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Prognostic accuracy for predicting ordinal competing risk outcomes using ROC surfaces

Author

Listed:
  • Song Zhang

    (University of Pittsburgh)

  • Yang Qu

    (University of Pittsburgh)

  • Yu Cheng

    (University of Pittsburgh)

  • Oscar L. Lopez

    (University of Pittsburgh)

  • Abdus S. Wahed

    (University of Pittsburgh)

Abstract

Many medical conditions are marked by a sequence of events in association with continuous changes in biomarkers. Few works have evaluated the overall accuracy of a biomarker in predicting disease progression. We thus extend the concept of receiver operating characteristic (ROC) surface and the volume under the surface (VUS) from multi-category outcomes to ordinal competing-risk outcomes that are also subject to noninformative censoring. Two VUS estimators are considered. One is based on the definition of the ROC surface and obtained by integrating the estimated ROC surface. The other is an inverse probability weighted U estimator that is built upon the equivalence of the VUS to the concordance probability between the marker and sequential outcomes. Both estimators have nice asymptotic results that can be derived using counting process techniques and U-statistics theory. We illustrate their good practical performances through simulations and applications to two studies of cognition and a transplant dataset.

Suggested Citation

  • Song Zhang & Yang Qu & Yu Cheng & Oscar L. Lopez & Abdus S. Wahed, 2022. "Prognostic accuracy for predicting ordinal competing risk outcomes using ROC surfaces," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 1-22, January.
    • Handle: RePEc:spr:lifeda:v:28:y:2022:i:1:d:10.1007_s10985-021-09539-z
    DOI: 10.1007/s10985-021-09539-z
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    References listed on IDEAS

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    1. Cheng, Yu & Fine, Jason P. & Kosorok, Michael R., 2007. "Nonparametric Association Analysis of Bivariate Competing-Risks Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1407-1415, December.
    2. Dabrowska, Dorota M., 1989. "Kaplan-Meier estimate on the plane: Weak convergence, LIL, and the bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 308-325, May.
    3. Thomas H. Scheike & Mei-Jie Zhang & Thomas A. Gerds, 2008. "Predicting cumulative incidence probability by direct binomial regression," Biometrika, Biometrika Trust, vol. 95(1), pages 205-220.
    4. P. Saha & P. J. Heagerty, 2010. "Time-Dependent Predictive Accuracy in the Presence of Competing Risks," Biometrics, The International Biometric Society, vol. 66(4), pages 999-1011, December.
    5. Yingye Zheng & Tianxi Cai & Yuying Jin & Ziding Feng, 2012. "Evaluating Prognostic Accuracy of Biomarkers under Competing Risk," Biometrics, The International Biometric Society, vol. 68(2), pages 388-396, June.
    6. Stephan Dreiseitl & Lucila Ohno-Machado & Michael Binder, 2000. "Comparing Three-class Diagnostic Tests by Three-way ROC Analysis," Medical Decision Making, , vol. 20(3), pages 323-331, July.
    7. Patrick J. Heagerty & Thomas Lumley & Margaret S. Pepe, 2000. "Time-Dependent ROC Curves for Censored Survival Data and a Diagnostic Marker," Biometrics, The International Biometric Society, vol. 56(2), pages 337-344, June.
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    Cited by:

    1. Yang Qu & Yu Cheng, 2023. "Volume under the ROC surface for high-dimensional independent screening with ordinal competing risk outcomes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 735-751, October.

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