AMS2006-19: Modeling stochastic order in the analysis of ROC data: Bayesian nonparametric approaches

Tim Hanson, Athanasios Kottas and Adam Branscum
12/31/2006 09:00 AM
Applied Mathematics & Statistics
The evaluation of the performance of a continuous diagnostic measure is a commonly encountered task in medical research. In this paper we develop Bayesian nonparametric models that use Dirichlet process mixtures and mixtures of Polya trees for the analysis of continuous serologic data. The modeling approach differs from traditional approaches to the analysis of receiver operating characteristic (ROC) curve data in that it incorporates a stochastic ordering constraint for the distributions of serologic values for the infected and noninfected populations. Biologically such a constraint is virtually always feasible because serologic values from infected individuals tend to be higher than those for noninfected individuals. The proposed models provide data-driven inferences for the infected and noninfected distributions, and for the ROC 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 using serologic data for Johne's disease in dairy cattle.

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