Bayesian latent class models with conditionally dependent diagnostic tests: a case study

In the assessment of the accuracy of diagnostic tests for infectious diseases, the true disease status of the subjects is often unknown due to the lack of a gold standard test. Latent class models with two latent classes, representing diseased and non-diseased subjects, are often used to analyze this type of data. In its basic format, latent class analysis requires the observed outcomes to be statistically independent conditional on the disease status. In most diagnostic settings, this assumption is highly questionable. During the last decade, several methods have been proposed to estimate latent class models with conditional dependence between the test results. A class of flexible fixed and random effects models were described by Dendukuri and Joseph in a Bayesian framework. We illustrate these models using the analysis of a diagnostic study of three field tests and an imperfect reference test for the diagnosis of visceral leishmaniasis. We show that, as observed earlier by Albert and Dodd, different dependence models may result in similar fits to the data while resulting in different inferences. Given this problem, selection of appropriate latent class models should be based on substantive subject matter knowledge. If several clinically plausible models are supported by the data, a sensitivity analysis should be performed by describing the results obtained from different models and using different priors.