2025/12/11 by Asaf Ben Arie, Arie, Asaf Ben, Malka Gorfine +1
Mathematics · #Advanced Causal Inference Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2512.10570
openalex publication_date 2025/12/11 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28
We propose a flexible deep neural network (DNN) framework for modeling survival data within a partially linear regression structure. The approach preserves interpretability through a parametric linear component for covariates of primary interest, while a nonparametric DNN component captures complex time-covariate interactions among nuisance variables. We refer to the method as FLEXI-Haz, a FLEXIble Hazard model with a partially linear structure. In contrast to existing DNN approaches for partially linear Cox models, FLEXI-Haz does not rely on the proportional hazards assumption. We establish theoretical guarantees: the neural network component attains minimax-optimal convergence rates over composite Hölder classes, the linear estimator is sqrt-n-consistent, asymptotically normal, and semiparametrically efficient, and we develop a cross-fitted one-step estimator of the cumulative hazard and survival function for a new subject, together with pointwise asymptotic confidence intervals. To the best of our knowledge, this is the first frequentist asymptotic pointwise inference result for a survival function in a DNN survival model, with or without a linear component. Simulations and real-data analyses demonstrate the utility of FLEXI-Haz as a principled and interpretable alternative to methods based on proportional hazards.