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Two transformation models for estimating an ROC curve derived from continuous data

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  • Kelly Zou
  • W. J. Hall

Abstract

A receiver operating characteristic (ROC) curve is a plot of two survival functions, derived separately from the diseased and healthy samples. A special feature is that the ROC curve is invariant to any monotone transformation of the measurement scale. We propose and analyse semiparametric and parametric transformation models for this two-sample problem. Following an unspecified or specified monotone transformation, we assume that the healthy and diseased measurements have two normal distributions with different means and variances. Maximum likelihood algorithms for estimating ROC curve parameters are developed. The proposed methods are illustrated on the marker CA125 in the diagnosis of gastric cancer.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:27:y:2000:i:5:p:621-631
    DOI: 10.1080/02664760050076443
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    Citations

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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. Y. Huang & M. S. Pepe, 2009. "A Parametric ROC Model-Based Approach for Evaluating the Predictiveness of Continuous Markers in Case–Control Studies," Biometrics, The International Biometric Society, vol. 65(4), pages 1133-1144, December.
    3. 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.
    4. Kelly Zou & W. J. Hall, 2002. "Semiparametric and parametric transformation models for comparing diagnostic markers with paired design," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(6), pages 803-816.
    5. Yin, Jingjing & Tian, Lili, 2014. "Joint inference about sensitivity and specificity at the optimal cut-off point associated with Youden index," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 1-13.
    6. 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.
    7. Alba M. Franco-Pereira & Christos T. Nakas & M. Carmen Pardo, 2020. "Biomarker assessment in ROC curve analysis using the length of the curve as an index of diagnostic accuracy: the binormal model framework," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 625-647, December.
    8. Gu, Minggao & Wu, Yueqin & Huang, Bin, 2014. "Partial marginal likelihood estimation for general transformation models," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 1-18.
    9. Zhongkai Liu & Howard D. Bondell, 2019. "Binormal Precision–Recall Curves for Optimal Classification of Imbalanced Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(1), pages 141-161, April.
    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. Wang, Dan & Tian, Lili, 2017. "Parametric methods for confidence interval estimation of overlap coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 12-26.

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