  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 regularizations 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 tran-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.
