Primary Submission Category: Applications in Health and Biology
Beyond Proportional Hazards: Double Machine Learning of the Causal Average Hazard
Authors: Xiang Meng, Hajime Uno, Kenneth Kehl, Lu Tian,
Presenting Author: Xiang Meng*
The Cox model and its hazard ratio (HR) are standard for treatment effects, yet face limitations like non-collapsibility and sensitivity to censoring. This paper develops a semiparametric framework for the average hazard with survival weight (AH), a model-free, population-level person-time event rate. We contrast the AH with pairwise win ratios, assumption-lean regression projections, and fixed-horizon risks, highlighting its utility as a marginal, rate-based estimand robust to non-proportional hazards and invariant to independent censoring.
We contribute to causal inference in three ways. First, we formalize the AH as a causal estimand using potential outcomes, identifying it under standard assumptions while clarifying its distinction from marginalized conditional rates. Second, we establish the pathwise differentiability of the AH and derive its efficient influence function (EIF). Third, we propose a cross-fitted, doubly robust estimator leveraging machine learning for nuisance estimation while maintaining sqrt{n}-consistency and asymptotic normality. Simulations show our estimator maintains near-nominal coverage and minimal bias, even with crossing hazards. Finally, we apply our method to the SEER-Medicare database, a massive health record system that links official cancer registries with long-term insurance data to show how well different treatments work for thousands of patients in real-world settings.