Bayesian joint selection of genes and pathways: applications in multiple myeloma genomics.

It is well-established that the development of a disease, especially cancer, is a complex process that results from the joint effects of multiple genes involved in various molecular signaling pathways. In this article, we propose methods to discover genes and molecular pathways significantly associated with clinical outcomes in cancer samples. We exploit the natural hierarchal structure of genes related to a given pathway as a group of interacting genes to conduct selection of both pathways and genes. We posit the problem in a hierarchical structured variable selection (HSVS) framework to analyze the corresponding gene expression data. HSVS methods conduct simultaneous variable selection at the pathway (group level) and the gene (within-group) level. To adapt to the overlapping group structure present in the pathway-gene hierarchy of the data, we developed an overlap-HSVS method that introduces latent partial effect variables that partition the marginal effect of the covariates and corresponding weights for a proportional shrinkage of the partial effects. Combining gene expression data with prior pathway information from the KEGG databases, we identified several gene-pathway combinations that are significantly associated with clinical outcomes of multiple myeloma. Biological discoveries support this relationship for the pathways and the corresponding genes we identified.