On Adaptive Extensions of Group Sequential Trials for Clinical Investigations
In group sequential trials, it is important to obtain adequate data to assess overall benefits and risks of an experimental treatment for patients. To achieve this goal, we provide a general, formal framework for adaptively extending a group sequential trial to stop at any interim analysis time, often after a significance boundary for a clinical endpoint is crossed. For statistical inference, we propose to order the sample space by a class of well-ordered group sequential tests. On this basis, we develop a unified sequential statistical inference approach that is applicable to both interim monitoring and final analysis. We also show that the new ordering provides the foundation for the repeated confidence intervals procedure of Jennison and Turnbull.