Common odds ratio test and interval estimation for stratified bilateral and unilateral data

In clinical research, data are commonly collected bilaterally from paired organs or bodily parts within individual subjects. However, unilateral data arise when constraints or limiting factors impede the collection of complete bilateral data. In this article, we propose three large-sample tests and five confidence interval methods for making inferences on the common treatment effect, measured by the odds ratio, in a stratified design under integrated bilateral and unilateral data. Our simulation results show that the likelihood ratio-based and score-based tests, along with their associated confidence interval methods, demonstrate robust control of type I error and close-to-nominal coverage probabilities. We apply the proposed methods to real-world datasets of acute otitis media and myopic eyes to showcase their validity and applicability in clinical practice.