Method of balanced adjustment in testing co-primary endpoints

Abstract

In a clinical trial, if there are three or more co-primary endpoints, the type II error could increase depending on the correlation among the endpoints and their treatment effect sizes. To keep the type II error under control one may have to consider larger sample sizes. However, in cases where treatment effect size of at least one of the endpoints is likely to be small, the required sample size estimates can exceed reasonable bounds. Patel (1991) proposed an approach that adjusts the significance level for testing each primary endpoint based on the idea of restricting the null space. In Chuang-Stein et al. (2007), the upward adjustment to the significance levels is based on controlling an average type I error rate. In the scenario that statistical significance of each individual hypothesis is not required, we introduce a compromise testing approach in which the significance level for a co-primary endpoint is adjusted upward only if the treatment shows high significance in one (or more than one) of the remaining co-primary endpoints. The adjustment depends on the correlation among the endpoints: larger adjustment is needed for cases of smaller correlation. The method is applicable for the scenario where the null space is restricted. Our testing approach controls maximum joint false positive rate over the restricted null space.