Formulating appropriate statistical hypotheses for treatment comparison in clinical trial design and analysis

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 H_o={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.