Semiparametric estimator for the covariate-specific receiver operating characteristic curve

The study of the predictive ability of a marker is mainly based on the accuracy measures provided by the so-called confusion matrix. Besides, the area under the receiver operating characteristic curve has become a popular index for summarizing the overall accuracy of a marker. However, the nature of the relationship between the marker and the outcome, and the role that potential confounders play in this relationship could be fundamental in order to extrapolate the observed results. Directed acyclic graphs commonly used in epidemiology and in causality, could provide good feedback for learning the possibilities and limits of this extrapolation applied to the binary classification problem. Both the covariate-specific and the covariate-adjusted receiver operating characteristic curves are valuable tools, which can help to a better understanding of the real classification abilities of a marker. Since they are strongly related with the conditional distributions of the marker on the positive (subjects with the studied characteristic) and negative (subjects without the studied characteristic) populations, the use of proportional hazard regression models arises in a very natural way. We explore the use of flexible proportional hazard Cox regression models for estimating the covariate-specific and the covariate-adjusted receiver operating characteristic curves. We study their large- and finite-sample properties and apply the proposed estimators to a real-world problem. The developed code (in R language) is provided on Supplemental Material.