SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks
This provides a scalable method for survival analysis in fields like healthcare, though it is incremental as it builds on existing neural network and ODE techniques.
The paper tackles survival analysis with censored data by modeling event time distributions through ordinary differential equations, enabling flexible continuous-time modeling and efficient large-scale estimation, and demonstrates effectiveness compared to state-of-the-art deep learning models in simulations and real-world data.
In this paper, we propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. One key technical challenge for directly applying maximum likelihood estimation (MLE) to censored data is that evaluating the objective function and its gradients with respect to model parameters requires the calculation of integrals. To address this challenge, we recognize that the MLE for censored data can be viewed as a differential-equation constrained optimization problem, a novel perspective. Following this connection, we model the distribution of event time through an ordinary differential equation and utilize efficient ODE solvers and adjoint sensitivity analysis to numerically evaluate the likelihood and the gradients. Using this approach, we are able to 1) provide a broad family of continuous-time survival distributions without strong structural assumptions, 2) obtain powerful feature representations using neural networks, and 3) allow efficient estimation of the model in large-scale applications using stochastic gradient descent. Through both simulation studies and real-world data examples, we demonstrate the effectiveness of the proposed method in comparison to existing state-of-the-art deep learning survival analysis models. The implementation of the proposed SODEN approach has been made publicly available at https://github.com/jiaqima/SODEN.