Abstract

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 that depends on composite Hölder classes, and the linear estimator is sqrt(n)–consistent, asymptotically normal, and semiparametrically efficient. Extensive simulations and real-data analyses demonstrate that FLEXI–Haz provides accurate estimation of the linear effect, offering a principled and interpretable alternative to modern methods based on proportional hazards. Code for implementing FLEXI-Haz, as well as scripts for reproducing data analyses and simulations is available at GitHub site https://github.com/AsafBanana/FLEXI-Haz.