Estimating disease prevalence in the absence of a gold standard

When estimating disease prevalence, it is not uncommon to have data from conditionally dependent diagnostic tests. In such a situation, the estimation of prevalence is difficult if none of the tests is considered to be a gold standard. In this paper we develop a Bayesian approach to estimating disease prevalence based on the results of two diagnostic tests, allowing for the possibility that the tests are conditionally dependent, but not conditioning on any particular dependence structure. This involves the construction of four models with various forms of conditional dependence and uses Bayesian model averaging, enabled by reversible jump MCMC, to obtain an overall estimate of the prevalence. This methodology is demonstrated using a study on the prevalence of Strongyloides infection.