Simulation studies on the estimation of sensitivity and specificity in the absence of a gold standard and with rare positive frequencies

In the absence of a gold standard, sensitivity and specificity could be evaluated using the Bayesian latent class model underlying true positives and true negatives. However, when the frequency of positivity is limited owing to low prevalence, the estimates may be strongly influenced by prior information or small-sample bias. In this study, we evaluated the performance of the Bayesian latent class model with two independent tests under a rare frequency of positivity, varying the strength and way of giving prior information under the conditional independence assumption is satisfied. Throughout the simulation experiments, a small-sample bias led to underestimation and overestimation when the frequency of positivity was low. Furthermore, we observed that placing an informative prior distribution for only one of the two tests resulted in a constant bias of sensitivity or specificity for the other test, regardless of the strength of the prior information.