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Efficient and Debiased Learning of Average Hazard Under Non-Proportional Hazards
Meng, Xiang, Tian, Lu, Kehl, Kenneth, Uno, Hajime
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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Drink Whole Milk, Eat Red Meat, and Use ChatGPT
Robert F. Kennedy Jr. is an AI guy. Last week, during a stop in Nashville on his Take Back Your Health tour, the Health and Human Services secretary brought up the technology between condemning ultra-processed foods and urging Americans to eat protein. "My agency is now leading the federal government in driving AI into all of our activities," he declared. An army of bots, Kennedy said, will transform medicine, eliminate fraud, and put a virtual doctor in everyone's pocket. RFK Jr. has talked up the promise of infusing his department with AI for months.
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