  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.
