Hierarchical models for estimating herd prevalence and test accuracy in the absence of a gold standard

A common assumption made in studies involving two or more binary diagnostic tests in the absence of a gold standard is one of conditional independence among tests given disease status. Although reasonable in some cases, often this assumption is untenable or untested and may lead to biased results. We propose a class of hierarchical models for the purpose of estimating the herd-level prevalence distribution and the accuracies of two tests in the absence of a gold standard when several exchangeable populations with differing disease prevalence are available for sampling, relaxing the assumption of conditional independence between tests. The models are used to estimate the prevalence of bovine brucellosis in Mexican cow herds and to estimate the error rates of two tests for the detection of swine pneumonia.