On implementation of the Gibbs sampler for estimating the accuracy of multiple diagnostic tests

Implementation of the Gibbs sampler for estimating the accuracy of multiple binary diagnostic tests in one population has been investigated. This method, proposed by Joseph, Gyorkos and Coupal, makes use of a Bayesian approach and is used in the absence of a gold standard to estimate the prevalence, the sensitivity and specificity of medical diagnostic tests. The expressions that allow this method to be implemented for an arbitrary number of tests are given. By using the convergence diagnostics procedure of Raftery and Lewis, the relation between the number of iterations of Gibbs sampling and the precision of the estimated quantiles of the posterior distributions is derived. An example concerning a data set of gastro-esophageal reflux disease patients collected to evaluate the accuracy of the water siphon test compared with 24h pH-monitoring, endoscopy and histology tests is presented. The main message that emerges from our analysis is that implementation of the Gibbs sampler to estimate the parameters of multiple binary diagnostic tests can be critical and convergence diagnostic is advised for this method. The factors which affect the convergence of the chains to the posterior distributions and those that influence the precision of their quantiles are analyzed.