Improved Trimmed Weighted Hochberg Procedures With Two Endpoints and Sample Size Optimization

Clinical trials with multiple endpoints often use prespecified weights to allocate the overall significance level unequally, reflecting the clinical importance of each endpoint, the probability of observing a treatment effect, or other considerations. To address the subjective nature of weight selection, we propose a quantitative approach where the optimal significance level allocation comes with the minimum sample size. Moreover, this innovative approach was specifically tailored and applied to weighted Hochberg-type procedures for two hypotheses, filling the existing gap in sample size optimization methods for these procedures. In addition, we propose a new Hochberg-type procedure with weights, referred to as the improved trimmed weighted Hochberg procedure, which provides increased statistical power and relaxes the dependence assumptions for familywise error rate control compared to the original weighted Hochberg procedure. Several examples and applications are provided to illustrate the methodology.