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.

翻译：流行病学筛查项目常采用具有较小但非零误诊概率的检测方法。本文假设目标总体有限且真实病例数固定，并对该总体中的个体样本应用已知灵敏度和特异度的非完美检测。在此设定下，我们提出一种增强推断方法，可与基于抽样的偏倚校正患病率估计结合使用。忽略总体的有限性会导致明显保守的估计，而直接应用标准有限总体校正（FPC）则会导致方差低估。我们发现一种间接利用典型FPC进行有效统计推断的途径。具体而言，针对这一特定但具有普遍性的诊断检测场景，我们推导出由误分类导致的额外方差分量，该分量易于估计。我们的方法所给出的标准误估计能恰当捕捉通常的偏倚校正患病率极大似然估计的抽样变异性。最后，我们构建了针对真实患病率的改进贝叶斯可信区间，相较于Wald型置信区间，该区间具有更优的频率学派性质（即覆盖率和宽度）。我们通过模拟结果展示了所提推断方法的增强性能。