Regularized Multivariate Regression for Identifying Master Predictors with Application to Integrative Genomics Study of Breast Cancer.
In this paper, we propose a new method remMap - REgularized Multivariate regression for identifying MAster Predictors - for fitting multivariate response regression models under the high-dimension-low-sample-size setting. remMap is motivated by investigating the regulatory relationships among different biological molecules based on multiple types of high dimensional genomic data. Particularly, we are interested in studying the influence of DNA copy number alterations on RNA transcript levels. For this purpose, we model the dependence of the RNA expression levels on DNA copy numbers through multivariate linear regressions and utilize proper regularization to deal with the high dimensionality as well as to incorporate desired network structures. Criteria for selecting the tuning parameters are also discussed. The performance of the proposed method is illustrated through extensive simulation studies. Finally, remMap is applied to a breast cancer study, in which genome wide RNA transcript levels and DNA copy numbers were measured for 172 tumor samples. We identify a trans-hub region in cytoband 17q12-q21, whose amplification influences the RNA expression levels of more than 30 unlinked genes. These findings may lead to a better understanding of breast cancer pathology.
Department of Statistics, University of California, Davis, CA, USA.
Jie
J
Peng
Department of Statistics, University of Michigan, Ann Arbor, MI, USA.
Ji
J
Zhu
Department of Genetics, Institute for Cancer Research, Rikshospitalet-Radiumhospitalet Medical Center, Oslo, Norway.
Anna
A
Bergamaschi
Cancer Research Institute and Department of Surgery, Seoul National University College of Medicine, Seoul, South Korea.
Wonshik
W
Han
Cancer Research Institute and Department of Surgery, Seoul National University College of Medicine, Seoul, South Korea.
Dong-Young
DY
Noh
Department of Pathology, Stanford University, CA, USA.
Jonathan R
JR
Pollack
Division of Public Health Science, Fred Hutchinson Cancer Research Center, Seattle, WA, USA.
Pei
P
Wang
DNA copy number alteration; MAP(MAster Predictor) penalty; RNA transcript level; sparse regression; v-fold cross validation