Robust ANOVA for microarray data

Abstract Analysis of Variance (ANOVA) separates the effects of different factors in a dataset. Typical examples for gene microarray data are the factors time and treatment. This separation can improve the interpretability of the results. However, the main effects and interactions, calculated in ANOVA, can be heavily influenced by outliers, large numbers of non-expressed genes with noise, and the heavy-tailedness of the distribution of expression values. Robust methods are less affected by these and will improve the analysis. In this paper, several methods to perform robust nonparametric ANOVA are applied to a large multi-treatment time series dataset. The results are compared with the results obtained with parametric ANOVA using Procrustes analysis. A further comparison is made by Gene Ontology (GO) enrichment analysis of groups of genes identified as significant by inspection of the interaction terms in ANOVA. It is shown that there are significant differences in the estimates of main effects and gene–treatment interactions. ROC curves show an improved representation of current biological knowledge for one particular robust form of ANOVA, using a combination of rank transformed data, with the median as location parameter.