Interpretable Deep Learning-Based Cox Proportional Hazards Model with Uncertainty Quantification
W.A.R.De Mel *
Department of Mathematics, University of Ruhuna, Matara, Sri Lanka.
Y.S. Nimesh
Department of Mathematics, University of Ruhuna, Matara, Sri Lanka.
*Author to whom correspondence should be addressed.
Abstract
Survival analysis is essential in clinical and actuarial domains, yet traditional models such as the Cox Proportional Hazards (CoxPH) model are constrained by linearity assumptions. This study introduces an Explainable DeepSurv with Uncertainty framework, which integrates deep neural networks into the CoxPH architecture to model non linear covariate effects while addressing interpretability and uncertainty estimation. The linear risk function is replaced by a non linear transformation learned by a neural network, enabling improved predictive performance. Uncertainty is quantified using Bayesian Neural Networks and Monte Carlo Dropout, while SHAP (SHapley Additive exPlanations) values and survival curves offer post hoc interpretability. The model was validated on a dataset predicting ten year coronary heart disease (CHD) risk, outperforming the baseline CoxPH (C Index = 0.5466) with a mean absolute error (MAE) of 0.2855 and a mean squared error (MSE) of 0.1555. Calibration metrics, including a Brier Score of 0.135 and Expected Calibration Error (ECE) of 0.074, ‘confirmed the model’s reliability, and a 5 fold cross validation yielded a mean C Index of 0.5464±0.0242 and MSE of 0.3164±0.0090. By addressing the core challenges of non linearity, censoring, and lack of transparency in survival models, this research presents a robust, interpretable, and uncertainty aware framework suitable for clinical decision making and personalized risk prediction.
Keywords: Survival analysis, deep learning, uncertainty estimation, Cox model, DeepSurv, SHAP, Bayesian Neural Networks, Monte Carlo Dropout, censored data