Single-arm studies in the early development phases of new treatments are not uncommon in the context of rare diseases or in paediatrics. If an assessment of efficacy is to be made at the end of such a study, the observed endpoints can be compared with reference values that can be derived from historical data. For a time-to-event endpoint, a statistical comparison with a reference curve can be made using the one-sample log-rank test. In order to ensure the interpretability of the results of this test, the role of the reference curve is crucial. This quantity is often estimated from a historical control group using a parametric procedure. Hence, it should be noted that it is subject to estimation uncertainty. However, this aspect is not taken into account in the one-sample log-rank test statistic. We analyse this estimation uncertainty for the common situation that the reference curve is estimated parametrically using the maximum likelihood method, and indicate how the variance estimation of the one-sample log-rank test can be adapted in order to take this variability into account. The resulting test procedures are illustrated using a data example and analysed in more detail using simulations, particularly in comparison with established two-sample methods.

翻译：在新疗法的早期开发阶段，针对罕见疾病或儿科领域的单臂研究并不少见。若需在此类研究结束时进行疗效评估，可将观察到的终点指标与从历史数据中推导的参考值进行比较。对于时间-事件终点，可使用单样本对数秩检验与参考曲线进行统计比较。为确保该检验结果的可解释性，参考曲线的作用至关重要。该量值通常通过参数化方法从历史对照组中估计得出，因此需注意其存在估计不确定性。然而，单样本对数秩检验统计量并未考虑这一方面。本文针对参考曲线通过最大似然法进行参数估计的常见情况，分析了这种估计不确定性，并阐明了如何调整单样本对数秩检验的方差估计以纳入该变异性。通过数据实例演示了所得检验程序，并借助模拟研究（特别是与成熟的双样本方法进行比较）进行了更深入的分析。