The receiver operating characteristic (ROC) curve is the most widely used measure for evaluating the discriminatory performance of a continuous biomarker. Incorporating covariates in the analysis can potentially enhance information gathered from the biomarker, as its discriminatory ability may depend on these. In this paper we propose a dependent Bayesian nonparametric model for conditional ROC estimation. Our model is based on dependent Dirichlet processes, where the covariate-dependent ROC curves are indirectly modeled using probability models for related probability distributions in the diseased and healthy groups. Our approach allows for the entire distribution in each group to change as a function of the covariates, provides exact posterior inference up to a Monte Carlo error, and can easily accommodate multiple continuous and categorical predictors. Simulation results suggest that, regarding the mean squared error, our approach performs better than its competitors for small sample sizes and nonlinear scenarios. The proposed model is applied to data concerning diagnosis of diabetes.