Modelling stochastic order in the analysis of receiver operating characteristic data: Bayesian non-parametric approaches

The evaluation of the performance of a continuous diagnostic measure is a commonly encountered task in medical research.We develop Bayesian non-parametric models that use Dirichlet process mixtures and mixtures of Polya trees for the analysis of continuous serologic data.The modelling approach differs from traditional approaches to the analysis of receiver operating characteristic curve data in that it incorporates a stochastic ordering constraint for the distributions of serologic values for the infected and non-infected populations. Biologically such a constraint is virtually always feasible because serologic values from infected individuals tend to be higher than those for non-infected individuals. The models proposed provide data-driven inferences for the infected and non-infected population distributions, and for the receiver operating characteristic curve and corresponding area under the curve.We illustrate and compare the predictive performance of the Dirichlet process mixture and mixture of Polya trees approaches by using serologic data for Johne’s disease in dairy cattle.