Department of Neurology and Neurological Sciences, Stanford University, Palo Alto, CA, USA.
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China.
Stat Methods Med Res. 2023 Jun;32(6):1082-1099. doi: 10.1177/09622802231158735. Epub 2023 Apr 4.
The restricted mean survival time (RMST), which evaluates the expected survival time up to a pre-specified time point , has been widely used to summarize the survival distribution due to its robustness and straightforward interpretation. In comparative studies with time-to-event data, the RMST-based test has been utilized as an alternative to the classic log-rank test because the power of the log-rank test deteriorates when the proportional hazards assumption is violated. To overcome the challenge of selecting an appropriate time point , we develop an RMST-based omnibus Wald test to detect the survival difference between two groups throughout the study follow-up period. Treating a vector of RMSTs at multiple quantile-based time points as a statistical functional, we construct a Wald test statistic and derive its asymptotic distribution using the influence function. We further propose a new procedure based on the influence function to estimate the asymptotic covariance matrix in contrast to the usual bootstrap method. Simulations under different scenarios validate the size of our RMST-based omnibus test and demonstrate its advantage over the existing tests in power, especially when the true survival functions cross within the study follow-up period. For illustration, the proposed test is applied to two real datasets, which demonstrate its power and applicability in various situations.
限制平均生存时间（RMST），用于评估特定时间点之前的预期生存时间，由于其稳健性和直接的解释，已被广泛用于总结生存分布。在具有生存时间数据的比较研究中，基于 RMST 的检验已被用作经典对数秩检验的替代方法，因为当比例风险假设被违反时，对数秩检验的功效会降低。为了克服选择适当时间点的挑战，我们开发了一种基于 RMST 的综合 Wald 检验，以检测整个研究随访期间两组之间的生存差异。将多个基于分位数的时间点的 RMST 向量视为统计函数，我们构建了 Wald 检验统计量，并使用影响函数推导出其渐近分布。我们进一步提出了一种基于影响函数的新方法来估计渐近协方差矩阵，而不是常用的自举方法。在不同场景下的模拟验证了我们基于 RMST 的综合检验的大小，并证明了它在功效方面优于现有检验，尤其是当真实生存函数在研究随访期间相交时。为了说明这一点，我们将提出的检验应用于两个真实数据集，展示了它在各种情况下的功效和适用性。
