Point and interval estimation of population prevalence using a fallible test and a non-probabilistic sample: post-stratification correction

Abstract

Accurate prevalence estimation is crucial for public health planning, particularly for rare diseases or low-prevalence conditions. This study evaluated frequentist and Bayesian methods for estimating prevalence, addressing challenges such as imperfect diagnostic tests, partial disease status verification, and non-probabilistic samples. Poststratification was applied as a novel method and was used to improve representativeness and correct biases. Three scenarios were analyzed: (1) complete verification using a gold standard, (2) estimation with a diagnostic test of known sensitivity and specificity, and (3) partial verification of disease status limited to test positives. In all scenarios, poststratification adjustments increased prevalence estimates and interval lengths, highlighting the importance of accounting for population variability. Bayesian methods demonstrated advantages in integrating prior information and modeling uncertainty, particularly under high-variability and low-prevalence conditions. Key findings included the flexibility of Bayesian approaches to maintain estimates within plausible ranges and the effectiveness of post-stratification in correcting biases in non-probabilistic samples. Frequentist methods provided narrower intervals but were limited in addressing inherent uncertainties. This study underscores the need for methodological adjustments in epidemiological studies, offering robust solutions for real-world challenges. These results have significant implications for improving public health decision-making and the design of prevalence studies in resource-constrained or non-probabilistic contexts.