Survival time is the primary endpoint of many randomized controlled trials, and a treatment effect is typically quantified by the hazard ratio under the assumption of proportional hazards. Awareness is increasing that in many settings this assumption is a-priori violated, e.g. due to delayed onset of drug effect. In these cases, interpretation of the hazard ratio estimate is ambiguous and statistical inference for alternative parameters to quantify a treatment effect is warranted. We consider differences or ratios of milestone survival probabilities or quantiles, differences in restricted mean survival times and an average hazard ratio to be of interest. Typically, more than one such parameter needs to be reported to assess possible treatment benefits, and in confirmatory trials the according inferential procedures need to be adjusted for multiplicity. By using the counting process representation of the mentioned parameters, we show that their estimates are asymptotically multivariate normal and we propose according parametric multiple testing procedures and simultaneous confidence intervals. Also, the logrank test may be included in the framework. Finite sample type I error rate and power are studied by simulation. The methods are illustrated with an example from oncology. A software implementation is provided in the R package nph.

翻译：生存时间是许多随机对照试验的主要终点，在比例风险假设下，治疗效果通常通过风险比进行量化。越来越多的认识表明，在许多情况下这一假设先验地被违背，例如由于药物效应的延迟起效。在这些情况下，风险比估计的解释存在歧义，需要对替代参数进行统计推断以量化治疗效果。我们考虑里程碑生存概率的差异或比率、分位数、受限平均生存时间的差异以及平均风险比作为关注参数。通常需要报告多个此类参数以评估可能的治疗获益，在验证性试验中，相应的推断过程需要针对多重性进行调整。通过利用上述参数的计数过程表示，我们证明其估计渐近服从多元正态分布，并据此提出参数化多重检验程序和同时置信区间。此外，logrank检验也可纳入该框架。通过模拟研究了有限样本下的第一类错误率和检验效能。通过肿瘤学实例展示了这些方法。所提供的软件实现包含在R包nph中。