Chen Shuyu, Wang Mengyao, Zhou Xingyou, Zhang Wenbin, Zhang Chengfeng, Chen Zheng
Department of Biostatistics, School of Public Health (Guangdong Provincial Key Laboratory of Tropical Disease Research), Southern Medical University, No. 1023, South Shatai Road, Guangzhou, China.
State Key Laboratory of Multi-Organ Injury Prevention and Treatment, Guangzhou, China.
BMC Med Res Methodol. 2025 May 3;25(1):123. doi: 10.1186/s12874-025-02563-9.
Restricted mean survival time (RMST) quantifies survival benefits in single-endpoint analysis, while restricted mean time lost (RMTL) measures event-related time loss in competing risks settings. Both provide clinically intuitive interpretations of treatment effects without relying on proportional hazards assumptions or parametric distributions. While existing RMST/RMTL methods focus primarily on two-group comparisons, multi-arm trials are common in practice. However, asymptotic approaches for these metrics suffer from inflated type I error in small samples, limiting their reliability.
We propose a global test framework using variable transformation methods (e.g., log, clog-log, arcsine square root, logit), which is applicable to multi-group comparisons of RMST and extends to RMTL in the presence of competing risks. Monte-Carlo simulations were conducted to evaluate type I error and power under various scenarios, and two illustrative examples were provided.
Simulations demonstrated that transformed RMST and RMTL global tests effectively controlled type I error across small samples and high censoring rates, while improving power compared to untransformed methods. For single-endpoint analysis, the RMST arcsine square root transformation is recommended. In competing risks settings, RMTL logit transformation is preferred when the event of interest occurs more frequently than competing events, whereas clog-log transformation performs better when competing events dominate.
The proposed transformation-based global tests offer researchers a flexible, assumption-free tool to compare treatment effects across multiple groups with enhanced reliability and interpretability. Additionally, an R package "compRM" was developed to implement the proposed methods.
受限平均生存时间（RMST）在单终点分析中量化生存获益，而受限平均时间损失（RMTL）在竞争风险环境中衡量与事件相关的时间损失。两者都能在不依赖比例风险假设或参数分布的情况下，对治疗效果提供临床直观的解释。虽然现有的RMST/RMTL方法主要侧重于两组比较，但多臂试验在实际中很常见。然而，这些指标的渐近方法在小样本中存在I型错误膨胀的问题，限制了它们的可靠性。
我们提出了一个使用变量变换方法（如对数、互补对数-对数、反正弦平方根、对数it）的全局检验框架，该框架适用于RMST的多组比较，并在存在竞争风险的情况下扩展到RMTL。进行了蒙特卡罗模拟，以评估各种情况下的I型错误和检验效能，并提供了两个说明性示例。
模拟表明，变换后的RMST和RMTL全局检验在小样本和高删失率情况下有效地控制了I型错误，同时与未变换的方法相比提高了检验效能。对于单终点分析，建议使用RMST反正弦平方根变换。在竞争风险环境中，当感兴趣的事件比竞争事件更频繁发生时，RMTL对数it变换更可取，而当竞争事件占主导时，互补对数-对数变换表现更好。
所提出的基于变换的全局检验为研究人员提供了一种灵活、无需假设的工具，以比较多组之间的治疗效果，具有更高的可靠性和可解释性。此外，还开发了一个R包“compRM”来实现所提出的方法。
