Controlling the local false discovery rate in the adaptive Lasso

Type
Article

Authors
Sampson, J. N.
Chatterjee, N.
Carroll, R. J.
Muller, S.

KAUST Grant Number
KUS-CI-016-04

Online Publication Date
2013-04-09

Print Publication Date
2013-09-01

Date
2013-04-09

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.

Acknowledgements
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).

Publisher
Oxford University Press (OUP)

Journal
Biostatistics

DOI
10.1093/biostatistics/kxt008

PubMed ID
23575212

PubMed Central ID
PMC3769997

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