Supervised principal component analysis for gene set enrichment of microarray data with continuous or survival outcomes

Motivation: Gene set analysis allows formal testing of subtle but coordinated changes in a group of genes, such as those defined by Gene Ontology (GO) or KEGG Pathway databases. We propose a new method for gene set analysis that is based on principal component analysis (PCA) of genes expression values in the gene set. PCA is an effective method for reducing high dimensionality and capture variations in gene expression values. However, one limitation with PCA is that the latent variable identified by the first PC may be unrelated to outcome. Results: In the proposed supervised PCA (SPCA) model for gene set analysis, the PCs are estimated from a selected subset of genes that are associated with outcome. As outcome information is used in the gene selection step, this method is supervised, thus called the Supervised PCA model. Because of the gene selection step, test statistic in SPCA model can no longer be approximated well using t-distribution. We propose a two-component mixture distribution based on Gumbel exteme value distributions to account for the gene selection step. We show the proposed method compares favorably to currently available gene set analysis methods using simulated and real microarray data. Software: The R code for the analysis used in this article are available upon request, we are currently working on implementing the proposed method in an R package.