A Bayesian framework for the analysis of microarray expression data: regularized t -test and statistical inferences of gene changes

Abstract

Motivation: DNA microarrays are now capable of providing genome-wide patterns of gene expression across many different conditions. The first level of analysis of these patterns requires determining whether observed differences in expression are significant or not. Current methods are unsatisfactory due to the lack of a systematic framework that can accommodate noise, variability, and low replication often typical of microarray data. Results: We develop a Bayesian probabilistic framework for microarray data analysis. At the simplest level, we model log-expression values by independent normal distributions, parameterized by corresponding means and variances with hierarchical prior distributions. We derive point estimates for both parameters and hyperparameters, and regularized expressions for the variance of each gene by combining the empirical variance with a local background variance associated with neighboring genes. An additional hyperparameter, inversely related to the number of empirical observations, determines the strength of the background variance. Simulations show that these point estimates, combined with a t -test, provide a systematic inference approach that compares favorably with simple t -test or fold methods, and partly compensate for the lack of replication. Availability: The approach is implemented in software called Cyber-T accessible through a Web interface at www.genomics.uci.edu/software.html. The code is available as Open Source and is written in the freely available statistical language R. Contact: pfbaldi@ics.uci.edu; tdlong@uci.edu * To whom correspondence should be addressed. 3 Also at Department of Biological Chemistry, College of Medicine, University of California, Irvine.