Incorporating Predictor Network in Penalized Regression with Application to Microarray Data
Article first published online: 23 JUL 2009
© 2009, The International Biometric Society
Volume 66, Issue 2, pages 474–484, June 2010
How to Cite
Pan, W., Xie, B. and Shen, X. (2010), Incorporating Predictor Network in Penalized Regression with Application to Microarray Data. Biometrics, 66: 474–484. doi: 10.1111/j.1541-0420.2009.01296.x
- Issue published online: 1 JUN 2010
- Article first published online: 23 JUL 2009
- Received April 2008. Revised March 2009. Accepted March 2009.
- Elastic net;
- Generalized boosted Lasso;
- L1 penalization;
- Microarray gene expression;
- Penalized likelihood
Summary We consider penalized linear regression, especially for “large p, small n” problems, for which the relationships among predictors are described a priori by a network. A class of motivating examples includes modeling a phenotype through gene expression profiles while accounting for coordinated functioning of genes in the form of biological pathways or networks. To incorporate the prior knowledge of the similar effect sizes of neighboring predictors in a network, we propose a grouped penalty based on the Lγ-norm that smoothes the regression coefficients of the predictors over the network. The main feature of the proposed method is its ability to automatically realize grouped variable selection and exploit grouping effects. We also discuss effects of the choices of the γ and some weights inside the Lγ-norm. Simulation studies demonstrate the superior finite-sample performance of the proposed method as compared to Lasso, elastic net, and a recently proposed network-based method. The new method performs best in variable selection across all simulation set-ups considered. For illustration, the method is applied to a microarray dataset to predict survival times for some glioblastoma patients using a gene expression dataset and a gene network compiled from some Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways.