Confirmatory Adaptive Hypothesis Tests in Markovian Illness-Death Models

Abstract: Classic adaptive designs for time-to-event trials are based on the log-rank statistic and its increments. Thereby, only information from the time-to-event endpoint on which the selected log-rank statistic is based may be used for data-dependent design modifications in interim analyses. Further information (e.g. surrogate parameters) may not be used. As pointed out in a letter by P. Bauer and M. Posch in 2004, adaptive tests on overall survival (OS) based on the log-rank statistic do in general not control the significance level if interim information on progression-free survival (PFS) is used for sample size adjustments, because progression is associated with increased risk of death. In contrast, in adaptive designs for time-to-event trials, which are constructed according to the principle of patient-wise separation, all trial data observed in interim analyses may be used for design modifications without compromizing type one error rate control. But by design, this comes at the price of incomplete use of the primary endpoint data in the final test decision or worst-case considerations which lead to a loss of power. Thus, the patient-wise separation approach cannot be regarded as a general solution to the problem described by Bauer and Posch. We address this problem within the framework of a comprehensive independent increments approach. We develop adaptive tests on OS in which sample size adjustments may be based on the observed interim data of both OS and PFS, while avoiding the problems of the patient-wise separation approach. We provide this methodology for both single-arm trials, in which a new therapy is compared with a pre-specified deterministic reference, and randomized trials, in which a new therapy is compared with a concurrent control group. The underlying assumption is that the joint distribution of OS and PFS is induced by a Markovian illness-death model.