Testing Homogeneity of Odds Ratio for Stratified Bilateral Correlated Data

In clinical studies such as ophthalmologic or otolaryngologic research, bilateral correlated data frequently arise when outcomes are collected from paired organs or body parts. Since the measurements from such paired observations are usually highly correlated, appropriate data analysis requires accounting for the intra-class correlation. Methodological developments for analyzing bilateral data have been extensively studied over the past several decades, including both inferential procedures and computational strategies. In some analyses, the center effect or confounding effect could lead to imbalance among treatment arms, making it necessary to adjust for stratification/confounding factors in the data analysis. In this article, we develop three testing procedures for assessing the homogeneity of odds ratios in stratified bilateral correlated data under the assumption of a common correlation structure. Monte Carlo simulation studies are conducted to evaluate the performance of the proposed methods. The results indicate that the Wald-type test based on a log-linear hypothesis and the score test maintain robust type I error rates and achieve high power across a range of scenarios, and are therefore recommended for practical application. The proposed methodologies are further illustrated using two real data examples.