新模型FLEXI-Haz突破比例风险假设,兼顾可解释性与复杂交互建模。
Flexible Deep Neural Networks for Partially Linear Survival Data: Estimation and Survival Inference
- 线性部分保留关键变量可解释性,神经网络捕捉复杂时变交互
- 理论证明线性估计量渐近正态且高效,累积风险函数具置信区间
- 首个无需比例风险假设的深度学习生存模型点推断方法,适合临床研究
我们提出一种灵活的深度神经网络(DNN)框架用于部分线性生存数据分析,称为FLEXI-Haz。该方法在部分线性结构下建模生存数据,通过参数线性部分保持主要协变量的可解释性,非参数DNN部分捕捉次要变量与时间的复杂交互关系。与现有基于比例风险假设的深度学习生存模型不同,FLEXI-Haz不依赖该假设。理论分析表明:神经网络组件在复合霍尔德类上达到极小极大最优收敛速率;线性估计量具有√n一致性、渐近正态性和半参数效率;同时提出交叉拟合的一步估计器,用于新个体的累积风险和生存函数估计,并给出逐点渐近置信区间。据我们所知,这是首个在含或不含线性成分的深度学习生存模型中实现生存函数频率学点推断的结果。模拟与真实数据验证了FLEXI-Haz作为比例风险方法的原理性且可解释的替代方案的有效性。
原文摘要 · Abstract (English)
We propose a flexible deep neural network (DNN) framework for modeling survival data within a partially linear regression structure. The approach preserves interpretability through a parametric linear component for covariates of primary interest, while a nonparametric DNN component captures complex time-covariate interactions among nuisance variables. We refer to the method as FLEXI-Haz, a FLEXIble Hazard model with a partially linear structure. In contrast to existing DNN approaches for partially linear Cox models, FLEXI-Haz does not rely on the proportional hazards assumption. We establish theoretical guarantees: the neural network component attains minimax-optimal convergence rates over composite Hölder classes, the linear estimator is sqrt-n-consistent, asymptotically normal, and semiparametrically efficient, and we develop a cross-fitted one-step estimator of the cumulative hazard and survival function for a new subject, together with pointwise asymptotic confidence intervals. To the best of our knowledge, this is the first frequentist asymptotic pointwise inference result for a survival function in a DNN survival model, with or without a linear component. Simulations and real-data analyses demonstrate the utility of FLEXI-Haz as a principled and interpretable alternative to methods based on proportional hazards.
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