DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network

Abstract: Medical practitioners use survival models to explore and understand the relationships between patients' covariates (e.g. clinical and genetic features) and the effectiveness of various treatment options. Standard survival models like the linear Cox proportional hazards model require extensive feature engineering or prior medical knowledge to model treatment interaction at an individual level. While nonlinear survival methods, such as neural networks and survival forests, can inherently model these high-level interaction terms, they have yet to be shown as effective treatment recommender systems. We introduce DeepSurv, a Cox proportional hazards deep neural network and state-of-the-art survival method for modeling interactions between a patient's covariates and treatment effectiveness in order to provide personalized treatment recommendations. We perform a number of experiments training DeepSurv on simulated and real survival data. We demonstrate that DeepSurv performs as well as or better than other state-of-the-art survival models and validate that DeepSurv successfully models increasingly complex relationships between a patient's covariates and their risk of failure. We then show how DeepSurv models the relationship between a patient's features and effectiveness of different treatment options to show how DeepSurv can be used to provide individual treatment recommendations. Finally, we train DeepSurv on real clinical studies to demonstrate how it's personalized treatment recommendations would increase the survival time of a set of patients. The predictive and modeling capabilities of DeepSurv will enable medical researchers to use deep neural networks as a tool in their exploration, understanding, and prediction of the effects of a patient's characteristics on their risk of failure.

• The paper introduces DeepSurv, a deep neural network that adapts Cox proportional hazards modeling to capture non-linear patient risks.
• The paper demonstrates improved predictive performance with higher concordance index scores over traditional survival analysis methods on simulated and real data.
• The paper presents a treatment recommender system that personalizes care by estimating individualized treatment effects, leading to increased median survival times.

Overview of DeepSurv: Personalized Treatment Recommender System Using a Cox Proportional Hazards Deep Neural Network

The paper under review introduces DeepSurv, an innovative deep learning model designed for survival analysis, leveraging a Cox proportional hazards (CPH) model structure adapted into a deep neural network (DNN). Developed by Jared L. Katzman et al., the model aims to enhance personalized treatment recommendations by learning and predicting the complex interrelationships between patient features and treatment outcomes.

Key Contributions

1. Powerful Predictive Model: DeepSurv effectively models non-linear interactions between covariates and iterates over the limitations of linear CPH models by avoiding the necessity for extensive feature engineering or domain-specific medical expertise.
2. Treatment-Recommendation System: The study demonstrates the utility of DeepSurv as a recommender system by evaluating its performance on both simulated and real clinical datasets.
3. State-of-the-Art Performance: The DNN aspect proves significant as the model outperforms traditional survival analysis techniques like the linear CPH and State-of-the-Art (SOTA) Random Survival Forests (RSFs) in terms of predictive accuracy as measured by concordance index (C-index).

Methodology

DeepSurv employs a multi-layer perceptron architecture to estimate a patient’s risk $\hat{h}_\theta(x)$ and features several advanced techniques:

• Loss Function: The model optimizes a modified CPH partial likelihood similar to the one used in traditional survival analysis methods.
• Modern Deep Learning Techniques: Implementation includes weight decay regularization, ReLU with batch normalization, dropout, and gradient-based optimization algorithms like Adam and Nesterov momentum.

The model calculates individualized treatment effects using a defined function $\rec_{ij}(x)$, which compares risks between different treatment options, providing a robust platform for medical decision support.

Experimental Design and Results

DeepSurv was evaluated through several experiments:

1. Simulated Data:
   • Linear Risk Function: The model performed comparably or exceeded the performance of linear CPH and RSF.
   • Non-Linear Risk Function: Demonstrated that DeepSurv accurately models complex relationships which linear CPH fails to capture, exhibiting superior predictive performance with a non-linear risk basis.
2. Real Survival Data:
   • Analyzed diverse clinical data sets including WHAS, SUPPORT, and METABRIC.
   • Performance metrics showed enhanced prediction capabilities; the model consistently achieved higher C-index scores compared to traditional methods, confirming its effectiveness on real-world data.
3. Simulated and Real Treatment Data:
   • DeepSurv effectively modeled the effect of treatments using its recommender system. Applied to simulated treatment data and real studies, such as Rotterdam and GBSG, the model significantly increased the median survival time for patients adhering to its recommendations.

Implications and Future Developments

The practical implications of DeepSurv are vast. By effectively modeling the complexities inherent in medical data, it provides a powerful tool for personalized patient care. DeepSurv's ability to offer treatment recommendations tailored to individual patient profiles could transform decision-making processes in clinical environments.

Future explorations could involve:

• Integration with Medical Imaging: Utilizing convolutional neural networks in conjunction with DeepSurv to predict risk based on imaging data.
• Broad Clinical Applicability: Extending the model for other diseases and integrating with electronic health record (EHR) systems for real-time treatment adjustments.

Conclusion

DeepSurv represents a significant milestone in survival analysis, incorporating modern deep learning techniques to deliver a highly predictive model capable of providing personalized treatment recommendations. Its successful application on both simulated and real-world datasets validates its robustness and potential as a standard tool in clinical decision-making. The model's flexibility and superior performance signal promising future applications in broader clinical contexts and further research in AI-driven personalized medicine.