Most microarray experiments are carried out with the purpose of identifying genes whose expression varies in relation with specific conditions or in response to environmental stimuli. In such studies, genes showing similar mean expression values between two or more groups are considered as not differentially expressed, even if hidden subclasses with different expression values may exist. In this paper we propose a new method for identifying differentially expressed genes, based on the area between the ROC curve and the rising diagonal (ABCR). ABCR represents a more general approach than the standard area under the ROC curve (AUC), because it can identify both proper (i.e., concave) and not proper ROC curves (NPRC). In particular, NPRC may correspond to those genes that tend to escape standard selection methods.