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In this paper, we propose a new method remMap -- REgularized Multivariateregression for identifying MAster Predictors -- for fitting multivariateresponse regression models under the high-dimension-low-sample-size setting.remMap is motivated by investigating the regulatory relationships amongdifferent biological molecules based on multiple types of high dimensionalgenomic data. Particularly, we are interested in studying the influence of DNAcopy number alterations on RNA transcript levels. For this purpose, we modelthe dependence of the RNA expression levels on DNA copy numbers throughmultivariate linear regressions and utilize proper regularizations to deal withthe high dimensionality as well as to incorporate desired network structures.Criteria for selecting the tuning parameters are also discussed. Theperformance of the proposed method is illustrated through extensive simulationstudies. Finally, remMap is applied to a breast cancer study, in which genomewide RNA transcript levels and DNA copy numbers were measured for 172 tumorsamples. We identify a tran-hub region in cytoband 17q12-q21, whoseamplification influences the RNA expression levels of more than 30 unlinkedgenes. These findings may lead to a better understanding of breast cancerpathology.

Regularized Multivariate Regression for Identifying Master Predictors with Application to Integrative Genomics Study of Breast Cancer