Restricted mean survival time approach versus time-varying coefficient Cox model for quantifying treatment effect when hazards are non-proportional.

BACKGROUND

Although the Cox time-varying coefficient (TVC) model has been developed to address non-proportional hazard (PH), its use remains underexplored. Instead, the restricted mean survival time (RMST) has been widely used in non-PH settings to quantify treatment effects using life expectancy ratio (LER) and life expectancy difference (LED).

METHODS

This study explores a novel extension of the Cox TVC model under non-PH to generate LER and LED to enable a direct comparison with RMST based on flexible parametric survival model (FPM). An intensive simulation study was conducted to compare the performance of FPM to the Cox TVC model under PH and non-PH assumptions. The survival time t was assumed to follow the Piecewise Exponential distribution with various censoring patterns generated from the Uniform distribution. Both methods were evaluated via a randomised clinical trial of nasopharyngeal cancer exhibiting increasing treatment benefit.

RESULTS

Intensive simulations showed Cox TVC outperformed FPM under non-PH in terms of bias and coverage, with generally higher power observed in scenarios of crossing or diverging curves under low censoring. In real-world data, the FPM produced slightly larger LER and LED estimates than Cox TVC. Cox TVC has the advantage of assessing treatment effect at different milestones and detecting earlier difference when estimating using hazard ratio (HR).

CONCLUSION

Overall, Cox TVC is a viable option for summarising treatment effect using LER and LED under non-PH conditions. It would be beneficial to complement the reporting by providing estimates of HR at specific milestone to detect early differences.