Flexible Deep Neural Networks for Partially Linear Survival Data

2025-12-11

AI Summary

This paper addresses the challenge in survival analysis where the proportional hazards (PH) assumption fails, yet interpretability of key covariates and flexible modeling of complex time-varying confounding effects are both required. We propose FLEXI-Haz—a partially linear deep survival model—comprising an interpretable parametric linear component (for main effects) and a nonparametric deep neural network component (to flexibly capture time-varying confounding). It is the first partially linear framework to fully relax the PH assumption. Theoretically, we establish that the neural network estimator achieves the minimax optimal convergence rate over composite Hölder classes, while the linear estimator is √n-consistent, asymptotically normal, and semiparametrically efficient. Extensive simulations and real-data analyses demonstrate substantial improvements in main-effect estimation accuracy. The implementation is publicly available on GitHub, offering clinicians and epidemiologists a new tool that jointly delivers high predictive performance and statistical interpretability.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 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

Problem

• Models survival data with partially linear structure
• Captures complex interactions without proportional hazards assumption
• Provides interpretable linear effects and efficient nonparametric estimation

Innovation

• Flexible DNN framework for survival data
• Partially linear structure with interpretable parametric component
• Nonparametric DNN captures complex time-covariate interactions