Self-Consistent Equation-guided Neural Networks for Censored Time-to-Event Data

2025-03-12

AI Summary

This paper addresses nonparametric estimation of the conditional survival function for high-dimensional, strongly correlated predictors under right-censored survival data. We propose a novel framework that couples generative adversarial networks (GANs) with the self-consistency equation—a fundamental constraint in censored data analysis. Unlike shallow neural network approaches relying on the Cox proportional hazards assumption, our method is fully model-free: it intrinsically corrects censoring bias by embedding the self-consistency equation as a hard constraint within the GAN architecture. We establish theoretical guarantees showing that the resulting estimator achieves the optimal nonparametric convergence rate. Crucially, this design avoids distortion of the risk set induced by mini-batch training, thereby substantially improving computational efficiency. Extensive experiments on synthetic and multiple real-world datasets demonstrate that our method consistently outperforms state-of-the-art deep survival models in predictive accuracy, as measured by integrated Brier score (IBS) and concordance index (C-index).

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Multiagent Systems: Adversarial Agents

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

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.

Problem

• Estimating conditional survival functions with high-dimensional predictors.
• Overcoming computational intensity in deep learning for survival analysis.
• Proposing a model-free, non-parametric deep learning approach using GANs.

Innovation

• Generative adversarial networks for survival analysis
• Model-free non-parametric conditional survival estimation
• Self-consistent equations guide neural network training