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

TL;DR

This paper introduces an improved statistical inference method for estimating disease prevalence in finite populations using imperfect tests, accounting for misclassification errors and providing more accurate confidence intervals.

Contribution

It develops a novel variance estimation approach that incorporates misclassification and finite population correction, enhancing prevalence inference accuracy.

Findings

The method accurately captures sampling variability in prevalence estimates.

Simulation results show improved coverage and narrower intervals.

The approach effectively adjusts for test misclassification in finite populations.

Abstract

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.