Bayesian Models for Gene Expression With DNA Microarray Data
Two of the critical issues that arise when examining DNA microarray data are (1) determination of which genes best discriminate among the different types of tissue, and (2) characterization of expression patterns in tumor tissues. For (1), there are many genes that characterize DNA expression, and it is of critical importance to try and identify a small set of genes that best discriminate between normal and tumor tissues. For (2), it is critical to be able to characterize the DNA expression of the normal and tumor tissue samples and develop suitable models that explain patterns of DNA expression for these types of tissues. Toward this goal, we propose a novel Bayesian model for analyzing DNA microarray data and propose a model selection methodology for identifying subsets of genes that show different expression levels between normal and cancer tissues. In addition, we propose a novel class of hierarchical priors for the parameters that allow us to borrow strength across genes for making inference. The properties of the priors are examined in detail. We introduce a Bayesian model selection criterion for assessing the various models, and develop Markov chain Monte Carlo algorithms for sampling from the posterior distributions of the parameters and for computing the criterion. We present a detailed case study in endometrial cancer to demonstrate our proposed methodology.