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

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  • Timothy E. Hanson
  • Athanasios Kottas
  • Adam J. Branscum

Abstract

Summary. 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.

Suggested Citation

  • Timothy E. Hanson & Athanasios Kottas & Adam J. Branscum, 2008. "Modelling stochastic order in the analysis of receiver operating characteristic data: Bayesian non‐parametric approaches," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(2), pages 207-225, April.
  • Handle: RePEc:bla:jorssc:v:57:y:2008:i:2:p:207-225
    DOI: 10.1111/j.1467-9876.2007.00609.x
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    Cited by:

    1. Chen, Yuhui & Hanson, Timothy E., 2014. "Bayesian nonparametric k-sample tests for censored and uncensored data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 335-346.
    2. Antonio R. Linero & Michael J. Daniels, 2015. "A Flexible Bayesian Approach to Monotone Missing Data in Longitudinal Studies With Nonignorable Missingness With Application to an Acute Schizophrenia Clinical Trial," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 45-55, March.
    3. Haiming Zhou & Timothy Hanson & Jiajia Zhang, 2017. "Generalized accelerated failure time spatial frailty model for arbitrarily censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 495-515, July.
    4. Beom Seuk Hwang & Zhen Chen, 2015. "An Integrated Bayesian Nonparametric Approach for Stochastic and Variability Orders in ROC Curve Estimation: An Application to Endometriosis Diagnosis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 923-934, September.

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