An adaptive empirical Bayesian thresholding procedure for analysing microarray experiments with replication

Rebecca E. Walls, Stuart Barber, John T. Kent, & Mark S. Gilthorpe

A typical microarray experiment attempts to ascertain which genes display differential expression between various different samples. Supposing we were testing just one gene with a large number of replicates, the conventional method to establish this would be some form of significance testing. However, experiments of this sort often involve looking at the levels of expression for as many as 20,000 genes per slide and the issues of multiple testing associated with such high-dimensional datasets, combined with the problem of an insufficient number of replicates makes significance testing infeasible. This paper develops an empirical Bayesian thresholding procedure, originally introduced for thresholding wavelet coefficients, as an alternative to the existing frequentist methods for the purpose of determining differential expression across thousands of genes. The method is built upon sound theoretical properties and has easy computer implementation in the R statistical package. Furthermore, we consider improvements to the standard empirical Bayesian procedure for when replication is present in order to increase the robustness and reliability of the method. We provide an introduction to microarrays for those unfamilar with the field and the proposed procedure is demonstrated with applications to both 2-channel cDNA microarray experiments and data obtained from the Affymetrix platform.

Keywords: empirical Bayesian, linear additive model, microarray, residual sum of squares, thresholding