Evaluating co-primary endpoints collectively in clinical trials

Often a treatment is assessed by co-primary endpoints so that a comprehensive picture of the treatment effect can be obtained. Co-primary endpoints can be different medical assessments angled at different aspects of a disease, therefore, are used collectively to strengthen evidence for the treatment effect. It is common sense that if a treatment is ineffective, the chance to show that the treatment is effective in all co-primary endpoints should be small. Therefore, it may not be necessary to require all the co-primary endpoints to be statistically significant at the 1-sided 0.025 level to control the error rate of wrongly approving an ineffective treatment. Rather it is reasonable to allow certain variation for the p -values within a range close to 0.025. In this paper, statistical methods are developed to derive decision rules to evaluate co-primary endpoints collectively. The decision rules control the error rate of wrongly accepting an ineffective treatment at the level of 0.025 for a study and the error rate at a slightly higher level for a treatment that works for all the co-primary endpoints except perhaps one. The decision rules also control the error rates for individual endpoints. Potential applications in clinical trials are presented.