Interim Design Modifications in Time-to-Event Studies

We propose a flexible method for interim design modifications in time-to-event studies. With this method, it is possible to inspect the data at any time during the course of the study, without the need for prespecification of a learning phase, and to make certain types of design modifications depending on the interim data without compromising the Type I error risk. The method can be applied to studies designed with a conventional statistical test, fixed sample, or group sequential, even when no adaptive interim analysis and no specific method for design adaptations (such as combination tests) had been foreseen in the protocol. Currently, the method supports design changes such as an extension of the recruitment or follow-up period, as well as certain modifications of the number and the schedule of interim analyses as well as changes of inclusion criteria. In contrast to existing methods offering the same flexibility, our approach allows us to make use of the full interim information collected until the time of the adaptive data inspection. This includes time-to-event data from patients who have already experienced an event at the time of the data inspection, and preliminary information from patients still alive, even if this information is predictive for survival, such as early treatment response in a cancer clinical trial. Our method is an extension of the so-called conditional rejection probability (CRP) principle. It is based on the conditional distribution of the test statistic given the final value of the same test statistic from a subsample, namely the learning sample. It is developed in detail for the example of the logrank statistic, for which we derive this conditional distribution using martingale techniques.