Asymmetric and symmetric properties of constant shape Bi-Weibull ROC curve described by Kullback-Leibler divergences

Abstract

Receiver Operating Characteristic (ROC) Curve is used for assessing the ability of a biomarker/screening test to discriminate between nondiseased and diseased subject. In this paper, the parametric ROC curve is studied by assuming Constant Shape Bi-Weibull distribution to the biomarker values. The ROC model developed under this assumption is called Constant Shape Bi-Weibull ROC (WROC) model. Here, the research interest is to know how far the biomarker will make a distinction between diseased and non-diseased subjects when the gold standard is available using parametric WROC curve. The accuracy of diagnostic test is depends on two populations and their characteristics. The properties of WROC curve that explains the behavior of the WROC curve are also discussed. In order to explain WROC properties, the concept of Kullback Leibler Divergence (KLD) is used to study the symmetric and asymmetry properties of WROC Curve. To explain this phenomenon, KLD has been estimated using a simulation study and a real data set.