Optimal Power Analyses for Hierarchical Endpoints Testing in Group Sequential Design

The increasing demand for drug efficacy research highlights the need to address hypothesis testing for both primary and secondary endpoints in clinical trial design, requiring multiplicity adjustments, particularly in hierarchical endpoints. In group sequential designs, controlling the overall type I error rate while maintaining adequate power for secondary endpoints is challenging, as traditional gatekeeping procedures and alpha splitting often lead to overly conservative family-wise error rates (FWER) for secondary endpoints, resulting in insufficient power and inefficiencies such as excessive sample sizes or additional trials. To address this, a model-based optimal power analysis approach is proposed, enabling simultaneous evaluation of primary and secondary endpoints within a single trial, ensuring FWER control while enhancing power and minimizing sample size requirements. Focusing on cross-sectional and longitudinal continuous endpoints, the methodology employs a Gaussian copula for joint probabilities and a linear mixed-effects model to account for correlated increments in group sequential designs with two stages. Results demonstrate the approach’s effectiveness in controlling error rates, improving secondary endpoint power, and reducing sample size requirements. A real clinical trial on LDL apheresis treatment further illustrates its practical benefits, including considerations for sample size re-estimation and extending to strong FWER control.