Abstract: 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 do not involve covariates other than the biomarker and cannot be used to estimate the ROC curve adjusted for covariates. To account for the covariate effect, we propose a joint model approach which assumes that the hazard of failure depends on the biomarker and the covariates through a proportional hazards model and that the biomarker depends the covariates through a semiparametric location model. We propose semiparametric estimators 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.
Key words and phrases: Location model, proportional hazards model, receiver operating characteristic curve, survival analysis.