Interpretation of ANOVA models for microarray data using PCA

ANOVA is a technique, which is frequently used in the analysis of microarray data, e.g. to assess the significance of treatment effects, and to select interesting genes based on P-values. However, it does not give information about what exactly is causing the effect. Our purpose is to improve the interpretation of the results from ANOVA on large microarray datasets, by applying PCA on the individual variance components. Interaction effects can be visualized by biplots, showing genes and variables in one plot, providing insight in the effect of e.g. treatment or time on gene expression. Because ANOVA has removed uninteresting sources of variance, the results are much more interpretable than without ANOVA. Moreover, the combination of ANOVA and PCA provides a simple way to select genes, based on the interactions of interest.

It is shown that the components from an ANOVA model can be summarized and visualized with PCA, which improves the interpretability of the models. The method is applied to a real time-course gene expression dataset of mesenchymal stem cells. The dataset was designed to investigate the effect of different treatments on osteogenesis. The biplots generated with the algorithm give specific information about the effects of specific treatments on genes over time. These results are in agreement with the literature. The biological validation with GO annotation from the genes present in the selections shows that biologically relevant groups of genes are selected.

R code with the implementation of the method for this dataset is available from http://www.cac.science.ru.nl under the heading "Software".