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Estimation of the volume under the ROC surface in presence of nonignorable verification bias

Author

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  • Khanh To Duc

    (University of Padova)

  • Monica Chiogna

    (University of Bologna)

  • Gianfranco Adimari

    (University of Padova)

Abstract

The volume under the receiver operating characteristic surface (VUS) is useful for measuring the overall accuracy of a diagnostic test when the possible disease status belongs to one of three ordered categories. In medical studies, the VUS of a new test is typically estimated through a sample of measurements obtained by some suitable sample of patients. However, in many cases, only a subset of such patients has the true disease status assessed by a gold standard test. In this paper, for a continuous-scale diagnostic test, we propose four estimators of the VUS which accommodate for nonignorable missingness of the disease status. The estimators are based on a parametric model which jointly describes both the disease and the verification process. Identifiability of the model is discussed. Consistency and asymptotic normality of the proposed estimators are shown, and variance estimation is discussed. The finite-sample behavior is investigated by means of simulation experiments. An illustration is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:28:y:2019:i:4:d:10.1007_s10260-019-00451-3
    DOI: 10.1007/s10260-019-00451-3
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    References listed on IDEAS

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    1. Rotnitzky, Andrea & Faraggi, David & Schisterman, Enrique, 2006. "Doubly Robust Estimation of the Area Under the Receiver-Operating Characteristic Curve in the Presence of Verification Bias," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1276-1288, September.
    2. Xiao-Hua Zhou & Pete Castelluccio, 2004. "Adjusting for Non-Ignorable Verification Bias in Clinical Studies for Alzheimer's Disease," UW Biostatistics Working Paper Series 1044, Berkeley Electronic Press.
    3. Danping Liu & Xiao-Hua Zhou, 2010. "A Model for Adjusting for Nonignorable Verification Bias in Estimation of the ROC Curve and Its Area with Likelihood-Based Approach," Biometrics, The International Biometric Society, vol. 66(4), pages 1119-1128, December.
    4. 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.
    5. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    6. 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.
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    Cited by:

    1. Chinyereugo M Umemneku Chikere & Kevin Wilson & Sara Graziadio & Luke Vale & A Joy Allen, 2019. "Diagnostic test evaluation methodology: A systematic review of methods employed to evaluate diagnostic tests in the absence of gold standard – An update," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-25, October.

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