Point and Interval Estimation of Population Prevalence Using a Fallible Test and a Non-Probabilistic Sample: Post-Stratification Correction

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. Post-stratification 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, post-stratification 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.