A Robust Estimator of Hazard Ratio Using the Interquartile Time Window

This study examines methods for estimating the hazard ratio, a widely used measure for comparing risks between two groups in survival analysis, and proposes a new estimation approach to address limitations inherent in existing methods. While the Cox proportional hazards model is the standard tool for estimating hazard ratios, it assumes constant hazard rates over time (the proportional hazards assumption). However, this assumption is frequently violated in real-world survival data, often showing substantial variability at different observation periods, especially early or late in studies. Consequently, traditional methods may yield distorted hazard ratio estimates, potentially misleading interpretations regarding treatment effects. We propose a new hazard ratio estimator based on the ratio of log survival functions derived from Kaplan-Meier survival curves. Specifically, by averaging the ratio of log survival functions within the central 50% of the observation period (the 25%-75% quantile interval), our method reduces instability that often occurs at extreme time points, thus providing more stable and interpretable hazard ratio estimates. In simulations with exponential and Weibull models under the proportional hazards assumption, the interquartile range averaged estimator showed improved stability - especially with smaller samples or higher censoring - whereas at larger sample sizes (n=500) differences were negligible as all estimators converged to the true HR. Accordingly, the proposed method should be viewed as a variance-stabilized HR summary under PH, rather than a tool for handling non-proportional hazards or crossing survival curves.