Modeling skewness in human transcriptomes

Abstract

Gene expression data are influenced by multiple biological and technological factors leading to a wide range of dispersion scenarios, although skewed patterns are not commonly addressed in microarray analyses. In this study, the distribution pattern of several human transcriptomes has been studied on free-access microarray gene expression data. Our results showed that, even in previously normalized gene expression data, probe and differential expression within probe effects suffer from substantial departures from the commonly assumed symmetric gaussian distribution. We developed a flexible mixed model for non-competitive microarray data analysis that accounted for asymmetric and heavy-tailed (Student's t distribution) dispersion processes. Random effects for gene expression data were modeled under asymmetric Student's t distributions where the asymmetry parameter (λ) took values from perfect symmetry (λ = 0) to right- (λ>0) or left-side (λ>0) over-expression patterns. This approach was applied to four free-access human data sets and revealed clearly better model performance when comparing with standard approaches accounting for traditional symmetric gaussian distribution patterns. Our analyses on human gene expression data revealed a substantial degree of right-hand asymmetry for probe effects, whereas differential gene expression addressed both symmetric and left-hand asymmetric patterns. Although these results cannot be extrapolated to all microarray experiments, they highlighted the incidence of skew dispersion patterns in human transcriptome; moreover, we provided a new analytical approach to appropriately address this biological phenomenon. The source code of the program accommodating these analytical developments and additional information about practical aspects on running the program are freely available by request to the corresponding author of this article.

Figure 1

Distribution of mean estimates for probe (a) and differential expression within-probe (b) effects under Model SG (grey line) and Model AT (black line) for data set 3.