Risk difference tests for stratified binary data under Dallal's model

In medical studies, the binary data is often encountered when the paired organs or body parts receive treatment. However, the same treatment may lead to different therapeutic effects based on the stratified factors or confounding effects. Under Dallal's model, the paper proposes the homogeneity test of risk difference to determine the necessity of stratified treatment. When the stratification is not necessary, common test is introduced to investigate if the risk difference is equal to a fixed constant between two groups. Several statistical tests are derived to analyze homogeneity and common hypotheses, respectively. Monte Carlo simulations show that the score tests behave well in both of hypotheses. Wald-type and Rosner's statistics are always liberal but have higher empirical powers. Especially, the likelihood ratio statistic is better for the homogeneity test in the case of smaller data with larger strata. Two real examples are provided to illustrate the effectiveness of the proposed methods in ankle instability and otolaryngology studies.