  Epidemiologic screening programs often make use of tests with small, but
non-zero probabilities of misdiagnosis. In this article, we assume the target
population is finite with a fixed number of true cases, and that we apply an
imperfect test with known sensitivity and specificity to a sample of
individuals from the population. In this setting, we propose an enhanced
inferential approach for use in conjunction with sampling-based bias-corrected
prevalence estimation. While ignoring the finite nature of the population can
yield markedly conservative estimates, direct application of a standard finite
population correction (FPC) conversely leads to underestimation of variance. We
uncover a way to leverage the typical FPC indirectly toward valid statistical
inference. In particular, we derive a readily estimable extra variance
component induced by misclassification in this specific but arguably common
diagnostic testing scenario. Our approach yields a standard error estimate that
properly captures the sampling variability of the usual bias-corrected maximum
likelihood estimator of disease prevalence. Finally, we develop an adapted
Bayesian credible interval for the true prevalence that offers improved
frequentist properties (i.e., coverage and width) relative to a Wald-type
confidence interval. We report the simulation results to demonstrate the
enhanced performance of the proposed inferential methods.
