Multi-group global tests for restricted mean survival time and restricted mean time lost: a variable transformation...

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.