Kingston General Health Research Institute, Queen's University, Kingston, Ontario, Canada.
Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada.
Stat Med. 2024 Aug 30;43(19):3689-3701. doi: 10.1002/sim.10152. Epub 2024 Jun 18.
The Cox regression model or accelerated failure time regression models are often used for describing the relationship between survival outcomes and potential explanatory variables. These models assume the studied covariates are connected to the survival time or its distribution or their transformations through a function of a linear regression form. In this article, we propose nonparametric, nonlinear algorithms (deepAFT methods) based on deep artificial neural networks to model survival outcome data in the broad distribution family of accelerated failure time models. The proposed methods predict survival outcomes directly and tackle the problem of censoring via an imputation algorithm as well as re-weighting and transformation techniques based on the inverse probabilities of censoring. Through extensive simulation studies, we confirm that the proposed deepAFT methods achieve accurate predictions. They outperform the existing regression models in prediction accuracy, while being flexible and robust in modeling covariate effects of various nonlinear forms. Their prediction performance is comparable to other established deep learning methods such as deepSurv and random survival forest methods. Even though the direct output is the expected survival time, the proposed AFT methods also provide predictions for distributional functions such as the cumulative hazard and survival functions without additional learning efforts. For situations where the popular Cox regression model may not be appropriate, the deepAFT methods provide useful and effective alternatives, as shown in simulations, and demonstrated in applications to a lymphoma clinical trial study.
Cox 回归模型或加速失效时间回归模型常用于描述生存结局与潜在解释变量之间的关系。这些模型假设研究协变量通过线性回归形式的函数与生存时间或其分布或它们的变换相关联。在本文中，我们提出了基于深度人工神经网络的非参数、非线性算法（deepAFT 方法），用于在加速失效时间模型的广泛分布族中对生存结局数据进行建模。所提出的方法直接预测生存结局，并通过插补算法以及基于 censoring 逆概率的重新加权和变换技术来处理 censoring 问题。通过广泛的模拟研究，我们证实了所提出的 deepAFT 方法可以实现准确的预测。它们在预测精度方面优于现有的回归模型，同时在建模各种非线性形式的协变量效应方面具有灵活性和稳健性。它们的预测性能与其他已建立的深度学习方法（如 deepSurv 和随机生存森林方法）相当。尽管直接输出是预期的生存时间，但所提出的 AFT 方法也可以在无需额外学习的情况下对分布函数（如累积风险和生存函数）进行预测。对于 Cox 回归模型可能不适用的情况，深度 AFT 方法提供了有用且有效的替代方法，如模拟所示，并在对淋巴瘤临床试验研究的应用中得到了证明。
