Adaptive promising zone design for cancer immunotherapy with heterogeneous delayed treatment effect

Indirect mechanisms of cancer immunotherapies result in delayed treatment effects that vary among patients. Consequently, the use of the log-rank test in trial design and analysis can lead to significant power loss and pose additional challenges for interim decisions in adaptive designs. In this paper, we describe patients' survival using a piecewise proportional hazard model with random lag time and propose an adaptive promising zone design for cancer immunotherapy with heterogeneous delayed effects. We provide solutions for calculating conditional power and adjusting the critical value for the log-rank test with interim data. We divide the sample space into three zones - unfavourable, promising, and favourable -based on re-estimations of the survival parameters, the log-rank test statistic at the interim analysis, and the initial and maximum sample sizes. If the interim results fall into the promising zone, the sample size is increased; otherwise, it remains unchanged. We show through simulations that our proposed approach has greater overall power than the fixed sample design and similar power to the matched group sequential trial. Furthermore, we confirm that critical value adjustment effectively controls the type I error rate inflation. Finally, we provide recommendations on the implementation of our proposed method in cancer immunotherapy trials.