We present a method for estimating the correlation between log-rank test statistics evaluating separate null hypotheses for two time-to-event endpoints. The correlation is estimated using subject-level data by a non-parametric approach based on the independent and identically distributed (iid) decomposition of the log-rank test statistic under any alternative. Using the iid decomposition, we are able to make an assumption-lean estimation of the correlation. A motivating example using the developed approach is provided. Here, we illustrate how the suggested approach can be used to give a realistic quantification of expected conjunctive power that can guide the design of a new randomized clinical trial using historical data. Finally, we investigate the method's finite sample properties via a simulation study that confirms unbiased and consistent behavior of the proposed approach. In addition, the simulation study gives insight into the effects of censoring on the correlation between the log-rank test statistics.

翻译：我们提出了一种方法，用于评估两个时间-事件终点的独立零假设时，对数秩检验统计量之间的相关性估计。该方法基于对数秩检验统计量在任何备择假设下的独立同分布分解，采用非参数方法，利用个体水平数据来估计相关性。通过独立同分布分解，我们能够对相关性进行假设宽松的估计。本文提供了一个使用所开发方法的激励性示例。在此示例中，我们说明了如何利用所建议的方法对预期联合功效进行现实量化，从而指导利用历史数据设计新的随机临床试验。最后，我们通过模拟研究考察了该方法的有限样本性质，结果证实了所提方法具有无偏且一致的行为。此外，模拟研究还深入探讨了删失对对数秩检验统计量间相关性的影响。