Multivariate Gene Selection and Testing in Studying the Exposure Effects on a Gene Set.

Studying the association between a gene set (e.g., pathway) and exposures using multivariate regression methods is of increasing importance in genomic studies. Such an analysis is often more powerful and interpretable than individual gene analysis. Since many genes in a gene set are likely not affected by exposures, one is often interested in identifying a subset of genes in the gene set that are affected by exposures. This allows for better understanding of the underlying biological mechanism and for pursuing further biological investigation of these genes. The selected subset of "signal" genes also provides an attractive vehicle for a more powerful test for the association between the gene set and exposures. We propose two computationally simple Canonical Correlation Analysis (CCA) based variable selection methods: Sparse Outcome Selection (SOS) CCA and step CCA, to jointly select a subset of genes in a gene set that are associated with exposures. Several model selection criteria, such as BIC and the new Correlation Information Criterion (CIC), are proposed and compared. We also develop a global test procedure for testing the exposure effects on the whole gene set, accounting for gene selection. Through simulation studies, we show that the proposed methods improve upon an existing method when the genes are correlated and are more computationally efficient. We apply the proposed methods to the analysis of the Normative Aging DNA methylation Study to examine the effects of airborne particular matter exposures on DNA methylations in a genetic pathway.