A Direct Approach to Simultaneous Tests of Superiority and Noninferiority with Multiple Endpoints

Simultaneous tests of superiority and non-inferiority hypotheses on multiple endpoints are often performed in clinical trials to demonstrate that a new treatment is superior over a control on at least one endpoint and non-inferior on the remaining endpoints. Existing methods tackle this problem by testing the superiority and non-inferiority hypotheses separately and control the Type I error rate each at $\alpha$ level. In this paper we propose a unified approach to testing the superiority and non-inferiority hypotheses simultaneously. The proposed approach is based on the UI-IU test and the least favorable configurations of the combined superiority and non-inferiority hypotheses, which leads to the solution of an adjusted significance level $\alpha'$ for marginal tests that controls the overall Type I error rate at pre-defined $\alpha$. Simulations show that the proposed approach maintains a higher power than existing methods in the settings under investigation. Since the adjusted significance level $\alpha'$ is obtained by controlling the Type I error rate at $\alpha$, one can easily construct the exact $(1 - \alpha)\%$ simultaneous confidence intervals for treatment effects on all endpoints. The proposed approach is illustrated with two real examples.