Controlling the local false discovery rate in the adaptive Lasso

Handle URI:
http://hdl.handle.net/10754/597869
Title:
Controlling the local false discovery rate in the adaptive Lasso
Authors:
Sampson, J. N.; Chatterjee, N.; Carroll, R. J.; Muller, S.
Abstract:
The Lasso shrinkage procedure achieved its popularity, in part, by its tendency to shrink estimated coefficients to zero, and its ability to serve as a variable selection procedure. Using data-adaptive weights, the adaptive Lasso modified the original procedure to increase the penalty terms for those variables estimated to be less important by ordinary least squares. Although this modified procedure attained the oracle properties, the resulting models tend to include a large number of "false positives" in practice. Here, we adapt the concept of local false discovery rates (lFDRs) so that it applies to the sequence, λn, of smoothing parameters for the adaptive Lasso. We define the lFDR for a given λn to be the probability that the variable added to the model by decreasing λn to λn-δ is not associated with the outcome, where δ is a small value. We derive the relationship between the lFDR and λn, show lFDR =1 for traditional smoothing parameters, and show how to select λn so as to achieve a desired lFDR. We compare the smoothing parameters chosen to achieve a specified lFDR and those chosen to achieve the oracle properties, as well as their resulting estimates for model coefficients, with both simulation and an example from a genetic study of prostate specific antigen.
Citation:
Sampson JN, Chatterjee N, Carroll RJ, Muller S (2013) Controlling the local false discovery rate in the adaptive Lasso. Biostatistics 14: 653–666. Available: http://dx.doi.org/10.1093/biostatistics/kxt008.
Publisher:
Oxford University Press (OUP)
Journal:
Biostatistics
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
9-Apr-2013
DOI:
10.1093/biostatistics/kxt008
PubMed ID:
23575212
PubMed Central ID:
PMC3769997
Type:
Article
ISSN:
1465-4644; 1468-4357
Sponsors:
Sampson's and Chatterjee's research was supported by the Intramural Research Program of the NCI. Chatterjee's research was supported by a gene-environment initiative grant from the NHLBI (RO1-HL091172-01). Muller's research was supported by a grant from the Australian Research Council (DP110101998). Carroll's research was supported by a grant from the National Cancer Institute (R37-CA057030). Carroll was also supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorSampson, J. N.en
dc.contributor.authorChatterjee, N.en
dc.contributor.authorCarroll, R. J.en
dc.contributor.authorMuller, S.en
dc.date.accessioned2016-02-25T12:58:06Zen
dc.date.available2016-02-25T12:58:06Zen
dc.date.issued2013-04-09en
dc.identifier.citationSampson JN, Chatterjee N, Carroll RJ, Muller S (2013) Controlling the local false discovery rate in the adaptive Lasso. Biostatistics 14: 653–666. Available: http://dx.doi.org/10.1093/biostatistics/kxt008.en
dc.identifier.issn1465-4644en
dc.identifier.issn1468-4357en
dc.identifier.pmid23575212en
dc.identifier.doi10.1093/biostatistics/kxt008en
dc.identifier.urihttp://hdl.handle.net/10754/597869en
dc.description.abstractThe Lasso shrinkage procedure achieved its popularity, in part, by its tendency to shrink estimated coefficients to zero, and its ability to serve as a variable selection procedure. Using data-adaptive weights, the adaptive Lasso modified the original procedure to increase the penalty terms for those variables estimated to be less important by ordinary least squares. Although this modified procedure attained the oracle properties, the resulting models tend to include a large number of "false positives" in practice. Here, we adapt the concept of local false discovery rates (lFDRs) so that it applies to the sequence, λn, of smoothing parameters for the adaptive Lasso. We define the lFDR for a given λn to be the probability that the variable added to the model by decreasing λn to λn-δ is not associated with the outcome, where δ is a small value. We derive the relationship between the lFDR and λn, show lFDR =1 for traditional smoothing parameters, and show how to select λn so as to achieve a desired lFDR. We compare the smoothing parameters chosen to achieve a specified lFDR and those chosen to achieve the oracle properties, as well as their resulting estimates for model coefficients, with both simulation and an example from a genetic study of prostate specific antigen.en
dc.description.sponsorshipSampson's and Chatterjee's research was supported by the Intramural Research Program of the NCI. Chatterjee's research was supported by a gene-environment initiative grant from the NHLBI (RO1-HL091172-01). Muller's research was supported by a grant from the Australian Research Council (DP110101998). Carroll's research was supported by a grant from the National Cancer Institute (R37-CA057030). Carroll was also supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherOxford University Press (OUP)en
dc.subjectVariable selectionen
dc.subjectSmoothing Parameteren
dc.subjectAdaptive Lassoen
dc.subjectLocal False Discovery Rateen
dc.subject.meshFalse Positive Reactionsen
dc.subject.meshModels, Statisticalen
dc.titleControlling the local false discovery rate in the adaptive Lassoen
dc.typeArticleen
dc.identifier.journalBiostatisticsen
dc.identifier.pmcidPMC3769997en
dc.contributor.institutionDivision of Cancer Epidemiology and Genetics, National Cancer Institute, 6120 Executive Blvd, EPS 8038, Rockville, MD 20852, USA.en
kaust.grant.numberKUS-CI-016-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.