Bayesian Nonparametric Variable Selection as an Exploratory Tool for Finding Genes that Matter

Abstract

High-throughput scientific studies involving no clear a'priori hypothesis are common. For example, a large-scale genomic study of a disease may examine thousands of genes without hypothesizing that any specific gene is responsible for the disease. In these studies, the objective is to explore a large number of possible factors (e.g. genes) in order to identify a small number that will be considered in follow-up studies that tend to be more thorough and on smaller scales. For large-scale studies, we propose a nonparametric Bayesian approach based on random partition models. Our model thus divides the set of candidate factors into several subgroups according to their degrees of relevance, or potential effect, in relation to the outcome of interest. The model allows for a latent rank to be assigned to each factor according to the overall potential importance of its corresponding group. The posterior expectation or mode of these ranks is used to set up a threshold for selecting potentially relevant factors. Using simulated data, we demonstrate that our approach could be quite effective in finding relevant genes compared to several alternative methods. We apply our model to two large-scale studies. The first study involves transcriptome analysis of infection by human cytomegalovirus (HCMV). The objective of the second study is to identify differentially expressed genes between two types of leukemia.