Testing the homogeneity of odds ratio across strata for combined bilateral and unilateral data

Bilateral and unilateral combined data are commonly involved in clinical trials or observational studies designed to test the treatment effectiveness on paired organs or bodily parts within individual subjects. It is essential to examine if the treatment effect is consistent across different subgroups such as age, gender, or disease severity for understanding how the treatment works for various patient populations. In this paper, we propose three large-sample homogeneity tests of odds ratio in the stratified randomization setting using correlated combined data. Our simulation results show that the score test exhibits robust empirical type I error control and demonstrates strong power characteristics compared to other methods proposed. We apply the proposed tests to real-world datasets of acute otitis media and myopia to illustrate their practical application and utility.