In studies that use DNA arrays to assess changes in gene expression, it is preferable to measure the significance of treatment effects on a group of genes from a pathway or functional category such as gene ontology terms (GO terms, http://www.geneontology.org) because this facilitates the interpretation of effects and may markedly increase significance. A modified meta-analysis method to combine p-values was developed to measure the significance of an overall treatment effect on such functionally-defined groups of genes, taking into account the correlation structure among genes. For hypothesis testing that allows gene expression to change in both directions, p-values are calculated under the null distribution generated by a Monte Carlo method. As a test of this procedure, we attempted to distinguish altered pathways in microarray studies performed with Mitochips, oligonucleotide microarrays specific to mitochondrial DNA-encoded transcripts. We found that our analytic method improves the specificity of selection for altered pathways, due to incorporation of the inter-gene correlation structure in each pathway. It is thus a practical method to measure treatment effects on GO groups. In many actual applications, microarray experiments measure treatment effects under complicated design structures and with small sample sizes. For such applications to real data of limited statistical power, and also in computer simulations, we demonstrate that our method gives reasonable test results.

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 technical 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 variance 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 different weeks. Each week there were reference and test samples with a dye-flip replicate in two hybridization days. The variance 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 reference 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 summary, the largest variation observed is the week-to-week effect. Another important source of variability is the animal-to-animal variation. Finally, we describe the use of variance-component estimates to determine optimal numbers of animals, arrays per animal and sections per array in planning microarray experiments.