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Estimation of the volume under the ROC surface with three ordinal diagnostic categories

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  • Kang, Le
  • Tian, Lili

Abstract

With three ordinal diagnostic categories, the most commonly used measure for the overall diagnostic accuracy is the volume under the ROC surface (VUS), which is the extension of the area under the ROC curve (AUC) for binary diagnostic outcomes. This article proposes two kernel smoothing based approaches for estimation of the VUS. In an extensive simulation study, the proposed estimators are compared with the existing parametric and nonparametric estimators in terms of bias and root mean square error. A real data example of 203 participants from a cohort study for the detection of Glycan biomarkers for liver cancer is discussed.

Suggested Citation

  • Kang, Le & Tian, Lili, 2013. "Estimation of the volume under the ROC surface with three ordinal diagnostic categories," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 39-51.
    • Handle: RePEc:eee:csdana:v:62:y:2013:i:c:p:39-51
    DOI: 10.1016/j.csda.2013.01.004
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    References listed on IDEAS

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    1. Hall, Peter G. & Hyndman, Rob J., 2003. "Improved methods for bandwidth selection when estimating ROC curves," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 181-189, August.
    2. Kelly Zou & W. J. Hall, 2000. "Two transformation models for estimating an ROC curve derived from continuous data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(5), pages 621-631.
    3. Lloyd, Chris J. & Yong, Zhou, 1999. "Kernel estimators of the ROC curve are better than empirical," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 221-228, September.
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    Cited by:

    1. Guogen Shan & Hua Zhang & Tao Jiang & Hanna Peterson & Daniel Young & Changxing Ma, 2016. "Exact p-Values for Simon’s Two-Stage Designs in Clinical Trials," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(2), pages 351-357, October.
    2. Khanh To Duc & Monica Chiogna & Gianfranco Adimari, 2019. "Estimation of the volume under the ROC surface in presence of nonignorable verification bias," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 695-722, December.
    3. Zhu, Rui & Ghosal, Subhashis, 2019. "Bayesian Semiparametric ROC surface estimation under verification bias," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 40-52.
    4. Coolen-Maturi, Tahani & Elkhafifi, Faiza F. & Coolen, Frank P.A., 2014. "Three-group ROC analysis: A nonparametric predictive approach," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 69-81.

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