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.

翻译：我们提出了一种灵活的深度神经网络（DNN）框架，用于在部分线性回归结构中对生存数据进行建模。该方法通过针对主要兴趣协变量的参数化线性分量保持了可解释性，而非参数化的DNN分量则能捕捉干扰变量中复杂的时-协变量交互作用。我们将此方法称为FLEXI-Haz，一种具有部分线性结构的灵活危险模型。与现有的针对部分线性Cox模型的DNN方法不同，FLEXI-Haz不依赖于比例风险假设。我们建立了理论保证：神经网络分量在复合Hölder类上达到了极小化最优收敛速度；线性估计量是sqrt-n相合的、渐近正态的且半参数有效的；我们还为新个体开发了一个交叉拟合的一步估计量用于累积危险函数和生存函数，并给出了逐点渐近置信区间。据我们所知，这是首次在含或不含线性分量的DNN生存模型中，给出生存函数的频率学派渐近逐点推断结果。模拟和真实数据分析均表明，FLEXI-Haz作为基于比例风险方法的一种有原则且可解释的替代方案，具有实用性。