Multiple Comparisons Procedures for Analyses of Joint Primary Endpoints and Secondary Endpoints.

One of the main challenges in drug development for rare diseases is selecting the appropriate primary endpoints for pivotal studies. Although many endpoints can effectively reflect clinical benefit, their sensitivity often varies, making it difficult to determine the required sample size for study design and to interpret final results, which may be underpowered for some or all endpoints. This complexity is further compounded when there is a desire to support regulatory claims for multiple clinical endpoints and dose regimens due to the issues of multiplicity and sample size constraints. Joint Primary Endpoints (JPEs) offer a compelling strategy to address these challenges; however, their analysis in conjunction with component endpoints presents additional complexities, particularly in managing multiplicity concerns for regulatory claims. To address these issues, this paper introduces a robust two-stage gatekeeping framework designed to test two hierarchically ordered families of hypotheses. A novel truncated closed testing procedure is employed in the first stage, enhancing flexibility and adaptability in the evaluation of primary endpoints. This approach strategically propagates a controlled fraction of the error rate to the second stage for assessing secondary endpoints, ensuring rigorous control of the global family-wise Type I error rate across both stages. Through extensive numerical simulations and real-world clinical trial applications, we demonstrate the efficiency, adaptability, and practical utility of this approach in advancing drug development for rare diseases while meeting stringent regulatory requirements.