In this paper we review the litterature on ROC curves in the presence of covariates. We discuss the different approaches that have been proposed in the litterature to define model, estimate and do asymptotics for ROC curves that incorporate covariates. For reasons of brevity, we mostly focus on nonparametric approaches, altough some parametric and semiparametric methods are also discussed. We also analyze endocrinological data on the body mass index to illustrate the methodology. Finally, me mention some research topics that need further investigation or that are still unexplored.
Pardo-Fernandez, J. C., Rodríguez-Álvarez, M. X., & Van Keilegom, I. (2013). A review on ROC curves in the presence of covariates (ISBA Discussion Paper 2013/50). https://hdl.handle.net/2078.5/199670