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Boss J, Rix A, Chen YH, Narisetty NN, Wu Z, Ferguson KK, McElrath TF, Meeker JD, Mukherjee B. A hierarchical integrative group least absolute shrinkage and selection operator for analyzing environmental mixtures. ENVIRONMETRICS 2021; 32:e2698. [PMID: 34899005 PMCID: PMC8664243 DOI: 10.1002/env.2698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2020] [Accepted: 06/28/2021] [Indexed: 06/14/2023]
Abstract
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 paper, we propose a general shrinkage and selection framework to identify noteworthy nonlinear main and interaction effects among a set of exposures. We design 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.
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Affiliation(s)
- Jonathan Boss
- Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, U.S.A
| | - Alexander Rix
- Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, U.S.A
| | | | - Naveen N. Narisetty
- Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, Illinois, U.S.A
| | - Zhenke Wu
- Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, U.S.A
| | - Kelly K. Ferguson
- Epidemiology Branch, National Institute of Environmental Health Sciences, Durham, North Carolina, U.S.A
| | - Thomas F. McElrath
- Department of Obstetrics and Gynecology, Brigham and Women’s Hospital, Boston, Massachusetts, U.S.A
| | - John D. Meeker
- Department of Environmental Health Sciences, University of Michigan, Ann Arbor, Michigan, U.S.A
| | - Bhramar Mukherjee
- Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, U.S.A
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