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Estimation of a Concordance Probability for Doubly Censored Time-to-Event Data

Author

Listed:
  • Kenichi Hayashi

    (Keio University)

  • Yasutaka Shimizu

    (Waseda University)

Abstract

Evaluating the relationship between a response variable and explanatory variables is important to establish better statistical models. Concordance probability is one measure of this relationship and is often used in biomedical research. Concordance probability can be seen as an extension of the area under the receiver operating characteristic curve. In this study, we propose estimators of concordance probability for time-to-event data subject to double censoring. A doubly censored time-to-event response is observed when either left or right censoring may occur. In the presence of double censoring, existing estimators of concordance probability lack desirable properties such as consistency and asymptotic normality. The proposed estimators consist of estimators of the left-censoring and the right-censoring distributions as a weight for each pair of cases, and reduce to the existing estimators in special cases. We show the statistical properties of the proposed estimators and evaluate their performance via numerical experiments.

Suggested Citation

  • Kenichi Hayashi & Yasutaka Shimizu, 2018. "Estimation of a Concordance Probability for Doubly Censored Time-to-Event Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 546-567, December.
    • Handle: RePEc:spr:stabio:v:10:y:2018:i:3:d:10.1007_s12561-018-9216-5
    DOI: 10.1007/s12561-018-9216-5
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    References listed on IDEAS

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    1. Mithat Gonen & Glenn Heller, 2005. "Concordance probability and discriminatory power in proportional hazards regression," Biometrika, Biometrika Trust, vol. 92(4), pages 965-970, December.
    2. Kim, Yongdai & Kim, Bumsoo & Jang, Woncheol, 2010. "Asymptotic properties of the maximum likelihood estimator for the proportional hazards model with doubly censored data," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1339-1351, July.
    3. Richard Peto, 1973. "Experimental Survival Curves for Interval‐Censored Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(1), pages 86-91, March.
    4. Shuang Ji & Limin Peng & Yu Cheng & HuiChuan Lai, 2012. "Quantile Regression for Doubly Censored Data," Biometrics, The International Biometric Society, vol. 68(1), pages 101-112, March.
    5. Lin, Guixian & He, Xuming & Portnoy, Stephen, 2012. "Quantile regression with doubly censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 797-812.
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