Analysis of variance components in gene expression data

Abstract

Motivation: A microarray experiment is a multi-step process, and each step is a potential source of variation. There are two major sources of variation: biological variation and tech- nical variation. This study presents a variance-components approach to investigating animal-to-animal, between-array, within-array and day-to-day variations for two data sets. The first data set involved estimation of technical variances for pooled control and pooled treated RNA samples. The vari- ance components included between-array, and two nested within-array variances: between-section (the upper- and lower- sections of the array are replicates) and within-section (two adjacent spots of the same gene are printed within each section). The second experiment was conducted on four differ- ent weeks. Each week there were reference and test samples with a dye-flip replicate in two hybridization days. The vari- ance components included week-to-week, animal-to-animal and between-array and within-array variances. Results: We applied the linear mixed-effects model to quantify different sources of variation. In the first data set, we found that the between-array variance is greater than the between- section variance, which, in turn, is greater than the within- section variance. In the second data set, for the refer- ence samples, the week-to-week variance is larger than the between-array variance, which, in turn, is slightly larger than the within-array variance. For the test samples, the week-to- week variance has the largest variation. The animal-to-animal variance is slightly larger than the between-array and within- array variances. However, in a gene-by-gene analysis, the animal-to-animal variance is smaller than the between-array variance in four out of five housekeeping genes. In sum- mary, the largest variation observed is the week-to-week effect. ∗To whom correspondence should be addressed.