Magirr, Dominic, Wang, Craig, Deng, Xinlei and Baillie, Mark (2025) Efficiency of nonparametric two-sample superiority tests based on restricted mean survival time under proportional hazards. Arxiv.

Abstract

Background

For randomized clinical trials with a time-to-event endpoint, proportional hazard models are typically used to estimate treatment effects and log-rank tests are commonly used for hypothesis testing. The summary measure of the primary estimand is frequently a hazard ratio. However, there is growing support for replacing this approach with a model-free summary measure and assumption-lean analysis method—a trend already observed for continuous and binary endpoints. One alternative is to base the analysis on the difference in restricted mean survival time (RMST) at a fixed timepoint. In a simple setting without covariates, an assumption-lean analysis can be achieved using nonparametric methods such as Kaplan-Meier estimation. The main advantage of moving to a model-free summary measure and assumption-lean analysis is that the interpretation of results no longer depends on the validity of the proportional hazards assumption. The potential disadvantage is that the nonparametric analysis may lose efficiency when the proportional hazards assumption holds. There is disagreement in recent literature on this issue, with some studies indicating similar efficiency between the two approaches, while others highlight significant advantages for proportional hazards models.

Methods

Existing asymptotic results are presented, and a simulation study is conducted to compare the efficiency of a proportional hazards analysis with a nonparametric analysis of the difference in RMST in a superiority trial. Previous studies have examined the effect of event rates on relative efficiency, as well as the impact of the censoring distribution separately. This investigation extends these findings by exploring the interactive effect of event rate and censoring distribution, helping to clarify the conflicting results from earlier research. Several illustrative examples are provided.

Results

In scenarios with high event rates and/or substantial censoring across a large proportion of the study window, and when both methods have access to the same amount of data, relative efficiency is close to unity. However, in cases with low or moderate event rates but when censoring is concentrated at the end of the study window, the proportional hazards analysis has a considerable efficiency advantage.

Conclusions

There are realistic combinations of event rates and censoring distributions where, if the proportional hazards assumption holds, the proportional hazards analysis is more efficient than a nonparametric RMST-based test. Additionally, the proportional hazards analysis can benefit from data collected beyond the restriction time. Therefore, it is inappropriate to assume that switching to a nonparametric RMST-based test would generally result in negligible efficiency loss, particularly when additional follow-up data is available but not used in the primary analysis. A key take-away from this study, is that the implications of requiring assumption-lean analysis methods should be carefully considered during the trial design phase.

Item Type:	Article
Keywords:	Hazard ratio, Restricted mean survival, Proportional hazards
Date Deposited:	01 Jul 2025 00:46
Last Modified:	01 Jul 2025 00:46
URI:	https://oak.novartis.com/id/eprint/55653