A two-stage group-sequential design for delayed treatment responses with the possibility of trial restart

Common statistical theory applicable to confirmatory phase III trial designs usually assumes that patients are enrolled simultaneously and there is no time gap between enrollment and outcome observation. However, in practice, patients are enrolled successively and there is a lag between the enrollment of a patient and the measurement of the primary outcome. For single-stage designs, the difference between theory and practice only impacts on the trial duration but not on the statistical analysis and its interpretation. For designs with interim analyses, however, the number of patients already enrolled into the trial and the number of patients with available outcome measurements differ, which can cause issues regarding the statistical analyses of the data. The main issue is that current methodologies either imply that at the time of the interim analysis there are so-called pipeline patients whose data are not used to make a statistical decision (like stopping early for efficacy) or the enrollment into the trial needs to be at least paused for interim analysis to avoid pipeline patients. There are methods for delayed responses available that introduced error-spending stopping boundaries for the enrollment of patients followed by critical values to reject the null hypothesis in case the stopping boundaries have been crossed beforehand. Here, we will discuss other solutions, considering different boundary determination algorithms using conditional power and introducing a design allowing for recruitment restart while keeping the type I error rate controlled.