# Debiased maximum-likelihood estimators for hazard ratios under kernel-based machine-learning adjustment

arXiv: https://arxiv.org/abs/2507.17686 · HTML: https://mlsanity.com/paper/2507.17686/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 62 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 8 of 8)

- [Estimating heterogeneous treatment effects with right-censored data via causal survival forests](https://mlsanity.com/paper/2001.09887/) (2020)
- [A Bayesian information criterion for singular models](https://mlsanity.com/paper/1309.0911/) (2013)
- [On structural and practical identifiability](https://mlsanity.com/paper/2102.05100/) (2021)
- [Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2505.13072/) (2025)
- [An Introduction to Double/Debiased Machine Learning](https://mlsanity.com/paper/2504.08324/) (2025)
- [Estimating Heterogeneous Treatment Effects on Survival Outcomes Using Counterfactual Censoring Unbiased Transformations](https://mlsanity.com/paper/2401.11263/) (2024)
- [Treatment Effect Quantification for Time-to-event Endpoints -- Estimands, Analysis Strategies, and beyond](https://mlsanity.com/paper/1711.07518/) (2017)
- [Doubly Robust Estimation under Possibly Misspecified Marginal Structural Cox Model](https://mlsanity.com/paper/2311.07752/) (2023)

## Built on by (most cited first, 1 of 1)

- [Fast Riemannian-manifold Hamiltonian Monte Carlo for hierarchical Gaussian-process models](https://mlsanity.com/paper/2511.06407/) (2025)

## Abstract (arXiv)

Previous studies have shown that hazard ratios between treatment groups estimated with the Cox model are uninterpretable because the unspecified baseline hazard of the model fails to identify temporal change in the risk set composition due to treatment assignment and unobserved factors among multiple, contradictory scenarios. To alleviate this problem, especially in studies based on observational data with uncontrolled dynamic treatment and real-time measurement of many covariates, we propose abandoning the baseline hazard and using kernel-based machine learning to explicitly model the change in the risk set with or without latent variables. For this framework, we clarify the context in which hazard ratios can be causally interpreted, and then develop a method based on Neyman orthogonality to compute debiased maximum-likelihood estimators of hazard ratios, proving necessary convergence results. Numerical simulations confirm that the proposed method identifies the true hazard ratios with minimal bias. These results lay the foundation for developing a useful, alternative method for causal inference with uncontrolled, observational data in modern epidemiology.