Are restricted mean survival time methods especially useful for noninferiority trials?

Abstract

Background: Restricted mean survival time methods compare the areas under the Kaplan-Meier curves up to a time τ for the control and experimental treatments. Extraordinary claims have been made about the benefits (in terms of dramatically smaller required sample sizes) when using restricted mean survival time methods as compared to proportional hazards methods for analyzing noninferiority trials, even when the true survival distributions satisfy proportional hazardss.

Methods: Through some limited simulations and asymptotic power calculations, the authors compare the operating characteristics of restricted mean survival time and proportional hazards methods for analyzing both noninferiority and superiority trials under proportional hazardss to understand what relative power benefits there are when using restricted mean survival time methods for noninferiority testing.

Results: In the setting of low-event rates, very large targeted noninferiority margins, and limited follow-up past τ, restricted mean survival time methods have more power than proportional hazards methods. For superiority testing, proportional hazards methods have more power. This is not a small-sample phenomenon but requires a low-event rate and a large noninferiority margin.

Conclusion: Although there are special settings where restricted mean survival time methods have a power advantage over proportional hazards methods for testing noninferiority, the larger issue in these settings is defining appropriate noninferiority margins. We find the restricted mean survival time methods lacking in these regards.

Trial registration: ClinicalTrials.gov NCT00310180.

Keywords: Cox model; Log-rank test; proportional hazardss; randomized clinical trials; survival analysis.

Figures

Figure 1:

Noncentrality parameters for testing noninferiority (left panels) and superiority (right panels) using proportional hazards (blue solid lines) and RMST methods (red dashed lines). Top panels (A, B), middle panels (C, D) and lower panels (E, F) are for low, medium and high event rates as in Tables 1 and 2. Horizontal axes correspond to noninferiority margin hazard ratios for noninferiority panels (A,C,E) and the inverses of the targeted hazard ratio alternatives for the superiority panels (B, D, F).