This paper discusses variable or covariate selection for high-dimensional quadratic Cox model. Although many variable selection methods have been developed for standard Cox model or high-dimensional standard Cox model, most of them cannot be directly applied since they cannot take into account the important and existing hierarchical model structure. For the problem, we present a penalized log partial likelihood-based approach and in particular, generalize the regularization algorithm under marginality principle (RAMP) proposed in Hao et al. (J Am Stat Assoc 2018;113:615–25) under the context of linear models. An extensive simulation study is conducted and suggests that the presented method works well in practical situations. It is then applied to an Alzheimer’s Disease study that motivated this investigation.

中文翻译：

---

高维二次 Cox 模型的变量选择及其在阿尔茨海默病中的应用


本文讨论高维二次 Cox 模型的变量或协变量选择。尽管针对标准Cox模型或高维标准Cox模型开发了许多变量选择方法，但大多数方法由于无法考虑重要且现有的层次模型结构而无法直接应用。针对这个问题，我们提出了一种基于惩罚对数偏似然的方法，特别是推广了Hao等人提出的边缘性原理（RAMP）下的正则化算法。 (J Am Stat Assoc 2018;113:615–25) 在线性模型的背景下。进行了广泛的模拟研究，结果表明所提出的方法在实际情况下效果良好。然后将其应用于引发本次调查的阿尔茨海默病研究。