Comparative Analysis of Exact Methods for Testing Equivalence of Prevalences in Bilateral and Unilateral Combined Data with and without Assumptions of Correlation

In clinical studies focusing on paired body parts, diseases can manifest on either both sides (bilateral) or just one side (unilateral) of the organs. Consequently, the data in these studies may consist of records from both bilateral and unilateral cases. There are two different methods of analyzing the data. One of the methods is assuming that the pair of measurements from the same subject are independent, while the other considers the correlation between paired organs. In terms of the homogeneity test of proportions, asymptotic methods have been proposed given the moderate size of data. This article extends the existing work by proposing exact methods to deal with the scenarios when the sample size is small and asymptotic methods perform poorly. The impact of the correlation assumption is also explored. Among the proposed methods, calculating p-values by replacing unknown parameters with estimated values while accounting for the correlation is recommended based on its satisfactory type I error controls and statistical powers. The proposed methods are applied to three real examples for illustration.