Environmental health studies are increasingly measuring multiple pollutants to characterize the joint health effects attributable to exposure mixtures. However, the underlying dose-response relationship between toxicants and health outcomes of interest may be highly nonlinear, with possible nonlinear interaction effects. Existing penalized regression methods that account for exposure interactions either cannot accommodate nonlinear interactions while maintaining strong heredity or are computationally unstable in applications with limited sample size. In this article, we propose a general shrinkage and selection framework to identify noteworthy nonlinear main and interaction effects among a set of exposures. We design the hierarchical integrative group least absolute shrinkage and selection operator (HiGLASSO) to (a) impose strong heredity constraints on two-way interaction effects (hierarchical), (b) incorporate adaptive weights without necessitating initial coefficient estimates (integrative), and (c) induce sparsity for variable selection while respecting group structure (group LASSO). We prove sparsistency of the proposed method and apply HiGLASSO to an environmental toxicants dataset from the LIFECODES birth cohort, where the investigators are interested in understanding the joint effects of 21 urinary toxicant biomarkers on urinary 8-isoprostane, a measure of oxidative stress. An implementation of HiGLASSO is available in the higlasso R package, accessible through the comprehensive R archive network.

中文翻译：

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用于分析环境混合物的分层综合群最小绝对收缩和选择算子


环境健康研究越来越多地测量多种污染物，以表征暴露混合物对联合健康的影响。然而，毒物与健康结果之间潜在的剂量反应关系可能是高度非线性的，可能存在非线性相互作用效应。现有的考虑暴露相互作用的惩罚回归方法要么无法在保持强遗传性的同时适应非线性相互作用，要么在样本量有限的应用中计算不稳定。在本文中，我们提出了一个通用的收缩和选择框架，以识别一组风险之间值得注意的非线性主要效应和交互效应。我们设计了分层综合组最小绝对收缩和选择算子（HiGLASSO），以（a）对双向相互作用效应施加强遗传约束（分层），（b）合并自适应权重，而无需初始系数估计（综合），以及（ c）在尊重群体结构（群体LASSO）的同时引入变量选择的稀疏性。我们证明了所提出方法的稀疏性，并将 HiGLASSO 应用于来自 LIFECODES 出生队列的环境毒物数据集，其中研究人员有兴趣了解 21 种尿毒物生物标志物对尿 8-异前列烷（氧化应激的一种量度）的联合影响。 higlasso R 包中提供了 HiGLASSO 的实现，可通过综合 R 存档网络进行访问。