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Bayesian Analysis of ROC Curves Using Markov-chain Monte Carlo Methods

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  • Fengchun Peng
  • W.Jack Hall

Abstract

The authors introduce a Bayesian approach to generalized linear regression models for rating data observed in the evaluation of a diagnostic technology. Such models were previously studied using a non-Bayesian approach. In a Bayesian analysis, the difficulties inherent in an ordinal rating scale are circumvented by using data-augmen tation techniques. Posterior distributions for the regression parameters—and thereby for receiver operating charactenstic (ROC) curve parameters and values, for the area under a ROC curve, differences between areas, etc.—may then be computed by Mar kov-chain Monte Carlo methods. Inferences are made in standard Bayesian ways. The methods are exemplified by a study of ultrasonography rating data for the detection of hepatic metastases in patients with colon or breast cancer (previously analyzed) and the results compared. Key words: diagnostic test; ordinal regression; sensitivity; spec ificity. (Med Decis Making 1996;16:404-411)

Suggested Citation

  • Fengchun Peng & W.Jack Hall, 1996. "Bayesian Analysis of ROC Curves Using Markov-chain Monte Carlo Methods," Medical Decision Making, , vol. 16(4), pages 404-411, October.
    • Handle: RePEc:sae:medema:v:16:y:1996:i:4:p:404-411
    DOI: 10.1177/0272989X9601600411
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    Cited by:

    1. Ma, Hua & Bandos, Andriy I. & Gur, David, 2018. "Informativeness of diagnostic marker values and the impact of data grouping," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 76-89.
    2. 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.
    3. Tian, Guo-Liang & Tang, Man-Lai & Yuen, Kam Chuen & Ng, Kai Wang, 2010. "Further properties and new applications of the nested Dirichlet distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 394-405, February.
    4. Martin Hellmich & Keith R. Abrams & Alex J. Sutton, 1999. "Bayesian Approaches to Meta-analysi of ROC Curves," Medical Decision Making, , vol. 19(3), pages 252-264, August.
    5. Martin Hellmich & Keith R. Abrams & David R. Jones & Paul C. Lambert, 1998. "A Bayesian Approach to a General Regression Model for ROC Curves," Medical Decision Making, , vol. 18(4), pages 436-443, October.

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