Hypotheses and type I error in active-control noninferiority trials

A fundamental assumption in the design and analysis of an active-control noninferiority trial is that the active control is truly effective. If this assumption does not hold, i.e., the active control is not effective, a harmful drug may be approved based on the result of a noninferiority trial. The assessment of the assumption is usually based on statistically significant results of historical randomized clinical trials on the active control, in which the conclusion may be falsely positive. This false positive rate, however, is not taken into consideration in current noninferiority trial test procedures. In this paper, various possible hypotheses for noninferiority trials are presented. The noninferiority hypotheses correctly associated with the objective of noninferiority trials are suggested. However, since there are no data collected for placebo in a noninferiority trial, this hypothesis cannot be directly tested by using data from noninferiority studies alone. The claim of noninferiority is based on the significant test for the control effect in historical trials and the significant test for noninferiority in a current noninferiority trial with a given fraction retention or margin. The false positive rate associated with such noninferiority test procedure is defined in this paper. The simulation result demonstrates the magnitude of the false positive rate inflation associated with the noninferiority test procedure.