Entropy 2013, 15(4), 1342-1356; doi:10.3390/e15041342
Article

Symmetry Properties of Bi-Normal and Bi-Gamma Receiver Operating Characteristic Curves are Described by Kullback-Leibler Divergences

1 Scotland's Rural College (SRUC), The King's Buildings, West Mains Road, Edinburgh EH9 3JG, UK 2 Department of Mathematics, Southern Illinois University, Carbondale, IL 62901-4408, USA
* Author to whom correspondence should be addressed.
Received: 26 February 2013; Accepted: 2 April 2013 / Published: 10 April 2013
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Abstract: Receiver operating characteristic (ROC) curves have application in analysis of the performance of diagnostic indicators used in the assessment of disease risk in clinical and veterinary medicine and in crop protection. For a binary indicator, an ROC curve summarizes the two distributions of risk scores obtained by retrospectively categorizing subjects as cases or controls using a gold standard. An ROC curve may be symmetric about the negative diagonal of the graphical plot, or skewed towards the left-hand axis or the upper axis of the plot. ROC curves with different symmetry properties may have the same area under the curve. Here, we characterize the symmetry properties of bi-Normal and bi-gamma ROC curves in terms of the Kullback-Leibler divergences (KLDs) between the case and control distributions of risk scores. The KLDs describe the known symmetry properties of bi-Normal ROC curves, and newly characterize the symmetry properties of constant-shape and constant-scale bi-gamma ROC curves. It is also of interest to note an application of KLDs where their asymmetry—often an inconvenience—has a useful interpretation.
Keywords: ROC curve; symmetry; asymmetry; Pareto distribution; bi-Normal; bi-exponential; bi-gamma; Kullback-Leibler divergence; relative entropy

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MDPI and ACS Style

Hughes, G.; Bhattacharya, B. Symmetry Properties of Bi-Normal and Bi-Gamma Receiver Operating Characteristic Curves are Described by Kullback-Leibler Divergences. Entropy 2013, 15, 1342-1356.

AMA Style

Hughes G, Bhattacharya B. Symmetry Properties of Bi-Normal and Bi-Gamma Receiver Operating Characteristic Curves are Described by Kullback-Leibler Divergences. Entropy. 2013; 15(4):1342-1356.

Chicago/Turabian Style

Hughes, Gareth; Bhattacharya, Bhaskar. 2013. "Symmetry Properties of Bi-Normal and Bi-Gamma Receiver Operating Characteristic Curves are Described by Kullback-Leibler Divergences." Entropy 15, no. 4: 1342-1356.

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