Novel metrics for evaluating improvement in discrimination: net reclassification and integrated discrimination improvement for normal variables and nested models

Net reclassification and integrated discrimination improvements have been proposed as alternatives to the increase in the area under the curve for evaluating improvement in the performance of risk assessment algorithms introduced by the addition of new phenotypic or genetic markers. In this paper, we demonstrate that in the setting of linear discriminant analysis, under the assumptions of multivariate normality, all three measures can be presented as functions of the squared Mahalanobis distance. This relationship affords an interpretation of the magnitude of these measures in the familiar language of effect size for uncorrelated variables. Furthermore, it allows us to conclude that net reclassification improvement can be viewed as a universal measure of effect size. Our theoretical developments are illustrated with an example based on the Framingham Heart Study risk assessment model for high-risk men in primary prevention of cardiovascular disease.