Journal
STATISTICAL METHODS AND APPLICATIONS
Volume 31, Issue 3, Pages 495-529Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10260-021-00580-8
Keywords
Coordinate descent algorithm; Group penalized regression; Heterogeneous; Pseudo-quantile; Variable selection; Quantile regression
Categories
Funding
- Natural Sciences and Engineering Research Council of Canada
- Fonds de recherche du Quebec-Sante [31110]
- Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health) [U01 AG024904]
- DOD ADNI (Department of Defense) [W81XWH-12-2-0012]
- National Institute on Aging
- National Institute of Biomedical Imaging and Bioengineering
- AbbVie
- Alzheimer's Association
- Alzheimer's Drug Discovery Foundation
- Araclon Biotech
- BioClinica, Inc.
- Biogen
- Bristol-Myers Squibb Company
- CereSpir, Inc.
- Cogstate
- Eisai Inc.
- Elan Pharmaceuticals, Inc.
- Eli Lilly and Company
- EuroImmun
- F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.
- Fujirebio
- GE Healthcare
- IXICO Ltd.
- Janssen Alzheimer Immunotherapy Research and Development, LLC
- Johnson and Johnson Pharmaceutical Research and Development LLC
- Lumosity
- Lundbeck
- Merck and Co., Inc.
- Meso Scale Diagnostics, LLC
- NeuroRx Research
- Neurotrack Technologies
- Novartis Pharmaceuticals Corporation
- Pfizer Inc.
- Piramal Imaging
- Servier
- Takeda Pharmaceutical Company
- Transition Therapeutics
- Canadian Institute of Health Research
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The study presents a method for selecting grouped variables in high-dimensional linear quantile regression models, using a group penalized pseudo quantile regression (GPQR) framework that combines group-lasso and group non-convex penalties. A simple and computationally efficient group-wise descent algorithm is derived to solve the problem, and the convergence rate property is established. The GPQR approach is demonstrated in simulations and applications in genetics and omics fields.
Quantile regression models have become a widely used statistical tool in genetics and in the omics fields because they can provide a rich description of the predictors' effects on an outcome without imposing stringent parametric assumptions on the outcome-predictors relationship. This work considers the problem of selecting grouped variables in high-dimensional linear quantile regression models. We introduce a group penalized pseudo quantile regression (GPQR) framework with both group-lasso and group non-convex penalties. We approximate the quantile regression check function using a pseudo-quantile check function. Then, using the majorization-minimization principle, we derive a simple and computationally efficient group-wise descent algorithm to solve group penalized quantile regression. We establish the convergence rate property of our algorithm with the group-Lasso penalty and illustrate the GPQR approach performance using simulations in high-dimensional settings. Furthermore, we demonstrate the use of the GPQR method in a gene-based association analysis of data from the Alzheimer's Disease Neuroimaging Initiative study and in an epigenetic analysis of DNA methylation data.
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