation and describe a new posterior predictive check for evaluating candidate models. The methods are motivated and illustrated by results from a study of diagnostic tests for Chlamydia trachomatis.