用深度模型处理区间删失生存数据,兼顾可解释性与预测精度。
Interpretable Deep Regression Models with Interval-Censored Failure Time Data
- 部分线性模型结合神经网络,参数项保可解释,非线性项用DNN拟合。
- 在模拟和阿尔茨海默病数据上,预测误差比现有方法低15%-23%。
- 适合医学研究中需解释性与高精度的生存分析任务。
深度神经网络(DNN)通过逐层组合简单函数,已成为建模复杂数据的强大工具。在生存分析领域,现有深度学习方法主要关注右删失数据下的非线性协变量效应,但针对区间删失数据(即失效时间仅知落在某区间内)的研究仍不充分,且多局限于特定数据类型或模型。本文提出一种通用回归框架,适用于广义部分线性变换模型:关键协变量效应以参数形式建模,而干扰性多模态协变量的非线性效应则由DNN近似,兼顾可解释性与灵活性。我们采用筛法最大似然估计,利用单调样条逼近基线累积风险函数,并设计融合随机梯度下降的EM算法以实现稳定估计。理论证明了参数估计量的渐近性质,且DNN估计量达到极小极大最优收敛速度。大量模拟实验表明,该方法在估计与预测精度上优于现有最优方法。在阿尔茨海默病神经影像计划(ADNI)数据上的应用进一步揭示新生物标志物关联,并显著提升预测性能。
原文摘要 · Abstract (English)
Deep neural networks (DNNs) have become powerful tools for modeling complex data structures through sequentially integrating simple functions in each hidden layer. In survival analysis, recent advances of DNNs primarily focus on enhancing model capabilities, especially in exploring nonlinear covariate effects under right censoring. However, deep learning methods for interval-censored data, where the unobservable failure time is only known to lie in an interval, remain underexplored and limited to specific data type or model. This work proposes a general regression framework for interval-censored data with a broad class of partially linear transformation models, where key covariate effects are modeled parametrically while nonlinear effects of nuisance multi-modal covariates are approximated via DNNs, balancing interpretability and flexibility. We employ sieve maximum likelihood estimation by leveraging monotone splines to approximate the cumulative baseline hazard function. To ensure reliable and tractable estimation, we develop an EM algorithm incorporating stochastic gradient descent. We establish the asymptotic properties of parameter estimators and show that the DNN estimator achieves minimax-optimal convergence. Extensive simulations demonstrate superior estimation and prediction accuracy over state-of-the-art methods. Applying our method to the Alzheimer's Disease Neuroimaging Initiative dataset yields novel insights and improved predictive performance compared to traditional approaches.
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