Abstract
We discuss the problem of properly defining treatment superiority through the specification of hypotheses in clinical trials. The need to precisely define the notion of superiority in a one-sided hypothesis test problem has been well recognized by many authors. Ideally designed null and alternative hypotheses should correspond to a partition of all possible scenarios of underlying true probability models P={P(ω):ω∈Ω} such that the alternative hypothesis Ha={P(ω):ω∈Ωa} can be inferred upon the rejection of null hypothesis Ho={P(ω):ω∈Ω(o)} However, in many cases, tests are carried out and recommendations are made without a precise definition of superiority or a specification of alternative hypothesis. Moreover, in some applications, the union of probability models specified by the chosen null and alternative hypothesis does not constitute a completed model collection P (i.e., H(o)∪H(a) is smaller than P). This not only imposes a strong non-validated assumption of the underlying true models, but also leads to different superiority claims depending on which test is used instead of scientific plausibility. Different ways to partition P fro testing treatment superiority often have different implications on sample size, power, and significance in both efficacy and comparative effectiveness trial design. Such differences are often overlooked. We provide a theoretical framework for evaluating the statistical properties of different specification of superiority in typical hypothesis testing. This can help investigators to select proper hypotheses for treatment comparison inclinical trial design.