arXiv:2503.09097stat.MLcs.LG2025-03

用自洽方程引导的生成对抗网络,无假设地估计带删失数据的生存函数。

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

  • 基于自洽方程设计生成对抗网络,无需预设生存函数形式。
  • 理论证明了生存函数估计器的收敛速度,确保稳定性。
  • 适合高维复杂预测变量的生存分析,尤其适用于真实医疗数据。

在生存分析中,给定预测变量估计条件生存函数是核心目标。近年来,针对高维且复杂关联的预测变量,深度学习方法在处理删失时间-事件数据方面发展迅速。现有方法多通过浅层前馈神经网络替代Cox模型中的线性预测项,但仍需维持比例风险假设,且因每次迭代使用全数据集,计算成本高,批处理可能扭曲部分似然函数中的风险集。为此,本文提出一种新型深度学习方法,利用生成对抗网络结合自洽方程,实现条件生存函数的非参数估计。该方法无需任何参数假设,具有模型无关性。我们建立了所提估计器的收敛速率,并通过模拟研究评估性能,同时在真实世界数据集上验证了其应用效果。

原文摘要 · Abstract (English)

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.

生存分析生成对抗网络删失数据深度学习

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