Homogeneity Test and Sample Size of Relative Risk Ratios for Complex Paired Data Under Dalla’s Model

In clinical research, unilateral data and bilateral data are commonly collected when paired organs or body parts of people receive treatment. Existing models are often inadequate for the research of combined unilateral and bilateral data. Considering population heterogeneity, this paper proposes three statistical tests and sample size estimation methods for the relative risk ratio in stratified unilateral and bilateral data under Dallal’s model. We derive test statistics (i.e., likelihood ratio, Wald-type, and score statistics) and evaluate their performance in terms of type I error rates and powers. Then, sample size determination is performed using an iterative algorithm. Monte Carlo simulations demonstrate that the score test performs well across various parameter configurations. Moreover, the estimated powers for determining sample size based on the score test are closer to the actual empirical powers. Two real examples of otolaryngology and myopathy are provided to illustrate the effectiveness of the proposed methods.