Homogeneity Test of Ratios of Two Proportions in Stratified Bilateral and Unilateral Data

In paired-organ studies such as ophthalmology, otolaryngology, and rheumatology, etc., various approaches take highly correlated bilateral data into account for homogeneity tests but are less likely to focus on combined bilateral and unilateral data structures. Also, it is necessary and important to adjust the effect of confounders on stratified combined bilateral and unilateral data since, in these data structures, ignoring intra-class correlation and confounding effects can cause biased statistical inference. This article derived three homogeneity tests (the likelihood ratio test, the Wald test, and the score test) concerning these cooperative structure data to detect if ratios of proportions retain consistency across strata. Simulation shows that the score test provides a robust Type I error rate and satisfactory power performance. Finally, a real example is applied to demonstrate the application of these three proposed tests.