Simultaneous tests of non inferiority and superiority in three-arm clinical studies with heterogeneous variance

Non inferiority (NI) trials with the possibility of multiple experimental treatments have been increasingly used to find substitutes for standard therapies (e.g., to reduce side effects). NI trials seek to determine whether an experimental treatment can provide a suitable replacement for the standard treatment by examining the clinical significance of the loss of efficacy that is associated with the new treatment. In this article, we focus on three-arm NI trials, which include a placebo to provide direct verification of the assay sensitivity. Furthermore, it is reasonable to conduct superiority tests for experimental treatments that have been confirmed to be non inferior to the standard treatment. Several methodologies have recently been developed to provide stage-wise test procedures for this purpose. However, the applicability of these methods is limited owing to their requirement of homogeneity of variance. In this article, we seek to generalize the existing methods to more practical settings that allow the treatment variance to be heterogeneous. We also discuss sample size determination when the test power is given. Clinical examples are used to illustrate our proposed procedures.