Testing the Homogeneity of Differences between Two Proportions for Stratified Bilateral and Unilateral Data across Strata

Medical comparative studies often involve collecting data from paired organs, which can produce either bilateral or unilateral data. While many testing procedures are available that account for the intra-class correlation between paired organs for bilateral data, more research needs to be conducted to determine how to analyze combined correlated bilateral and unilateral data. In practice, stratification is often used in analysis to ensure participants are allocated equally to each experimental condition. In this paper, we propose three Maximum Likelihood Estimation (MLE)-based methods for testing the homogeneity of differences between two proportions for stratified bilateral and unilateral data across strata using Donner’s model. We compare the performance of these methods with a model-based method based on Generalized Estimating Equations using Monte Carlo simulations. We also provide a real example to illustrate the proposed methodologies. Our findings suggest that the Score test performs well and offers a valuable alternative to the exact tests in future studies.