Nested combination tests with a time-to-event endpoint using a short-term endpoint for design adaptations.

Adaptive trial methodology for multiarmed trials and enrichment designs has been extensively discussed in the past. A general principle to construct test procedures that control the family-wise Type I error rate in the strong sense is based on combination tests within a closed test. Using survival data, a problem arises when using information of patients for adaptive decision making, which are under risk at interim. With the currently available testing procedures, either no testing of hypotheses in interim analyses is possible or there are restrictions on the interim data that can be used in the adaptation decisions as, essentially, only the interim test statistics of the primary endpoint may be used. We propose a general adaptive testing procedure, covering multiarmed and enrichment designs, which does not have these restrictions. An important application are clinical trials, where short-term surrogate endpoints are used as basis for trial adaptations, and we illustrate how such trials can be designed. We propose statistical models to assess the impact of effect sizes, the correlation structure between the short-term and the primary endpoint, the sample size, the timing of interim analyses, and the selection rule on the operating characteristics.