Issues of simultaneous tests for noninferiority and superiority.

In simultaneous testing for noninferiority and superiority, Morikawa and Yoshida (Morikawa, T., Yoshida, M. (1995). A useful testing strategy in phase III trails: Combined test of superiority and test of equivalence. J. Biopharmaceutical Statistics 5:297-306) argue that multiplicity adjustment is not necessary by using the closed testing (CT) principle. In fact, using the same argument, no multiplicity adjustment is necessary in simultaneous testing of any number of nested null hypotheses. However, simultaneous testing of many nested null hypotheses is problematic in a confirmatory trial because such simultaneous testing is similar to post-hoc specification of the null hypothesis. Thus, simultaneous testing for noninferiority and superiority may be viewed as an initial step towards exploratory analysis and may be best used cautiously in confirmatory evaluation.