title: Variable selection in monotone single-index models via the adaptive LASSO.
abstract: We consider the problem of variable selection for monotone single-index models. A single-index model assumes that the expectation of the outcome is an unknown function of a linear combination of covariates. Assuming monotonicity of the unknown function is often reasonable and allows for more straightforward inference. We present an adaptive LASSO penalized least squares approach to estimating the index parameter and the unknown function in these models for continuous outcome. Monotone function estimates are achieved using the pooled adjacent violators algorithm, followed by kernel regression. In the iterative estimation process, a linear approximation to the unknown function is used, therefore reducing the situation to that of linear regression and allowing for the use of standard LASSO algorithms, such as coordinate descent. Results of a simulation study indicate that the proposed methods perform well under a variety of circumstances and that an assumption of monotonicity, when appropriate, noticeably improves performance. The proposed methods are applied to data from a randomized clinical trial for the treatment of a critical illness in the intensive care unit.
authors: Department of Biostatistics, University of Michigan, Ann Arbor, MI, 48109, U.S.A.
authors: Jared C
authors: JC
authors: Foster
authors: Jeremy M G
authors: JM
authors: Taylor
authors: Bin
authors: B
authors: Nan
mesh_terms: D000465:Algorithms; D002986:Clinical Trials as Topic / Q000379:methods*; D003198:Computer Simulation; D016638:Critical Illness / Q000628:therapy; D006801:Humans; D016018:Least-Squares Analysis; D015233:Models, Statistical; D016019:Survival Analysis
keywords: adaptive LASSO; isotonic regression; kernel estimator; single-index models; variable selection
references: Med Care. 1976 May;14(5 Suppl):116-8
references: 132585
references: Ann Stat. 2009;37(4):1733-1751
references: 20445770
references: Ann Stat. 2010 Dec 1;38(6):3811-3836
references: 21625330
references: Stat Med. 2011 Oct 30;30(24):2867-80
references: 21815180