Classification error as a measure of gene relevance in cancer diagnosis

One of the main problems in cancer diagnosis by using DNA microarray data is selecting genes relevant for the pathology by analyzing their expression profiles in tissues in two different phenotypical conditions. The question we pose is the following: how do we measure the relevance of a single gene in a given pathology? A gene is relevant for a particular disease if it is possible to correctly predict the occurrence of the pathology in new patients on the basis of expression level of this gene only. In other words, a gene is informative for the disease if its expression levels are useful for training a classifier able to generalize, that is, able to correctly predict the status of new patients. In this paper we present a selection bias free, statistically well founded method for finding relevant genes on the basis of their classification ability. We applied the method on a colon cancer data set and produced a list of relevant genes, ranked on the basis of their prediction accuracy. We found, out of more than 6500 available genes, 54 overexpressed in normal tissue and 77 overexpressed in tumor tissue having prediction accuracy greater than 70% with p-value p les 0.05.