Kullback-Leibler Divergence for Medical Diagnostics Accuracy and Cut-point Selection Criterion: How it is related to the Youden Index

Recently, the Kullback-Leibler divergence (KL), which captures the disparity between two distributions, has been considered as an index for determining the diagnostic performance of markers. In this work, we propose using a total KL discrete version (TKLdiscrete), after the discretization of a continuous biomarker, as an optimization criterion for cut-point selection. We linked the proposed TKLdiscrete measure with the Youden index, which is the most commonly used cut-point selection criterion. In addition, we present theoretically and numerically the derived relations in situations of one cut-point (two categories) as well as multiple category markers under binary disease status. This study also investigates a variety of applications of KL divergence in medical diagnostics. For example, KL can serve as an overall measure of diagnostic accuracy, which measures the before-test rule-in and rule-out potential. Graphically, KL divergence depicted through the information graph. A comprehensive data analysis of the Dutch Breast Cancer Data provided to illustrate the proposed applications. Other standard Receiver Operating Characteristic (ROC) measures are also discussed and shown in the data example as competing measures. Using simulation methods, we conducted a power study to compare the performance of our proposed methods with the Youden Index