Enhanced Inference for Finite Population Sampling-Based Prevalence Estimation with Misclassification Errors

Abstract

Epidemiologic screening programs often make use of tests with small, but nonzero 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.

KEYWORDS:

• Bias correction
• Credible interval
• Finite population correction
• Random sampling
• Sensitivity
• Specificity

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

This work was supported by the National Institute of Health (NIH)/National Institute of Allergy and Infectious Diseases (P30AI050409; Del Rio PI), the NIH/National Center for Advancing Translational Sciences (UL1TR002378; Taylor PI), the NIH/National Cancer Institute (R01CA234538; Ward/Lash MPIs), and the NIH/National Cancer Institute (R01CA266574; Lyles/Waller MPIs).