PDF(Pubmed)
Abstract：
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, for example, 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. A simple Bonferroni adjustment may be too conservative because the different parameters of interest typically show considerable correlation. Hence simultaneous inference procedures that take into account the correlation are warranted. By using the counting process representation of the mentioned parameters, we show that their estimates are asymptotically multivariate normal and we provide an estimate for their covariance matrix. We propose according to the 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.
摘要：
生存时间是许多随机对照试验的主要终点，治疗效果通常在比例风险假设下通过风险比进行量化。意识到在许多情况下，这个假设是先验违反的，例如,由于药物作用的延迟发作。在这些情况下,对风险比估计的解释是模糊的，并且有必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或分位数的差异或比率，限制平均生存时间的差异，和平均危险比值得关注。通常,需要报告一个以上的参数以评估可能的治疗益处，在验证性试验中，根据推理程序需要针对多重性进行调整。简单的Bonferroni调整可能过于保守，因为不同的感兴趣参数通常显示出相当大的相关性。因此，需要考虑相关性的同时推理程序。通过使用上述参数的计数过程表示，我们证明了它们的估计是渐近多变量正态的，并给出了它们的协方差矩阵的估计。我们根据参数提出了多个测试程序和同时的置信区间。此外，logrank测试可能包含在框架中。通过仿真研究了有限样本I型错误率和功率。用来自肿瘤学的实例说明所述方法。在R包nph中提供了软件实现。
