Although the Cox proportional hazards model is well established and extensively used in the analysis of survival data, the proportional hazards (PH) assumption may not always hold in practical scenarios. The class of semiparametric transformation models extends the Cox model and also includes many other survival models as special cases. This paper introduces a deep partially linear transformation model (DPLTM) as a general and flexible regression framework for right-censored data. The proposed method is capable of avoiding the curse of dimensionality while still retaining the interpretability of some covariates of interest. We derive the overall convergence rate of the maximum likelihood estimators, the minimax lower bound of the nonparametric deep neural network (DNN) estimator, and the asymptotic normality and the semiparametric efficiency of the parametric estimator. Comprehensive simulation studies demonstrate the impressive performance of the proposed estimation procedure in terms of both the estimation accuracy and the predictive power, which is further validated by an application to a real-world dataset.

翻译：尽管Cox比例风险模型在生存数据分析中已得到广泛确立和应用，但在实际场景中比例风险（PH）假设可能并不总是成立。半参数变换模型类扩展了Cox模型，并将许多其他生存模型作为特例包含其中。本文提出了一种深度部分线性变换模型（DPLTM），作为右删失数据的通用且灵活的回归框架。该方法能够避免维度灾难，同时保留部分关注协变量的可解释性。我们推导了最大似然估计量的整体收敛速率、非参数深度神经网络（DNN）估计量的极小极大下界，以及参数估计量的渐近正态性与半参数有效性。综合模拟研究表明，所提出的估计方法在估计精度和预测能力方面均表现出优异性能，这一结论通过对真实世界数据集的应用得到了进一步验证。