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Bayesian Semiparametric ROC surface estimation under verification bias

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  • Zhu, Rui
  • Ghosal, Subhashis

Abstract

The Receiver Operating Characteristic (ROC) surface is a generalization of the ROC curve and is widely used for assessment of the accuracy of diagnostic tests on three categories. Verification bias occurs when not all subjects have their labels observed. This is a common problem in disease diagnosis since the gold standard test to get labels, i.e., the true disease status, can be invasive and expensive. The same situation happens in the evaluation of semi-supervised learning, where the unlabeled data are incorporated. A Bayesian approach for estimating the ROC surface is proposed based on continuous data under a semi-parametric trinormality assumption. The proposed method is then extended to situations in the presence of verification bias. The posterior distribution is computed under the trinormality assumption using a rank-based likelihood. The consistency of the posterior under a mild condition is also established. The proposed method is compared with existing methods for estimating an ROC surface. Simulation results show that it performs well in terms of accuracy. The method is applied to evaluate the performance of CA125 and HE4 in the diagnosis of epithelial ovarian cancer (EOC) as a demonstration.

Suggested Citation

  • Zhu, Rui & Ghosal, Subhashis, 2019. "Bayesian Semiparametric ROC surface estimation under verification bias," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 40-52.
    • Handle: RePEc:eee:csdana:v:133:y:2019:i:c:p:40-52
    DOI: 10.1016/j.csda.2018.09.003
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    References listed on IDEAS

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    1. 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.
    2. Yueh-Yun Chi & Xiao-Hua Zhou, 2008. "Receiver operating characteristic surfaces in the presence of verification bias," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(1), pages 1-23.
    3. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265.
    4. Todd A. Alonzo & Margaret Sullivan Pepe, 2005. "Assessing accuracy of a continuous screening test in the presence of verification bias," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 173-190, January.
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