The partial linear Cox model for interval-censoring is well-studied under the additive assumption but is still under-investigated without this assumption. In this paper, we propose to use a deep ReLU neural network to estimate the nonparametric components of a partial linear Cox model for interval-censored data. This model not only retains the nice interpretability of the parametric component but also improves the predictive power compared to the partial linear additive Cox model. We derive the convergence rate of the proposed estimator and show that it can break the curse of dimensionality under some certain smoothness assumptions. Based on such rate, the asymptotic normality and the semiparametric efficiency are also established. Intensive simulation studies are carried out to demonstrate the finite sample performance on both estimation and prediction. The proposed estimation procedure is illustrated on a real dataset.

翻译：区间删失情形下的部分线性Cox模型在可加性假设下已得到充分研究，但无此假设下的模型仍鲜有探索。本文提出使用深度ReLU神经网络估计区间删失数据部分线性Cox模型的非参数成分。该模型不仅保留了参数成分良好的可解释性，相较于部分线性可加Cox模型还提升了预测能力。我们推导了所提出估计量的收敛速度，并证明在特定光滑性假设下可打破维度灾难。基于该收敛速度，进一步建立了渐近正态性和半参数有效性。通过大量仿真研究验证了所提方法在估计与预测方面的有限样本表现，并将所发展的估计流程应用于真实数据集的分析。