Tian Tian, Sun Jianguo
Department of Statistics, University of Missouri, Columbia, USA, MO.
Biom J. 2023 Jan;65(1):e2100310. doi: 10.1002/bimj.202100310. Epub 2022 Aug 3.
The standard Cox model is perhaps the most commonly used model for regression analysis of failure time data but it has some limitations such as the assumption on linear covariate effects. To relax this, the nonparametric additive Cox model, which allows for nonlinear covariate effects, is often employed, and this paper will discuss variable selection and structure estimation for this general model. For the problem, we propose a penalized sieve maximum likelihood approach with the use of Bernstein polynomials approximation and group penalization. To implement the proposed method, an efficient group coordinate descent algorithm is developed and can be easily carried out for both low- and high-dimensional scenarios. Furthermore, a simulation study is performed to assess the performance of the presented approach and suggests that it works well in practice. The proposed method is applied to an Alzheimer's disease study for identifying important and relevant genetic factors.
标准的Cox模型可能是用于失效时间数据回归分析最常用的模型，但它有一些局限性，比如对协变量效应线性的假设。为了放宽这一假设，常采用允许协变量效应非线性的非参数加法Cox模型，本文将讨论该一般模型的变量选择和结构估计。针对这个问题，我们提出一种使用伯恩斯坦多项式逼近和分组惩罚的惩罚筛最大似然方法。为了实现所提出的方法，开发了一种有效的分组坐标下降算法，并且该算法在低维和高维情形下都能轻松实现。此外，进行了一项模拟研究以评估所提出方法的性能，结果表明该方法在实际应用中效果良好。所提出的方法被应用于一项阿尔茨海默病研究，以识别重要且相关的遗传因素。
