On parametric empirical Bayes methods for comparing multiple groups using replicated gene expression profiles

Abstract

DNA microarrays provide for unprecedented large-scale views of gene expression and, as a result, have emerged as a fundamental measurement tool in the study of diverse biological systems. Statistical questions abound, but many traditional data analytic approaches do not apply, in large part because thousands of individual genes are measured with relatively little replication. Empirical Bayes methods provide a natural approach to microarray data analysis because they can significantly reduce the dimensionality of an inference problem while compensating for relatively few replicates by using information across the array. We propose a general empirical Bayes modelling approach which allows for replicate expression profiles in multiple conditions. The hierarchical mixture model accounts for differences among genes in their average expression levels, differential expression for a given gene among cell types, and measurement fluctuations. Two distinct parameterizations are considered: a model based on Gamma distributed measurements and one based on log-normally distributed measurements. False discovery rate and related operating characteristics of the methodology are assessed in a simulation study. We also show how the posterior odds of differential expression in one version of the model is related to the ratio of the arithmetic mean to the geometric mean of the two sample means. The methodology is used in a study of mammary cancer in the rat, where four distinct patterns of expression are possible.

On the utility of pooling biological samples in microarray experiments

“…Shown is one gene where the averages on the raw intensity scale are quite similar across the individuals and pools. After a log transformation, as often recommended for microarray data (20)(21)(22)(23)(24)(25), the averages in the individuals are smaller than those in the pools. This is a biological realization of the well known Jensen's inequality (26), which states that the average of log transformed values will always be less than or equal to the log of the average of the untransformed values.…”

“…The solid line gives an average performer across the subsets; the dashed line gives the worst case performer. Plots were also generated by using reference lists obtained from a Wilcoxon statistic and a statistic measuring the posterior odds of differential expression (20). Results remained unchanged.…”

Variability-specific differential gene expression across reproductive stages in sows

“…As recently demonstrated at a gene-specific level (Lo and Gottardo, 2007), an accurate modeling of residual dispersion patterns allows for a more realistic fit of gene expression data, reducing the rate of false positives when differential gene expression is characterized in terms of mathematical expectations or their differences (Kendziorski et al, 2003;Newton et al, 2004;Lo and Gottardo, 2007). Moreover, the analysis of heterogeneous residual dispersion patterns opens up promising research possibilities within the gene expression framework, where heterogeneity in residual variability could be viewed as an alternative and plausible characterization of differential expression patterns.…”

“…Assuming null residual (co)variances (Kendziorski et al, 2003;Newton et al, 2004;, heteroskedasticity between physiological stages was analyzed by stating…”

Bayesian statistics in medicine: a 25 year review

“…In Statistics in Medicine this work has not yet made a big impact, but data from DNA microarrays were analysed using empirical Bayes to reduce the dimensionality whilst allowing for relative lack of replication [597,598], tree-based models for homogeneous groupings of multinomials were illustrated on genetic sequence data [599] and genetic model-free approach was used for the meta-analysis of genetic association studies [600]. …”