Jachno Kim, Heritier Stephane, Wolfe Rory
School of Public Health and Preventive Medicine, Monash University, Melbourne, Victoria, Australia.
BMC Med Res Methodol. 2021 Aug 28;21(1):177. doi: 10.1186/s12874-021-01372-0.
Non-proportional hazards are common with time-to-event data but the majority of randomised clinical trials (RCTs) are designed and analysed using approaches which assume the treatment effect follows proportional hazards (PH). Recent advances in oncology treatments have identified two forms of non-PH of particular importance - a time lag until treatment becomes effective, and an early effect of treatment that ceases after a period of time. In sample size calculations for treatment effects on time-to-event outcomes where information is based on the number of events rather than the number of participants, there is crucial importance in correct specification of the baseline hazard rate amongst other considerations. Under PH, the shape of the baseline hazard has no effect on the resultant power and magnitude of treatment effects using standard analytical approaches. However, in a non-PH context the appropriateness of analytical approaches can depend on the shape of the underlying hazard.
A simulation study was undertaken to assess the impact of clinically plausible non-constant baseline hazard rates on the power, magnitude and coverage of commonly utilized regression-based measures of treatment effect and tests of survival curve difference for these two forms of non-PH used in RCTs with time-to-event outcomes.
In the presence of even mild departures from PH, the power, average treatment effect size and coverage were adversely affected. Depending on the nature of the non-proportionality, non-constant event rates could further exacerbate or somewhat ameliorate the losses in power, treatment effect magnitude and coverage observed. No single summary measure of treatment effect was able to adequately describe the full extent of a potentially time-limited treatment benefit whilst maintaining power at nominal levels.
Our results show the increased importance of considering plausible potentially non-constant event rates when non-proportionality of treatment effects could be anticipated. In planning clinical trials with the potential for non-PH, even modest departures from an assumed constant baseline hazard could appreciably impact the power to detect treatment effects depending on the nature of the non-PH. Comprehensive analysis plans may be required to accommodate the description of time-dependent treatment effects.
生存时间数据中，非比例风险很常见，但大多数随机临床试验（RCT）在设计和分析时采用的方法都假定治疗效果符合比例风险（PH）。肿瘤治疗领域的最新进展发现了两种特别重要的非PH形式——治疗开始起效前的时间滞后，以及一段时间后停止的早期治疗效果。在基于事件数量而非参与者数量计算治疗对生存时间结局的效果的样本量时，除其他考虑因素外，正确设定基线风险率至关重要。在PH假设下，使用标准分析方法时，基线风险的形状对所得功效和治疗效果大小没有影响。然而，在非PH情况下，分析方法的适用性可能取决于潜在风险的形状。
进行了一项模拟研究，以评估临床上合理的非恒定基线风险率对常用的基于回归的治疗效果测量指标的功效、大小和覆盖范围的影响，以及对具有生存时间结局的RCT中使用的这两种非PH形式的生存曲线差异检验的影响。
即使与PH有轻微偏差，功效、平均治疗效果大小和覆盖范围也会受到不利影响。根据非比例性的性质，非恒定事件发生率可能会进一步加剧或在一定程度上减轻观察到的功效、治疗效果大小和覆盖范围的损失。没有单一的治疗效果汇总测量指标能够在保持名义水平功效的同时充分描述潜在的限时治疗益处的全部范围。
我们的结果表明，当预期治疗效果存在非比例性时，考虑合理的潜在非恒定事件发生率的重要性增加。在规划可能存在非PH的临床试验时，根据非PH的性质，即使与假定的恒定基线风险有适度偏差，也可能会显著影响检测治疗效果的功效。可能需要综合分析计划来描述时间依赖性治疗效果。
