Statistical Modelling 8 (2008), 8196
Multivariate mixtures of Polya trees for modeling ROC data
Timothy E Hanson
Division of Biostatistics,
University of Minnesota School of Public Health,
A460 Mayo Building MMC 303,
420 Delaware Street S.E.,
Minneapolis, MN 55455
USA
eMail:
hanson@biostat.umn.edu
Adam J Branscum
Departments of Biostatistics, Statistics, and Epidemiology,
University of Kentucky,
USA
Ian A Gardner
Department of Medicine and Epidemiology,
University of California at Davis
USA
Abstract:
Receiver operating characteristic (ROC) curves provide a graphical
measure of diagnostic test accuracy. Because ROC curves are determined
using the distributions of diagnostic test outcomes for noninfected and
infected populations, there is an increasing trend to develop flexible
models for these component distributions. We present methodology for
joint nonparametric estimation of several ROC curves from multivariate
serologic data. We develop an empirical Bayes approach that allows for
arbitrary noninfected and infected component distributions that are
modelled using Bayesian multivariate mixtures of finite Polya trees
priors. Robust, data-driven inferences forROCcurves and the area under
the curve are obtained, and a straightforward method for testing a
Dirichlet process versus a more general Polya tree model is presented.
Computational challenges can arise when using Polya trees to model
large multivariate data sets that exhibit clustering. We discuss and
implement practical procedures for addressing these obstacles, which
are applied to bivariate data used to evaluate the performances of
two ELISA tests for detection of Johne's disease.
Keywords:
Bayesian nonparametrics; diagnostic test evaluation; empirical Bayes
back