Estimation of operating characteristics for dependent diagnostic tests based on latent Markov models

We describe a method for making inferences about the joint operating characteristics of multiple diagnostic tests applied longitudinally and in the absence of a definitive reference test. Log-linear models are adopted for the classification distributions conditional on the latent state, where inclusion of appropriate interaction terms accommodates conditional dependencies among the tests. A marginal likelihood is constructed by marginalizing over a latent two-state Markov process. Specific latent processes we consider include a first-order Markov model, a second-order Markov model, and a time-nonhomogeneous Markov model, although the method is described in full generality. Adaptations to handle missing data are described. Model diagnostics are considered based on the bootstrap distribution of conditional residuals. The methods are illustrated by application to a study of diffuse bilateral infiltrates among patients in intensive care wards in which the objective was to assess aspects of validity and clinical agreement.