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

  • Kenichi Hayashi
  • Yasutaka Shimizu


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.


Concordance probability Doubly censored data Time-to-event response 



The authors are grateful to Drs. Yasuhiko Sakata, Daisaku Nakatani, and Yasushi Sakata for allowing us to utilize the dataset used in [6]. The authors would like to acknowledge the associate editor and anonymous reviewers for very useful comments and suggestions that improve the presentation of the paper. K. Hayashi is supported by JSPS KAKENHI (Grant-in-Aid for Scientific Research) Grant Number 15K15950. S. Shimizu is supported by JSPS KAKENHI (Grant-in-Aid for Scientific Research) Grant Number 70423085.


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Copyright information

© International Chinese Statistical Association 2018

Authors and Affiliations

  1. 1.Department of MathematicsKeio UniversityYokohamaJapan
  2. 2.Department of Applied MathematicsWaseda UniversityTokyoJapan

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