Cumulative/dynamic ROC curve estimation under interval censorship

The receiver operating characteristic (ROC) curve is a graphical tool commonly used to assess the discriminatory ability of continuous markers in binary classification problems. Different extensions of the ROC curve have been proposed in the prognosis context, where the characteristics in the study are time-dependent events. Perhaps the most direct generalization is the so-called cumulative/dynamic (C/D) ROC curve. The main particularity when dealing with the C/D ROC curve estimation is the presence of incomplete information. Several approximation methods addressing this censoring problem have been suggested in the statistical literature, most of them focused on the right-censored case. Interval censorship arises naturally from those studies where subjects undergo periodical follow-ups. They may miss a scheduled appointment and the exact event times are only known to fall in a certain range. A new approach for estimating the C/D ROC curve under the particular scheme of interval censorship is presented in this work. Its finite-sample behaviour is studied via Monte Carlo simulations on two different scenarios. Results suggest that the proposed approximation is better than the existing one in terms of absolute error. Its direct application is illustrated in the real-world data set which motivated this research. The uniform strong consistency and a suitable R function for its practical implementation are provided as Appendices.