An Integrated Bayesian Nonparametric Approach for Stochastic and Variability Orders in ROC Curve Estimation: An Application to Endometriosis Diagnosis
Beom Seuk Hwang, Zhen Chen · Journal of the American Statistical Association · 2015
Beom Seuk Hwang & Zhen ChenBeom Seuk Hwang is Postdoctoral Fellow (E-mail: ) and Zhen Chen is Investigator (E-mail: ), Biostatistics and Bioinformatics Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD 20892. This research was supported by the Intramural Research Program of the Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health. This study used the high-performance computational capabilities of the Biowulf Linux cluster at the National Institutes of Health, Bethesda, MD (http://biowulf.nih.gov). The authors thank Athanasios Kottas, Paul S. Albert, the editor, associate editor, and two anonymous reviewers for insightful and helpful comments.In estimating ROC curves of multiple tests, some a priori constraints may exist, either between the healthy and diseased populations within a test or between tests within a population. In this article, we proposed an integrated modeling approach for ROC curves that jointly accounts for stochastic and variability orders. The stochastic order constrains the distributional centers of the diseased and healthy populations within a test, while the variability order constrains the distributional spreads of the tests within each of the populations. Under a Bayesian nonparametric framework, we used features of the Dirichlet process mixture to incorporate these order constraints in a natural way. We applied the proposed approach to data from the Physician Reliability Study that investigated the accuracy of diagnosing endometriosis using different clinical information. To address the issue of no gold standard in the real data, we used a sensitivity analysis approach that exploited diagnosis from a panel of experts. To demonstrate the performance of the methodology, we conducted simulation studies with varying sample sizes, distributional assumptions, and order constraints. Supplementary materials for this article are available online.