Testing the equality of response rate functions for paired binary data with multiple groups

In clinical trials, we often encounter observations from patients' paired organs. In paired correlated data, there exist various measures to evaluate the therapeutic responses, such as risk difference, relative risk ratio, and odds ratio. These measures are essentially some forms of response rate functions. Based on this point, this article aims to test the equality of response rate functions such that the homogeneity tests of the above measures are special cases. Under an interclass correlation model, the global and constrained maximum likelihood estimations are obtained through algorithms. Furthermore, we construct likelihood ratio, score, and Wald-type statistics and provide the explicit expressions of the corresponding tests based on the risk difference, relative risk ratio, and odds ratio. Monte Carlo simulations are conducted to compare the performance of the proposed methods in terms of the empirical type I error rates and powers. The results show that the score tests perform satisfactorily as their type I error rates are close to the specified nominal level, followed by the likelihood ratio test. The Wald-type tests exhibit poor performance, especially for small sample sizes. A real example is given to illustrate the three proposed test statistics.