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.
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