Bayesian Interval Estimation for the Difference in TPRs and FPRs of Two Diagnostic Tests with Unverified Negatives

We derive Bayesian interval estimators for the differences in the true positive rates and false positive rates of two dichotomous diagnostic tests applied to the members of two distinct populations. The populations have varying disease prevalences with unverified negatives. We compare the performance of the Bayesian credible interval to the Wald interval using Monte Carlo simulation for a spectrum of different TPRs, FPRs, and sample sizes. For the case of a low TPR and low FPR, we found that a Bayesian credible interval with relatively noninformative priors performed well. We obtain similar interval comparison results for the cases of a high TPR and high FPR, a high TPR and low FPR, and of a high TPR and mixed FPR after incorporating mildly informative priors.