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Using logistic regression procedures for estimating receiver operating characteristic curves

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  • Jing Qin

Abstract

Estimation of a receiver operating characteristic, ROC, curve is usually based either on a fully parametric model such as a normal model or on a fully nonparametric model. In this paper, we explore a semiparametric approach by assuming a density ratio model for disease and disease-free densities. This model has a natural connection with the logistic regression model. The proposed semiparametric approach is more robust than a fully parametric approach and is more efficient than a fully nonparametric approach. Two real examples demonstrate that the ROC curve estimated by our semiparametric method is much smoother than that estimated by the nonparametric method. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Jing Qin, 2003. "Using logistic regression procedures for estimating receiver operating characteristic curves," Biometrika, Biometrika Trust, vol. 90(3), pages 585-596, September.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:3:p:585-596
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    Citations

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    Cited by:

    1. Wang, Suohong & Zhang, Biao, 2014. "Semiparametric empirical likelihood confidence intervals for AUC under a density ratio model," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 101-115.
    2. Jiang, Shan & Tu, Dongsheng, 2012. "Inference on the probability P(T1," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1069-1078.
    3. Yousef, Waleed A. & Kundu, Subrata & Wagner, Robert F., 2009. "Nonparametric estimation of the threshold at an operating point on the ROC curve," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4370-4383, October.
    4. Cheam, Amay S.M. & McNicholas, Paul D., 2016. "Modelling receiver operating characteristic curves using Gaussian mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 192-208.
    5. Siyan Liu & Qinglong Tian & Yukun Liu & Pengfei Li, 2024. "Joint Statistical Inference for the Area under the ROC Curve and Youden Index under a Density Ratio Model," Mathematics, MDPI, vol. 12(13), pages 1-21, July.
    6. B Rey deCastro, 2019. "Cumulative ROC curves for discriminating three or more ordinal outcomes with cutpoints on a shared continuous measurement scale," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-16, August.
    7. Margaret Sullivan Pepe, 2008. "Discussions," Biometrics, The International Biometric Society, vol. 64(1), pages 256-258, March.
    8. Zhong Guan & Cheng Peng, 2011. "A rank-based empirical likelihood approach to two-sample proportional odds model and its goodness of fit," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 763-780.
    9. Wan, Shuwen & Zhang, Biao, 2008. "Comparing correlated ROC curves for continuous diagnostic tests under density ratio models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 233-245, September.
    10. Alicja Jokiel-Rokita & Rafał Topolnicki, 2019. "Minimum distance estimation of the binormal ROC curve," Statistical Papers, Springer, vol. 60(6), pages 2161-2183, December.
    11. Zhang, Biao, 2006. "A semiparametric hypothesis testing procedure for the ROC curve area under a density ratio model," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1855-1876, April.
    12. William M. Briggs & Russell Zaretzki, 2008. "The Skill Plot: A Graphical Technique for Evaluating Continuous Diagnostic Tests," Biometrics, The International Biometric Society, vol. 64(1), pages 250-256, March.
    13. Gu Wen & Pepe Margaret, 2009. "Measures to Summarize and Compare the Predictive Capacity of Markers," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-49, October.
    14. Luo, Jingqin & Xiong, Chengjie, 2012. "DiagTest3Grp: An R Package for Analyzing Diagnostic Tests with Three Ordinal Groups," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i03).

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