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Estimators for ROC curves with missing biomarkers values and informative covariates

Author

Listed:
  • Ana M. Bianco

    (Universidad de Buenos Aires and CONICET)

  • Graciela Boente

    (Universidad de Buenos Aires and CONICET)

  • Wenceslao González–Manteiga

    (Universidad de Santiago de Compostela)

  • Ana Pérez–González

    (Universidad de Vigo)

Abstract

In this paper, we present three estimators of the $${\hbox {ROC}}$$ ROC curve when missing observations arise among the biomarkers. Two of the procedures assume that we have covariates that allow to estimate the propensity and and from this information, the estimators are obtained using an inverse probability weighting method or a smoothed version of it. The third one assumes that the covariates are related to the biomarkers through a regression model which enables us to construct convolution–based estimators of the distribution and quantile functions. Consistency results are obtained under mild conditions. Through a numerical study we evaluate the finite sample performance of the different proposals. A real data set is also analysed.

Suggested Citation

  • Ana M. Bianco & Graciela Boente & Wenceslao González–Manteiga & Ana Pérez–González, 2023. "Estimators for ROC curves with missing biomarkers values and informative covariates," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 931-956, September.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:3:d:10.1007_s10260-022-00680-z
    DOI: 10.1007/s10260-022-00680-z
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    References listed on IDEAS

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    1. Yang, Hanfang & Zhao, Yichuan, 2015. "Smoothed jackknife empirical likelihood inference for ROC curves with missing data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 123-138.
    2. Pardo-Fernandez, Juan Carlos & Rodriguez-Alvarez, Maria Xose & Van Keilegom, Ingrid, 2014. "A review on ROC curves in the presence of covariates," LIDAM Reprints ISBA 2014044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. GonzAlez-Manteiga, Wenceslao & Pardo-FernAndez, Juan Carlos & Van Keilegom, Ingrid, 2011. "ROC Curves in Non-Parametric Location-Scale Regression Models," LIDAM Reprints ISBA 2011010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Qi Long & Xiaoxi Zhang & Brent A. Johnson, 2011. "Robust Estimation of Area Under ROC Curve Using Auxiliary Variables in the Presence of Missing Biomarker Values," Biometrics, The International Biometric Society, vol. 67(2), pages 559-567, June.
    5. Michał Pulit, 2016. "A new method of kernel-smoothing estimation of the ROC curve," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 603-634, July.
    6. Shanshan Li & Yang Ning, 2015. "Estimation of covariate‐specific time‐dependent ROC curves in the presence of missing biomarkers," Biometrics, The International Biometric Society, vol. 71(3), pages 666-676, September.
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