Summary measure of discrimination in survival models based on cumulative/dynamic time-dependent ROC curves

Assessments of the discriminative performance of prognostic models have led to the development of several measures that extend the concept of discrimination as evaluated by the receiver operating characteristics curve and the area under the receiver operating characteristic curve (AUC) of diagnostic settings. Thus, several time-dependent-receiver operating characteristic curve and AUC(t) have been proposed. One of the most used, the cumulative/dynamic AUC(C,D)(t) is the probability that, given two randomly chosen patients, one having failed before t and the other having failed after t, the prognostic marker will be correctly ranked. In this paper, we propose a weighted AUC(C,D)(t) with time- and data-dependent weights as a summary measure of the mean AUC(C,D)(t), restricted to a finite time range to ensure its clinical relevance. A simulation study shows that estimated restricted mean AUC increased with the strength of association of the covariate with the outcome, with low impact of censoring, and adequate coverage of bootstrap confidence intervals. We illustrate this methodology to two real datasets from two randomized clinical trials to assess the prognostic factors of the overall mortality in patients who have compensated cirrhosis and to assess the prognostic factors of event-free survival in patients who have acute myeloid leukemia.