Group sequential designs for clinical trials when the maximum sample size is uncertain

Motivated by the experience of COVID-19 trials, we consider clinical trials in the setting of an emerging disease in which the uncertainty of natural disease course and potential treatment effects makes advance specification of a sample size challenging. One approach to such a challenge is to use a group sequential design to allow the trial to stop on the basis of interim analysis results as soon as a conclusion regarding the effectiveness of the treatment under investigation can be reached. As such a trial may be halted before a formal stopping boundary is reached, we consider the final analysis under such a scenario, proposing alternative methods for when the decision to halt the trial is made with or without knowledge of interim analysis results. We address the problems of ensuring that the type I error rate neither exceeds nor falls unnecessarily far below the nominal level. We also propose methods in which there is no maximum sample size, the trial continuing either until the stopping boundary is reached or it is decided to halt the trial.