Debiased Maximum Likelihood Estimators of Hazard Ratios Under Kernel-Based Machine Learning Adjustment

Takashi Hayakawa () and Satoshi Asai
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Takashi Hayakawa: Division of Pharmacology, Department of Biomedical Sciences, Nihon University School of Medicine, 30-1 Oyaguchi-Kami Machi, Itabashi-ku, Tokyo 173-8610, Japan
Satoshi Asai: Division of Pharmacology, Department of Biomedical Sciences, Nihon University School of Medicine, 30-1 Oyaguchi-Kami Machi, Itabashi-ku, Tokyo 173-8610, Japan

Mathematics, 2025, vol. 13, issue 19, 1-32

Abstract: 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, 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 the development of a useful alternative method for causal inference with uncontrolled, observational data in modern epidemiology.

Keywords: survival analysis; hazard ratio; machine learning; causal inference; kernel method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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