Abstract
Investigators often face ultra-high dimensional multi-omics data, where identifying significant genes and omics within a gene is of interest. In such data, each gene forms a group consisting of its multiple omics. Moreover, some genes may also be highly correlated. This leads to a tri-level hierarchical structured data: the cluster level, which is the group of correlated genes, the subgroup level, which is the group of omics of the same gene, and the individual level, which consists of omics. Screening is widely used to remove unimportant variables so that the number of remaining variables becomes smaller than the sample size. Penalized regression with the remaining variables after performing screening is then used to identify important variables. To screen unimportant genes, we propose to cluster genes and conduct screening. We show that the proposed screening method possesses the sure screening property. Extensive simulations show that the proposed screening method outperforms competing methods. We apply the proposed variable selection method to the TCGA breast cancer dataset to identify genes and omics that are related to breast cancer.