  Risk stratification is most directly and informatively summarized as a risk
distribution curve. From this curve the ROC curve, predictiveness curve, and
other curves depicting risk stratification can be derived, demonstrating that
they present similar information. A mathematical expression for the ROC curve
AUC is derived which clarifies how this measure of discrimination quantifies
the overlap between patients who have and don't have events. This expression is
used to define the positive correlation between the dispersion of the risk
distribution curve and the ROC curve AUC. As more disperse risk distributions
and greater separation between patients with and without events characterize
superior risk stratification, the ROC curve AUC provides useful information.
