Testing Risk Difference of Two Proportions for Combined Unilateral and Bilateral Data

In clinical studies with paired organs, binary outcomes often exhibit intra-subject correlation and may include a mixture of unilateral and bilateral observations. Under Donner's constant correlation model, we develop three likelihood-based test statistics (the likelihood ratio, Wald-type, and score tests) for assessing the risk difference between two proportions. Simulation studies demonstrate good control of type I error and comparable power among the three tests, with the score test showing slightly more favorable performance, particularly for moderate to large sample sizes, supporting its use in practical applications and future studies involving combined unilateral and bilateral data. Applications to otolaryngologic and ophthalmologic data illustrate the methods. An online calculator is also provided for power analysis and risk difference testing.