Efficient and Debiased Learning of Average Hazard Under Non-Proportional Hazards

• URL: http://arxiv.org/abs/2602.13475v1
• Date: Fri, 13 Feb 2026 21:30:49 GMT
• Title: Efficient and Debiased Learning of Average Hazard Under Non-Proportional Hazards
• Authors: Xiang Meng, Lu Tian, Kenneth Kehl, Hajime Uno,
• Abstract summary: Average hazard (AH) is a population-level person-time event rate that remains well-defined and interpretable without assuming proportional hazards.<n>We develop a semi-parametric, doubly robust framework for co-adjusted AH.<n>We demonstrate practical utility in comparative effectiveness research by comparing immunotherapy regimens for advanced melanoma using SEER-Medicare linked data.
• Score: 9.620492866279326
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The hazard ratio from the Cox proportional hazards model is a ubiquitous summary of treatment effect. However, when hazards are non-proportional, the hazard ratio can lose a stable causal interpretation and become study-dependent because it effectively averages time-varying effects with weights determined by follow-up and censoring. We consider the average hazard (AH) as an alternative causal estimand: a population-level person-time event rate that remains well-defined and interpretable without assuming proportional hazards. Although AH can be estimated nonparametrically and regression-style adjustments have been proposed, existing approaches do not provide a general framework for flexible, high-dimensional nuisance estimation with valid sqrt{n} inference. We address this gap by developing a semiparametric, doubly robust framework for covariate-adjusted AH. We establish pathwise differentiability of AH in the nonparametric model, derive its efficient influence function, and construct cross-fitted, debiased estimators that leverage machine learning for nuisance estimation while retaining asymptotically normal, sqrt{n}-consistent inference under mild product-rate conditions. Simulations demonstrate that the proposed estimator achieves small bias and near-nominal confidence-interval coverage across proportional and non-proportional hazards settings, including crossing-hazards regimes where Cox-based summaries can be unstable. We illustrate practical utility in comparative effectiveness research by comparing immunotherapy regimens for advanced melanoma using SEER-Medicare linked data.

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