Evaluation of Laplace distribution-based ANOVA models applied to microarray data

In a microarray experiment, intensity measurements tend to vary due to various systematic and random effects, which enter at the different stages of the measurement process. Common test statistics do not take these effects into account. An alternative is to use, for example, ANOVA models. In many cases, we can, however, not make the assumption of normally distributed error terms. Purdom and Holmes [6] have concluded that the distribution of microarray intensity measurements can often be better approximated by a Laplace distribution. In this paper, we consider the analysis of microarray data by using ANOVA models under the assumption of Laplace-distributed error terms. We explain the methodology and discuss problems related to fitting of this type of models. In addition to evaluating the models using several real-life microarray experiments, we conduct a simulation study to investigate different aspects of the models in detail. We find that, while the normal model is less sensitive to model misspecifications, the Laplace model has more power when the data are truly Laplace distributed. However, in the latter situation, neither of the models is able to control the false discovery rate at the pre-specified significance level. This problem is most likely related to sample size issues.