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使用误诊概率较小但非零的检测手段。本文假设目标总体有限且真实病例数目固定，我们采用已知灵敏度和特异度的非完美检测对来自总体的个体样本进行检测。在此背景下，我们提出一种与基于抽样的偏误校正患病率估计相结合的增强推断方法。忽视总体的有限性会导致显著保守的估计值，而直接应用标准有限总体校正（FPC）反而会导致方差低估。我们发现可通过间接方式利用标准FPC实现有效的统计推断。具体而言，我们推导出在此特定但常见的诊断检测场景中由误分类引起的可简便估计的额外方差分量。该方法所得标准误估计能恰当捕获常用偏误校正患病率极大似然估计量的抽样变异性。最终，我们构建了针对真实患病率的适应性贝叶斯可信区间，相较于Wald型置信区间具有更优的频率学性质（即覆盖率和区间宽度）。仿真结果验证了所提推断方法的性能提升效果。