Self-Consistent Equation-guided Neural Networks for Censored Time-to-Event Data
This addresses the need for efficient, non-parametric survival analysis methods in fields like healthcare, offering a solution to computational limitations in existing deep learning approaches, though it is incremental in applying GANs to this specific domain.
The paper tackles the problem of estimating conditional survival functions from censored time-to-event data with high-dimensional predictors by proposing a novel deep learning approach using generative adversarial networks and self-consistent equations, achieving a model-free method with established convergence rates and validated performance through simulations and real-world data.
In survival analysis, estimating the conditional survival function given predictors is often of interest. There is a growing trend in the development of deep learning methods for analyzing censored time-to-event data, especially when dealing with high-dimensional predictors that are complexly interrelated. Many existing deep learning approaches for estimating the conditional survival functions extend the Cox regression models by replacing the linear function of predictor effects by a shallow feed-forward neural network while maintaining the proportional hazards assumption. Their implementation can be computationally intensive due to the use of the full dataset at each iteration because the use of batch data may distort the at-risk set of the partial likelihood function. To overcome these limitations, we propose a novel deep learning approach to non-parametric estimation of the conditional survival functions using the generative adversarial networks leveraging self-consistent equations. The proposed method is model-free and does not require any parametric assumptions on the structure of the conditional survival function. We establish the convergence rate of our proposed estimator of the conditional survival function. In addition, we evaluate the performance of the proposed method through simulation studies and demonstrate its application on a real-world dataset.