Mixture-based gatekeeping procedures in adaptive clinical trials

Clinical trials with data-driven decision rules often pursue multiple clinical objectives such as the evaluation of several endpoints or several doses of an experimental treatment. These complex analysis strategies give rise to "multivariate" multiplicity problems with several components or sources of multiplicity. A general framework for defining gatekeeping procedures in clinical trials with adaptive multistage designs is proposed in this paper. The mixture method is applied to build a gatekeeping procedure at each stage and inferences at each decision point (interim or final analysis) are performed using the combination function approach. An advantage of utilizing the mixture method is that it enables powerful gatekeeping procedures applicable to a broad class of settings with complex logical relationships among the hypotheses of interest. Further, the combination function approach supports flexible data-driven decisions such as a decision to increase the sample size or remove a treatment arm. The paper concludes with a clinical trial example that illustrates the methodology by applying it to develop an adaptive two-stage design with a mixture-based gatekeeping procedure.