Nonparametric estimation of ROC curves based on Bayesian models when the true disease state is unknown |
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Authors: | Chong Wang Bruce W Turnbull Yrjö T Gröhn Søren S Nielsen |
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Institution: | 1.Department of Mathematics, College of Veterinary Medicine,Cornell University,Ithaca;2.Postdoctoral Associate, Department of Population Medicine and Diagnostic Sciences, College of Veterinary Medicine,Cornell University,Ithaca;3.School of Operations Research and Industrial Engineering and Department of Statistical Science,Cornell University,Ithaca;4.Department of Population Medicine and Diagnostic Sciences, College of Veterinary Medicine,Cornell University,Ithaca;5.Department of Large Animal Sciences,The Royal Veterinary and Agricultural University,Frederiksberg C,Denmark |
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Abstract: | We develop a Bayesian methodology for 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, that is, 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 which assures the natural 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 that 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 non diseased in these populations. We discuss an application to an analysis of ELISA scores in the diagnostic
testing of paratuberculosis (Johne’s Disease) for several herds of dairy cows and compare the results to those obtained from
some previously proposed methods. |
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