Spike and Slab Gene Selection for Multigroup Microarray Data

DNA microarrays can provide insight into genetic changes that characterize different stages of a disease process. Accurate identification of these changes has significant therapeutic and diagnostic implications. Statistical analysis for multistage (multigroup) data is challenging, however. ANOVA-based extensions of two-sample Z-tests, a popular method for detecting differentially expressed genes in two groups, do not work well in multigroup settings. False detection rates are high because of variability of the ordinary least squares estimators and because of regression to the mean induced by correlated parameter estimates. We develop a Bayesian rescaled spike and slab hierarchical model specifically designed for the multigroup gene detection problem. Data preprocessing steps are introduced to deal with unique features of microarray data and to enhance selection performance. We show theoretically that spike and slab models naturally encourage sparse solutions through a process called selective shrinkage. This translates into oracle-like gene selection risk performance compared with ordinary least squares estimates. The methodology is illustrated on a large microarray repository of samples from different clinical stages of metastatic colon cancer. Through a functional analysis of selected genes, we show that spike and slab models identify important biological signals while minimizing biologically implausible false detections.