CoxSE: Exploring the Potential of Self-Explaining Neural Networks with Cox Proportional Hazards Model for Survival Analysis

TL;DR

The paper introduces self-explaining Cox-based survival models (CoxSE and CoxSENAM) that deliver intrinsic, locally linear explanations via SENN/NAM frameworks while maintaining competitive predictive accuracy relative to black-box baselines. It demonstrates that SENN-based approaches offer more stable, consistent explanations and better alignment with ground-truth attributions than NAM-only methods, though NAM-based designs show robustness to non-informative features. A hybrid CoxSENAM further improves robustness to noise, trading some interaction capacity for stability. Across synthetic and real datasets, the proposed methods yield explanations that correlate well with post-hoc SHAP explanations and demonstrate clinical plausibility in case studies like SEER breast cancer. The work highlights the trade-offs between explanatory stability, interaction modeling, and robustness, and points to future work on non-proportional hazards and integrating interpretable feature extraction for opaque inputs.

Abstract

The Cox Proportional Hazards (CPH) model has long been the preferred survival model for its explainability. However, to increase its predictive power beyond its linear log-risk, it was extended to utilize deep neural networks, sacrificing its explainability. In this work, we explore the potential of self-explaining neural networks (SENN) for survival analysis. We propose a new locally explainable Cox proportional hazards model, named CoxSE, by estimating a locally-linear log-hazard function using the SENN. We also propose a modification to the Neural additive (NAM) model, hybrid with SENN, named CoxSENAM, which enables the control of the stability and consistency of the generated explanations. Several experiments using synthetic and real datasets are presented, benchmarking CoxSE and CoxSENAM against a NAM-based model, a DeepSurv model explained with SHAP, and a linear CPH model. The results show that, unlike the NAM-based model, the SENN-based model can provide more stable and consistent explanations while maintaining the predictive power of the black-box model. The results also show that, due to their structural design, NAM-based models demonstrate better robustness to non-informative features. Among the models, the hybrid model exhibits the best robustness.

Figures (15)

• Figure 1: CoxNAM Model architecture
• Figure 2: SENN Model architecture
• Figure 3: CoxSE and CoxSENAM models' architecture
• Figure 4: Lin Dataset Aggregated Explanations
• Figure 5: NonLin Dataset Aggregated Explanations