Bayesian Estimation Of Area Under The ROC Curve With The Binormal Model

The receiver operating characteristic(ROC)curve stems from the statistical decision theory.It has been widely used in the field of medical diagnosis for a long time.Especially in the medical imaging field,the ROC curve plays a decisive role.And,the area under the curve(AUC)is the one of most important indexes to evaluate the superiority-inferiority of diagnostic systems.Thus,to estimate the AUC accurately is of great significance.In this paper,we propose a Bayesian estimation method to estimate the area under the ROC curve with the binormal model.Firstly,using the “truth-state-runs” method to process the continuously-distributed data.By using the ordinal category data likelihood and following the MCMC(Markov Chain Monte Carlo)procedure,we compute the posterior distribution of the binormal parameters intercept and slope,as well as the group boundaries parameters.Meanwhile,we establish the posterior consistency.In simulation studies,we compare our Bayesian estimation method with other estimation methods and conclude that our estimator generally performs better than its competitors.Finally,we conduct the clinical aneurysmal subarachnoid hemorrhage data analysis to evaluate the applicability of the proposed Bayesian estimation method.