The log-rank test and the Cox proportional hazards model are commonly used to compare time-to-event data in clinical trials, as they are most powerful under proportional hazards. But there is a loss of power if this assumption is violated, which is the case for some new oncology drugs like immunotherapies. We consider a two-stage test procedure, in which the weighting of the log-rank test statistic depends on a pre-test of the proportional hazards assumption. I.e., depending on the pre-test either the log-rank or an alternative test is used to compare the survival probabilities. We show that if naively implemented this can lead to a substantial inflation of the type-I error rate. To address this, we embed the two-stage test in a permutation test framework to keep the nominal level alpha. We compare the operating characteristics of the two-stage test with the log-rank test and other tests by clinical trial simulations.

翻译：对数秩检验和Cox比例风险模型常用于比较临床试验中的时间事件数据，因为它们在比例风险假设下具有最大检验效能。但当该假设被违反时（如某些新型肿瘤药物如免疫疗法的情况），检验效能会下降。本文考虑一种两阶段检验程序，其中对数秩检验统计量的加权取决于对比例风险假设的前期检验结果。即根据前期检验结果，选用对数秩检验或替代检验来比较生存概率。我们证明，若简单实施该方法会导致I类错误率显著膨胀。为此，我们将两阶段检验嵌入置换检验框架以维持名义显著性水平alpha。通过临床试验模拟，我们比较了两阶段检验与对数秩检验及其他检验的操作特征。