Sample size calculation for comparing time-averaged responses in k-group repeated-measurement studies

Many clinical trials compare the efficacy of K (<3) treatments in repeated measurement studies. However, the design of such trials has received relatively less attention from researchers. Zhang and Ahn (2012) derived a closed-form sample size formula for two-sample comparisons of time-averaged responses using the generalized estimating equation (GEE) approach, which takes into account different correlation structures and missing data patterns. In this paper, we extend the sample size formula to scenarios where K (<3) treatments are compared simultaneously to detect time-averaged differences in treatment effect. A closed-form sample size formula based on the noncentral χ ² test statistic is derived. We conduct simulation studies to assess the performance of the proposed sample size formula under various correlation structures from a damped exponential family, random and monotone missing patterns, and different observation probabilities. Simulation studies show that empirical powers and type I errors are close to their nominal levels. The proposed sample size formula is illustrated using a real clinical trial example.