Overcoming limitations of the Rogan–Gladen correction: A closed-form solution to a simplified Bayesian method for true prevalence estimation

Prevalence estimation is a cornerstone of epidemiology, but diagnostic misclassifications often result in the measurement of "apparent" rather than "true" prevalence. Correction methods are used to address this problem. The frequentist Rogan-Gladen method, known for its simplicity, can lead to implausible results, especially for extreme prevalence values. Bayesian methods overcome these limitations and have many statistical advantages but can be complex and deter potential users. To improve accessibility, we have developed a simplified Bayesian model that allows for a closed-form solution. The simplification consists of neglecting uncertainties in the sensitivity and specificity values and assuming a non-informative prior distribution for the true prevalence. The result is a correction method that is as easy to use as the Rogan-Gladen method but mitigates some of its drawbacks. We compared this new approach with existing methods in a large simulation study. It showed that traditional Bayesian credible intervals consistently achieved coverage near 95%, whereas simplified Bayes and Rogan-Gladen generally exhibited undercoverage, especially under large uncertainty in sensitivity/specificity. Simplified Bayes, however, improved boundary behaviour and coverage over Rogan-Gladen at low prevalences. Thus, the newly developed method represents a practical compromise: it improves upon Rogan-Gladen without the computational burden of traditional Bayes estimates and provides reliable performance when uncertainty in test characteristics is limited.