The purpose of a non-inferiority trial is to assert the efficacy of an experimental treatment compared with a reference treatment by showing that the experimental treatment retains a substantial proportion of the efficacy of the reference treatment. Statistical methods have been developed to test multiple experimental treatments in three-arm non-inferiority trials. In this paper, we report the development of procedures that simultaneously test the non-inferiority and the superiority of experimental treatments after the assay sensitivity has been established. The advantage of the proposed test procedures is the additional ability to identify superior treatments while retaining an non-inferiority testing power comparable to that of existing testing procedures. Single-step and stepwise procedures are derived and then compared with each other to determine their relative testing power and testing error in a simulation study. Finally, the suggested procedures are illustrated with two clinical examples.
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