New Applications of Kullback-Leibler Information as a Measure of Diagnostic Accuracy and Its Relation to Common ROC Indices

The Receiver Operating Characteristic curve (ROC) is used for evaluating and comparing diagnostic tests. The Kullback-Leibler distance measure (D), which captures the disparity between two distributions, can be considered as one of the indices for determining the diagnostic performance of markers. This study presents some new applications of Kullback-Leibler distance in medical diagnostics, including overall measure of before-test rule-in and rule-out potential as well as an optimization criteria for cut point selection. Furthermore, the paper links Kullback-Leibler distance with some common ROC measures and demonstrates analytically and numerically the relations in situations of one cut point as well as multiple cut points. Moreover, a graphical application and interpretation of Kullback-Leibler distance, which is referred as the information graph is discussed. Numerical examples as well as a real data analysis are provided to illustrate the proposed new applications.