Pareto depth sampling distributions for gene ranking

In this paper we propose a method for gene ranking from microarray experiments using multiple discriminants. The novelty of our approach is that a gene's relative rank is determined according to the ordinal theory of multiple objective optimization. Furthermore, the distribution of each gene's rank, called Pareto depth, is determined by resampling over the microarray replicates. This distribution is called the Pareto depth sampling distribution (PDSD) and it is used to assess the stability of each ranking. Graphical representation of the PDSD as an image communicates information about the stability of each gene's rank. We illustrate on data from a mouse retina microarray experiment.