Global Health Trials Unit, Liverpool School of Tropical Medicine, Liverpool, UK.
Division of Biometrics I, OB/OTS/CDER, US FDA, Silver Spring, Maryland, USA.
J Biopharm Stat. 2023 Jul 4;33(4):488-501. doi: 10.1080/10543406.2023.2170393. Epub 2023 Feb 7.
Many clinical trials include time-to-event or survival data as an outcome. To compare two survival distributions, the log-rank test is often used to produce a -value for a statistical test of the null hypothesis that the two survival curves are identical. However, such a -value does not provide the magnitude of the difference between the curves regarding the treatment effect. As a result, the -value is often accompanied by an estimate of the hazard ratio from the proportional hazards model or Cox model as a measurement of treatment difference. However, one of the most important assumptions for Cox model is that the hazard functions for the two treatment groups are proportional. When the hazard curves cross, the Cox model could lead to misleading results and the log-rank test could also perform poorly. To address the problem of crossing curves in survival analysis, we propose the use of the win ratio method put forward by Pocock et al. as an estimand for analysing such data. The subjects in the test and control treatment groups are formed into all possible pairs. For each pair, the test treatment subject is labelled a winner or a loser if it is known who had the event of interest such as death. The win ratio is the total number of winners divided by the total number of losers and its standard error can be estimated using Bebu and Lachin method. Using real trial datasets and Monte Carlo simulations, this study investigates the power and type I error and compares the win ratio method with the log-rank test and Cox model under various scenarios of crossing survival curves with different censoring rates and distribution parameters. The results show that the win ratio method has similar power as the log-rank test and Cox model to detect the treatment difference when the assumption of proportional hazards holds true, and that the win ratio method outperforms log-rank test and Cox model in terms of power to detect the treatment difference when the survival curves cross.
许多临床试验将时间事件或生存数据作为结果。为了比较两种生存分布，对数秩检验通常用于产生统计检验零假设的 p 值，即两条生存曲线完全相同。然而，这样的 p 值并不能提供关于治疗效果的曲线之间差异的幅度。因此，p 值通常伴随着来自比例风险模型或 Cox 模型的风险比估计，作为治疗差异的度量。然而，Cox 模型最重要的假设之一是两组治疗的危险函数是成比例的。当危险曲线交叉时，Cox 模型可能导致误导性的结果，对数秩检验也可能表现不佳。为了解决生存分析中曲线交叉的问题，我们提出使用 Pocock 等人提出的赢率方法作为分析此类数据的估计量。在测试和对照治疗组中的受试者被组成所有可能的对。对于每一对，如果已知谁发生了感兴趣的事件，如死亡，则将测试治疗的受试者标记为赢家或输家。赢率是赢家的总数除以输家的总数，其标准误差可以使用 Bebu 和 Lachin 方法来估计。本研究使用真实试验数据集和蒙特卡罗模拟，在不同的交叉生存曲线和不同的删失率和分布参数情况下，比较了赢率方法与对数秩检验和 Cox 模型的功效和 I 型错误，并对这两种方法进行了比较。结果表明，当比例风险假设成立时，赢率方法与对数秩检验和 Cox 模型具有相似的检测治疗差异的功效，并且当生存曲线交叉时，赢率方法在检测治疗差异的功效方面优于对数秩检验和 Cox 模型。
