Estimation of sensitivity and specificity of three conditionally dependent diagnostic tests in the absence of a gold standard

This article presents a model to evaluate the accuracy of diagnostic tests. Data from three tests for the detection of EF-positive Streptococcus suis serotype 2 strains in sows were analyzed. The data were collected in a field study in the absence of a gold standard, that is, the true disease status (noninfected or infected) of the tested animals was unknown. Two tests were based on a polymerase chain reaction (PCR); one test was applied to a tonsil swab (taken from the live animal), and the other test was applied to the whole tonsil (collected at slaughter). The third test was based on a bacterial examination (BE) of the whole tonsil. To reduce experimental cost BE was performed only for a subset of the animals in the sample. The model allows for dependence between tests, conditional upon the unknown true disease status of the animals. Accuracy was expressed in terms of sensitivity and specificity of the tests. A Bayesian analysis was performed that incorporated prior information about the accuracy of the tests. The model parameters have a simple interpretation and specification of priors is straightforward. Posterior inference was carried out with Markov chain Monte Carlo (MCMC) methods, employing the Gibbs sampler, as implemented in the WinBUGS program. Different parameterizations to allow for selection and missing values, use of different priors, practical problems in the analysis, and some interesting issues in a joint analysis of the binary (positive or negative) results of PCR and BE and two additional continuous enzyme-linked immunosorbent assays (ELISA) are discussed.