Two-stage receiver operating-characteristic curve estimator for cohort studies

The receiver operating-characteristic (ROC) curve is a graphical statistical tool routinely used for studying the classification accuracy in both, diagnostic and prognosis problems. Given the different nature of these situations, ROC curve estimation has been separately considered for binary (diagnostic) and time-to-event (prognosis) outcomes, even for data coming from the same study design. In this work, the authors propose a two-stage ROC curve estimator which allows to link both contexts through a general prediction model (first-stage) and the empirical cumulative estimator of the distribution function (second-stage) of the considered test (marker) on the total population. The so-called two-stage Mixed-Subject (sMS) approach proves its behavior on both, large-samples (theoretically) and finite-samples (via Monte Carlo simulations). Besides, a useful asymptotic distribution for the concomitant area under the curve is also computed. Results show the ability of the proposed estimator to fit non-standard situations by considering flexible predictive models. Two real-world examples, one with binary and one with time-dependent outcomes, help us to a better understanding of the proposed methodology on usual practical circumstances. The R code used for the practical implementation of the proposed methodology and its documentation is provided as supplementary material.