Modeling conditional dependence among multiple diagnostic tests

When multiple imperfect dichotomous diagnostic tests are applied to an individual, it is possible that some or all of their results remain dependent even after conditioning on the true disease status. The estimates could be biased if this conditional dependence is ignored when using the test results to infer about the prevalence of a disease or the accuracies of the diagnostic tests. However, statistical methods correcting for this bias by modelling higher-order conditional dependence terms between multiple diagnostic tests are not well addressed in the literature. This paper extends a Bayesian fixed effects model for 2 diagnostic tests with pairwise correlation to cases with 3 or more diagnostic tests with higher order correlations. Simulation results show that the proposed fixed effects model works well both in the case when the tests are highly correlated and in the case when the tests are truly conditionally independent, provided adequate external information is available in the form of fixed constraints or prior distributions. A data set on the diagnosis of childhood pulmonary tuberculosis is used to illustrate the proposed model.