Restricted Mean Survival Time-Based Adjustment of Hazard Ratio Confidence Intervals

Music City Center 

Restricted mean survival time ratios (RMSTRs) are widely used as an alternative to hazard ratios (HRs) from Cox proportional hazards models when the proportional hazards (PH) assumption is violated. However, RMSTRs are sensitive to censoring and prone to bias, whereas HRs are generally more robust. Thus, it is desirable to preserve the HR estimate from Cox models while using inference from RMSTRs. When the PH violation is mild or moderate, HRs remain interpretable, though their confidence intervals (CIs) may widen due to increased variation from crossing survival curves. We introduce a method to adjust HR CIs using RMSTR-derived variance estimates, ensuring inference consistency. Additionally, we propose a guideline to classify PH assumption violations as mild. Through simulations, we compare our approach with weighted Cox regression, demonstrating that HRs exhibit a linear relationship with weighted average HRs, supporting their robustness. Finally, we apply our method to real-world data with mild PH violation, showcasing its practical utility.

Restricted mean survival time ratio

Cox proportional hazard assumption

Weighted Cox model 

Biometrics Section