Extreme value theory in analysis of differential expression in microarrays where either only up- or down-regulated genes are relevant or expected

Abstract

Summary We propose an empirical Bayes method based on the extreme value theory (EVT) (BE) for the analysis of data from spotted microarrays where the interest of the investigator (e.g. to identify up-regulated gene markers of a disease) or the design of the experiment (e.g. in certain ‘wild-type versus mutant’ experiments) limits identification of differentially expressed genes to those regulated in a single direction (either up or down). In such experiments, unlike in genome-wide microarrays, analysis is restricted to the tail of the distribution (extremes) of all the genes in the genome. The EVT provides a platform to account for this extreme behaviour, and is therefore a natural candidate for inference about differential expression. We compared the performance of the developed BE method with two other empirical Bayes methods on two real ‘wild-type versus mutant’ datasets where a single direction of regulation was expected due to experimental design, and in a simulation study. The BE method appears to have a better fit to the real data. In the analysis of simulated data, the BE method showed better accuracy and precision while being robust to different characteristics of microarray experiments. The BE method, therefore, seems promising and useful for inference about differential expression in microarrays where either only up- or down-regulated genes are relevant or expected.

Differential variation and expression analysis

“…The two‐component mixture models of limma (Smyth, ) and lemma (Bar et al, ) implicitly assume that the DE genes are symmetrically up‐regulated and down‐regulated, which may or may not be reasonable depending on the data at hand (see, e.g., Ivanek et al, ). In the extreme case where only up‐regulated or down‐regulated genes are expected or relevant, Ivanek et al () proposed first using limma (Smyth, ) to estimate certain hyperparameters and rank the genes and then fitting an extreme value distribution to the tail of interest. Although the three‐component normal mixture of Bar et al () can adequately capture asymmetries in the numbers of overexpressed and underexpressed (dispersed) genes when they exist, the performance of the three‐component normal mixture model can be suboptimal when there is a large degree of overlap between the three mixture components.…”

“…As with the limma (Smyth, ) and lemma (Bar et al, ) models, Bar et al () used a mixture model, but in contrast to limma and lemma, it is based on a mixture of three normal distributions with one component designed to capture non‐DE (dispersed) genes and the remaining two components designed to capture underexpressed (underdispersed) and overexpressed (overdispersed) genes relative to a reference or baseline group. The two‐component mixture models of limma (Smyth, ) and lemma (Bar et al, ) implicitly assume that the DE genes are symmetrically up‐regulated and down‐regulated, which may or may not be reasonable depending on the data at hand (see, e.g., Ivanek et al, ). In the extreme case where only up‐regulated or down‐regulated genes are expected or relevant, Ivanek et al () proposed first using limma (Smyth, ) to estimate certain hyperparameters and rank the genes and then fitting an extreme value distribution to the tail of interest.…”

“…The two-component mixture models of limma (Smyth, 2004) and lemma (Bar et al, 2010) implicitly assume that the DE genes are symmetrically up-regulated and down-regulated, which may or may not be reasonable depending on the data at hand (see, e.g., Ivanek et al, 2008). In the extreme case where only up-regulated or down-regulated genes are expected or relevant, Ivanek et al (2008) proposed first using limma (Smyth, 2004) to estimate certain hyperparameters and rank the genes and then fitting an extreme value distribution to the tail of interest.…”

Differential variation and expression analysis

“…As with the limma [18] and lemma [1] models, Bar et al [2] uses a mixture model, but in contrast to limma and lemma, it is based on a mixture of three normal distributions with one component designed to capture the non-differentially expressed (dispersed) genes, and the remaining two components designed to capture the underexpressed (underdispersed) and overexpressed (overdispersed) genes relative to a reference group. The two-component mixture models of limma [18] and lemma [1] implicitly assume that the differentially expressed genes are symmetrically up-and down-regulated, which may or may not be reasonable depending on the data at hand (see, e.g., [11]). In the extreme case where only up-or down-regulated genes are expected or relevant, Ivanek et al [11] proposed first using limma [18] to estimate certain hyperparameters and rank the genes, and then fitting an extreme value distribution to the tail of interest.…”

“…The two-component mixture models of limma [18] and lemma [1] implicitly assume that the differentially expressed genes are symmetrically up-and down-regulated, which may or may not be reasonable depending on the data at hand (see, e.g., [11]). In the extreme case where only up-or down-regulated genes are expected or relevant, Ivanek et al [11] proposed first using limma [18] to estimate certain hyperparameters and rank the genes, and then fitting an extreme value distribution to the tail of interest. While the three-component Normal mixture of Bar et al [2] can adequately capture asymmetries in the numbers of over-and under-expressed (dispersed) genes when they exist, the performance of the threecomponent Normal mixture model can be suboptimal when there is a large degree of overlap between the three mixture components.…”