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Biostatistics Advance Access originally published online on April 11, 2007
Biostatistics 2008 9(1):30-50; doi:10.1093/biostatistics/kxm010
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© The Author 2007. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Penalized logistic regression for detecting gene interactions

Mee Young Park*

Google Inc., 1600 Amphitheatre Parkway, Mountain View, CA 94043, USA meeyoung{at}google.com

Trevor Hastie

Department of Statistics and Department of Health Research & Policy, Stanford University, Stanford, CA 94305, USA

* To whom correspondence should be addressed.

We propose using a variant of logistic regression (LR) with Formula-regularization to fit gene–gene and gene–environment interaction models. Studies have shown that many common diseases are influenced by interaction of certain genes. LR models with quadratic penalization not only correctly characterizes the influential genes along with their interaction structures but also yields additional benefits in handling high-dimensional, discrete factors with a binary response. We illustrate the advantages of using an Formula-regularization scheme and compare its performance with that of "multifactor dimensionality reduction" and "FlexTree," 2 recent tools for identifying gene–gene interactions. Through simulated and real data sets, we demonstrate that our method outperforms other methods in the identification of the interaction structures as well as prediction accuracy. In addition, we validate the significance of the factors selected through bootstrap analyses.

Keywords: Discrete factors; Gene interactions; High dimensional; Logistic regression; L2-regularization

Received May 26, 2006; revised February 6, 2007; accepted for publication March 2, 2007.


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