The receiver operating characteristic (ROC) curve has been extended to survival data recently, including the nonparametric approach by Heagerty, Lumley and Pepe (2000) and the semiparametric approach by Heagerty and Zheng (2005) using standard survival analysis techniques based on two different time-dependent ROC curve definitions. However, both approaches cannot adjust for the effect of covariates on the accuracy of the biomarker. To account for the covariate effect, we propose semiparametric models for covariate specific ROC curves corresponding to the two time-dependent ROC curve definitions, respectively. We show that the estimators are consistent and converge to Gaussian processes. In the case of no covariates, the estimators are demonstrated to be more efficient than the Heagerty-Lumley-Pepe estimator and the Heagerty-Zheng estimator via simulation studies. In addition, the estimators can be easily extended to other survival models. We apply these estimators to an HIV dataset.



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