Institute of Biostatistics and Clinical Research, University of Muenster, Muenster, Germany.
Stat Methods Med Res. 2020 Oct;29(10):2814-2829. doi: 10.1177/0962280220906590. Epub 2020 Mar 4.
The one-sample log-rank test allows to compare the survival of a single sample with a prefixed reference survival curve. It naturally applies in single-arm phase IIa trials with time-to-event endpoint. Several authors have described that the original one-sample log-rank test is conservative when sample size is small and have proposed strategies to correct the conservativeness. Here, we propose an alternative approach to improve the one-sample log-rank test. Our new one-sample log-rank statistic is based on the unique transformation of the underlying counting process martingale such that the moments of the limiting normal distribution have no shared parameters. Simulation results show that the new one-sample log-rank test gives type I error rate and power close to the nominal levels also when sample size is small, while relevantly reducing the required sample size to achieve the desired power as compared to current approaches to design studies to compare the survival outcome of a sample with a reference.
单样本对数秩检验可用于比较单个样本的生存情况与预先设定的参考生存曲线。它自然适用于具有时间事件终点的单臂 IIa 期临床试验。有几位作者描述了在样本量较小时，原始单样本对数秩检验具有保守性，并提出了校正保守性的策略。在这里，我们提出了一种改进单样本对数秩检验的替代方法。我们的新单样本对数秩统计量基于基础计数过程鞅的唯一变换，使得极限正态分布的矩没有共享参数。模拟结果表明，即使在样本量较小时，新的单样本对数秩检验也能保持 I 型错误率和功效接近名义水平，同时与当前用于设计研究以比较样本与参考的生存结果的方法相比，显著减少了实现所需功效所需的样本量。
