Institute of Biostatistics and Clinical Research, University of Münster, Münster, Germany.
PLoS One. 2022 Jul 21;17(7):e0271094. doi: 10.1371/journal.pone.0271094. eCollection 2022.
The one-sample log-rank test is the method of choice for single-arm Phase II trials with time-to-event endpoint. It allows to compare the survival of patients to a reference survival curve that typically represents the expected survival under standard of care. The one-sample log-rank test, however, assumes that the reference survival curve is known. This ignores that the reference curve is commonly estimated from historic data and thus prone to sampling error. Ignoring sampling variability of the reference curve results in type I error rate inflation. We study this inflation in type I error rate analytically and by simulation. Moreover we derive the actual distribution of the one-sample log-rank test statistic, when the sampling variability of the reference curve is taken into account. In particular, we provide a consistent estimate of the factor by which the true variance of the one-sample log-rank statistic is underestimated when reference curve sampling variability is ignored. Our results are further substantiated by a case study using a real world data example in which we demonstrate how to estimate the error rate inflation in the planning stage of a trial.
单组样本对数秩检验是具有生存时间终点的单臂 II 期试验的首选方法。它允许将患者的生存与参考生存曲线进行比较，该参考生存曲线通常代表标准治疗下的预期生存。然而，单组对数秩检验假设参考生存曲线是已知的。这忽略了参考曲线通常是根据历史数据估计的，因此容易受到抽样误差的影响。忽略参考曲线的抽样变异性会导致 I 型错误率膨胀。我们通过分析和模拟研究了这种 I 型错误率的膨胀。此外，我们还推导出了当考虑参考曲线的抽样变异性时，单组对数秩检验统计量的实际分布。特别是，我们提供了一个一致的估计，即在忽略参考曲线抽样变异性时，单组对数秩统计量的真实方差被低估的倍数。我们的结果还通过一个真实世界数据的案例研究得到了进一步证实，我们在该案例研究中展示了如何在试验的规划阶段估计误差率膨胀。
