Prevalence Estimation in Finite Populations Adjusted for Misclassification

Accurately estimating disease prevalence in finite populations is essential in epidemiology and ecological studies. Standard methods based on the binomial model often rely on assumptions of infinite populations and perfect diagnostic tests, which are frequently violated in practice. When sampling is without replacement from a finite population, the hypergeometric distribution provides the appropriate framework, but diagnostic misclassification must also be accounted for. In this paper, we present a framework for prevalence estimation in finite populations under imperfect diagnostic testing. The framework incorporates misclassification through diagnostic sensitivity and specificity, which may be treated either as fixed or as parameters estimated from independent studies. We evaluate multiple inferential approaches, including exact hypergeometric confidence intervals, a computationally efficient simulation-based approximation, a Bayesian formulation yielding posterior distributions, and a profile likelihood method that jointly accounts for uncertainty in sensitivity and specificity. Using extensive simulations we assess coverage, interval precision, and point estimate accuracy. Results show that hypergeometric-based methods consistently yield narrower and better-calibrated intervals than binomial-based alternatives. The profile likelihood approach achieves near-nominal coverage while appropriately propagating diagnostic uncertainty. An application to epidemiological surveillance data illustrates the practical relevance of the proposed methods.