Extending Cox Proportional Hazards Model with Symbolic Non-Linear Log-Risk Functions for Survival Analysis

2025-04-06

AI Summary

Conventional Cox proportional hazards (CPH) models rely on a restrictive linear log-hazard assumption, limiting generalizability; while deep survival models improve nonlinearity, they sacrifice interpretability. Method: We propose the Generalized Cox Proportional Hazards (GCPH) model—the first to integrate Kolmogorov–Arnold networks (KANs) into survival analysis—yielding a fully symbolic, differentiable, and analytically tractable nonlinear log-hazard function. GCPH preserves the CPH interpretability framework while overcoming linearity constraints, leveraging KAN structural priors, Cox partial likelihood loss, and symbolic regression optimization to jointly ensure transparency and predictive accuracy. Contribution/Results: GCPH achieves state-of-the-art performance on synthetic data and multiple public benchmarks (METABRIC, SUPPORT, FLCHAIN), significantly enhancing both clinical interpretability of the hazard function and out-of-distribution generalization capability.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical 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
• Web Mining and Content Analysis: Large pretrained models with web data
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The Cox proportional hazards (CPH) model has been widely applied in survival analysis to estimate relative risks across different subjects given multiple covariates. Traditional CPH models rely on a linear combination of covariates weighted with coefficients as the log-risk function, which imposes a strong and restrictive assumption, limiting generalization. Recent deep learning methods enable non-linear log-risk functions. However, they often lack interpretability due to the end-to-end training mechanisms. The implementation of Kolmogorov-Arnold Networks (KAN) offers new possibilities for extending the CPH model with fully transparent and symbolic non-linear log-risk functions. In this paper, we introduce Generalized Cox Proportional Hazards (GCPH) model, a novel method for survival analysis that leverages KAN to enable a non-linear mapping from covariates to survival outcomes in a fully symbolic manner. GCPH maintains the interpretability of traditional CPH models while allowing for the estimation of non-linear log-risk functions. Experiments conducted on both synthetic data and various public benchmarks demonstrate that GCPH achieves competitive performance in terms of prediction accuracy and exhibits superior interpretability compared to current state-of-the-art methods.

Problem

• Extend CPH model with symbolic non-linear log-risk functions
• Improve interpretability in non-linear survival analysis models
• Balance accuracy and transparency in survival outcome prediction

Innovation

• Extends CPH with symbolic non-linear log-risk functions
• Uses Kolmogorov-Arnold Networks for transparent mapping
• Maintains interpretability while improving generalization