Medical University of Vienna, Center for Medical Data Science, Institute of Medical Statistics, Austria.
Merck Healthcare KGaA, Germany.
Stat Methods Med Res. 2024 Apr;33(4):589-610. doi: 10.1177/09622802241231497. Epub 2024 Mar 11.
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.
生存时间是许多随机对照试验的主要终点，并且在假设比例风险的情况下，通常通过风险比来量化治疗效果。人们越来越意识到，在许多情况下，这种假设是先验违反的，例如，由于药物作用的延迟出现。在这些情况下，风险比估计的解释是模糊的，并且需要对替代参数进行统计推断，以量化治疗效果。我们认为生存概率或分位数的差异或比值、受限平均生存时间的差异以及平均风险比是感兴趣的。通常，需要报告多个这样的参数来评估可能的治疗益处，并且在确认性试验中，需要调整相应的推断程序以进行多重性调整。简单的 Bonferroni 调整可能过于保守，因为感兴趣的不同参数通常显示出相当大的相关性。因此，需要进行同时考虑相关性的推断程序。通过使用所提到参数的计数过程表示，我们证明了它们的估计值是渐近多变量正态的，并且我们提供了它们协方差矩阵的估计值。我们根据参数的多重检验程序和同时置信区间提出建议。此外，对数秩检验也可以包含在该框架中。通过模拟研究了有限样本的Ⅰ型错误率和功效。该方法通过肿瘤学的一个示例进行了说明。在 R 包 nph 中提供了软件实现。
