Sample size estimation for comparing rates of change in K-group repeated binary measurements studies

In clinical research, longitudinal trials are frequently conducted to evaluate the treatment effect by comparing trends in repeated measurements among different intervention groups. For such longitudinal trials, many researchers have developed the sample size estimation methods for comparison between two groups measurements. In contrast, relatively less attention has been paid to trials with K-group (Formula presented.) comparison. Jung and Ahn (2004) and Lou et al. (2017) derived the sample size formulas for comparing trends among K groups using the generalized estimating equations approach for repeated continuous and count outcomes, respectively. However, to the best of our knowledge, there has been no development in sample size calculation for binary outcomes in multi-arms trials. In this paper, we present a sample size formula for comparing trends in K-group repeated binary measurements that accommodates various missing patterns and correlation structures. Simulation results show that the proposed method performs well under a wide range of design parameter settings. We illustrate the proposed method through an example.