Bayesian Nonparametric Estimation of ROC Curves when the True Disease State Is Unknown

• Activity Number: 32
• Type: Contributed
• Date/Time: Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Chong Wang*+ and Bruce Turnbull and Yrjö Gröhn
• Companies: Cornell University and Cornell University and Cornell University
• Keywords: ROC (Receiver operating characteristic) curves ; No Gold Standard ; Bayesian estimate ; non-parametric estimate ; MCMC (Markov chain Monte Carlo) ; Sensitivityand Specificity

Abstract

We develop a methodology for Bayesian nonparametric estimation of ROC curves used for evaluation of the accuracy of a diagnostic procedure. We consider the situation where there is no perfect reference test (i.e., no ``gold standard''). The method is based on a multinomial model for the joint distribution of test-positive and test-negative observations. We use a Bayesian approach with proper priors that assures the monotonicity property of the resulting ROC curve estimate. MCMC methods are used to compute the posterior estimates of the sensitivities and specificities that provide the basis for inference concerning the accuracy of the diagnostic procedure. Because there is no gold standard, identifiability requires the data come from at least two populations with different prevalences. No assumption is needed concerning the shape of the distributions of test values of the diseased and nondiseased in these populations. We discuss an application to an analysis of ELISA scores in diagnostic testing of paratuberculosis (Johne's Disease) for several herds of dairy cows and compare the results to those obtained from previously proposed methods.