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This paper introduces FLEXI-Haz, a semiparametric deep learning framework designed to perform valid statistical inference on survival data without relying on the restrictive proportional hazards assumption. By combining an interpretable linear component with flexible nonparametric functions, the model achieves minimax optimal convergence rates and provides robust confidence intervals even when nuisance effects vary over time. The work represents a significant methodological advance in applying deep learning to causal inference and treatment effect estimation within clinical settings.
FLEXI-Haz: Semiparametric Deep Survival Inference Beyond Proportional Hazards
arXiv:2512.10570v3 Announce Type: replace-cross Abstract: Flexible survival prediction does not by itself ensure valid inference for covariate effects or subject-specific survival probabilities. We develop FLEXI-Haz, a semiparametric deep neural network model for right-censored data that combines an interpretable linear component in the log-hazard with a flexible function of time and adjustment covariates. This formulation permits nonproportional nuisance effects while retaining interpretable regression parameters. Under regularity conditions, we establish nuisance convergence rates that are minimax optimal up to logarithmic factors over composite Holder classes, together with root-n-consistent, asymptotically normal, and semiparametrically efficient estimation of the regression parameter. For adjustment covariates with finite support, we derive the explicit influence function for cumulative hazard and construct a cross-fitted one-step estimator yielding asymptotically valid pointwise confidence intervals for subject-specific survival. Simulations demonstrate reduced bias and improved coverage relative to a proportional hazards comparator under time-varying nuisance effects. An analysis of the Rotterdam breast cancer data illustrates the consequences of flexible adjustment for inference on treatment associations.
Abstract:Flexible survival prediction does not by itself ensure valid inference for covariate effects or subject-specific survival probabilities. We develop FLEXI-Haz, a semiparametric deep neural network model for right-censored data that combines an interpretable linear component in the log-hazard with a flexible function of time and adjustment covariates. This formulation permits nonproportional nuisance effects while retaining interpretable regression parameters. Under regularity conditions, we establish nuisance convergence rates that are minimax optimal up to logarithmic factors over composite Holder classes, together with root-n-consistent, asymptotically normal, and semiparametrically efficient estimation of the regression parameter. For adjustment covariates with finite support, we derive the explicit influence function for cumulative hazard and construct a cross-fitted one-step estimator yielding asymptotically valid pointwise confidence intervals for subject-specific survival. Simulations demonstrate reduced bias and improved coverage relative to a proportional hazards comparator under time-varying nuisance effects. An analysis of the Rotterdam breast cancer data illustrates the consequences of flexible adjustment for inference on treatment associations.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2512.10570 [stat.ML]
(or arXiv:2512.10570v3 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2512.10570 Focus to learn more arXiv-issued DOI via DataCite
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