Error-Pooling Empirical Bayes Model for Enhanced Statistical Discovery of Differential Expression in Microarray Data

Abstract

A number of statistical approaches have been proposed for evaluating the statistical significance of a differential expression in microarray data. The error estimation of these approaches is inaccurate when the number of replicated arrays is small. Consequently, their resulting statistics are often underpowered to detect important differential expression patterns in the microarray data with limited replication. In this paper, we propose an empirical Bayes (EB) heterogeneous error model (HEM) with error-pooling prior specifications for varying technical and biological errors in the microarray data. The error estimation of HEM is thus strengthened by and shrunk toward the EB priors that are obtained by the error-pooling estimation at each local intensity range. By using simulated and real data sets, we compared HEM with two widely used statistical approaches, significance analysis of microarray (SAM) and analysis of variance (ANOVA), to identify differential expression patterns across multiple conditions. The comparison showed that HEM is statistically more powerful than SAM and ANOVA, particularly when the sample size is smaller than five. We also suggest a resampling-based estimation of Bayesian false discovery rate to provide a biologically relevant cutoff criterion of HEM statistics.