Global Test for Superiority and Non-Inferiority Trials with Functional Endpoints Data

The global two-sided test for functional means difference got much attention in the literary works. While the global one-sided test for functional means difference has not been studied. However, that could have some applications and implications for longitudinal trials or trials with functional data outcomes. This work introduced superiority and noninferiority hypothesis tests for functional data outcomes, which were viewed as a one-sided problem for functional mean differences. Two global tests statistic have been proposed: a test based on integral and a test based on supremum. The performances of the tests have been evaluated via a simulation example. Both tests got an estimated actual type I error closer to the nominal type I error. The test based on supremum got good estimated power in all considered cases of the alternative hypothesis, while the test based on integral got very poor power performances for some cases of considered alternative hypothesis.