MEC-Cox: Machine-Learning-Assisted Generalized Entropy Calibration for ATT Marginal Hazard-Ratio Estimation

• URL: http://arxiv.org/abs/2606.08305v1
• Date: Sat, 06 Jun 2026 19:24:12 GMT
• Title: MEC-Cox: Machine-Learning-Assisted Generalized Entropy Calibration for ATT Marginal Hazard-Ratio Estimation
• Abstract summary: We target an average-treatment-effect-on-the-treated (ATT)-type marginal hazard-ratio estimand.<n>We estimate it using inverse-probability-weighted (IPW) Cox regression.<n> Valid inference is challenging because IPW Cox regression depends on the weights through both event contributions and risk-set averages.
• Score: 1.2425910171551517
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Externally controlled survival trials are increasingly used when concurrent randomized controls are infeasible, particularly in oncology and rare-disease settings with time-to-event endpoints. We target an average-treatment-effect-on-the-treated (ATT)-type marginal hazard-ratio estimand, comparing treatment with counterfactual control in the treated trial population, and estimate it using inverse-probability-weighted (IPW) Cox regression. Valid inference is challenging because IPW Cox regression depends on the weights through both event contributions and risk-set averages, making flexible machine-learning nuisance estimation difficult to incorporate directly. Building on machine-learning-assisted generalized entropy calibration (MEC) by Lee and Kim (2026), we propose MEC-Cox for ATT-weighted IPW Cox regression. The method begins with normalized source-propensity-score odds weights for external controls and then applies Bregman calibration to balance cross-fitted prognostic summaries between external controls and treated trial patients. The calibration basis may include control-survival predictions, Cox linear predictors, penalized-survival-model predictions, or other prognostic-score summaries. MEC-updated weights therefore play a dual role as source-transport and prognostic-score balancing weights. We establish consistency, characterize a calibration-induced efficiency gain, and develop a stacked sandwich variance estimator. Simulations show that MEC-Cox can reduce bias, increase efficiency, and improve coverage through flexible machine-learning-assisted adjustment.

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