Flexible Deep Neural Networks for Partially Linear Survival Data
This work addresses the problem of interpretable survival analysis for researchers and practitioners by offering an incremental improvement over existing DNN methods that relax the proportional hazards assumption.
The paper tackles modeling survival data without relying on the proportional hazards assumption by proposing FLEXI-Haz, a flexible deep neural network framework with a partially linear structure, which achieves root-n consistent and asymptotically normal estimation of linear effects while providing accurate results in simulations and real-data analyses.
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 based on composite Holder classes, and the linear estimator is root-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: https://github.com/AsafBanana/FLEXI-Haz