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When analyzing microarray data, hierarchical models are often used to shareinformation across genes when estimating means and variances or identifyingdifferential expression. Many methods utilize some form of the two-levelhierarchical model structure suggested by Kendziorski et al. [Stat. Med. (2003)22 3899-3914] in which the first level describes the distribution of latentmean expression levels among genes and among differentially expressedtreatments within a gene. The second level describes the conditionaldistribution, given a latent mean, of repeated observations for a single geneand treatment. Many of these models, including those used in Kendziorski's etal. [Stat. Med. (2003) 22 3899-3914] EBarrays package, assume that expressionlevel changes due to treatment effects have the same distribution as expressionlevel changes from gene to gene. We present empirical evidence that thisassumption is often inadequate and propose three-level hierarchical models asextensions to the two-level log-normal based EBarrays models to address thisinadequacy. We demonstrate that use of our three-level models dramaticallychanges analysis results for a variety of microarray data sets and verify thevalidity and improved performance of our suggested method in a series ofsimulation studies. We also illustrate the importance of accounting for theuncertainty of gene-specific error variance estimates when using hierarchicalmodels to identify differentially expressed genes.

The importance of distinct modeling strategies for gene and gene-specific treatment effects in hierarchical models for microarray data