CoxNAM: An interpretable deep survival analysis model

Survival analysis is widely used in medicine, engineering, economics and other fields as an effective method to model the relation between the time of an event of interest occurring and related features. However, traditional survival analysis models lack the ability to capture nonlinearity. In addition, most nonlinear survival analysis models, especially deep learning-based methods, lack interpretability, which limits the practical application of these models. For these gaps, we proposed an interpretable deep survival analysis model named CoxNAM. This model is based on the Cox proportion hazards model and uses neural additive model to predict the hazard function. We also used the backpropagation algorithm to train the model based on the corresponding loss function. When performing a survival analysis, we can obtain the survival functions, shape functions of features, and the importance of related features while predicting the probability of the occurrence of the event of interest. We conducted numerical experiments on two synthetic datasets and one public breast cancer dataset to verify the performance of the model, at the same time, we compared the interpretability with the SHAP framework on the two synthetic datasets and the results demonstrated the effectiveness of the proposed model's interpretation. We also applied the model for prognostic analysis of gastric cancer patients to illustrate its application. The experimental results indicate that the proposed model performs better on C-index than the classic statistical survival analysis model (i.e., Cox proportional hazards model) and machine learning-based survival analysis models (i.e., random survival forest and DeepSurv), and it can also provide the importance of features related to the time of the occurrence of events of interest and the effect of the feature values on the results. The proposed method shows promising performance and realistic interpretability. The model can potentially be extended to survival analysis problems in multiple domains for relevant decision-making.