Decision-Theoretic Views on Simultaneous Testing of Superiority and Noninferiority

In a simultaneous testing of noninferiority and superiority in clinical trials, there is no multiplicity penalty. Ng (2003), however, argues that even though there is no inflation of the Type I error rate, this type of simultaneous testing is problematic because it may lead to loss of power in the subsequent confirmatory trial. And he recommends to conduct only one test chosen on the basis of the sponsor's preliminary assessment. We view the question of whether one should simultaneously test for noninferiority and superiority from a decision-theoretic view point. We develop the loss function approach implicit in Ng's research and compare his recommendation to simultaneous testing procedures indexed by a variety of design parameters. We find that the simultaneous testing procedure generally provides smaller loss than Ng's method, except when the prior distribution allocates a large probability to equivalence of the two treatments.