Estimating the conditional false-positive rate for semi-latent data

When comparing tests for a disease, it is necessary to know whether individuals are diseased or nondiseased. In practice, the confirmatory (gold standard) procedure is often limited to individuals with positive test results, because the confirmatory procedure is not applied to individuals with negative test results. We present a model for estimating the sensitivity and specificity when two tests are compared and the gold standard classification is unavailable (semi-latent) for those individuals with negative results on both tests. The model does not assume independent error rates, and estimates of specificity conditional on a false-positive result for another test are derived. We use a Bayes approach for estimating the distributions of the performance parameters.