Review and comparison of ROC curve estimators for a time-dependent outcome with marker-dependent censoring: ROC estimators with marker-dependent censoring

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.

Estimating and comparing time-dependent areas under receiver operating characteristic curves for censored event times with competing risks

The area under the time-dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with subjects who undergo the competing events. In this work, we propose nonparametric inverse probability of censoring weighting estimators of the AUC corresponding to these two definitions, and we study their asymptotic properties. We derive confidence intervals and test statistics for the equality of the AUCs obtained with two markers measured on the same subjects. A simulation study is performed to investigate the finite sample behaviour of the test and the confidence intervals. The method is applied to the French cohort PAQUID to compare the abilities of two psychometric tests to predict dementia onset in the elderly accounting for death without dementia competing risk. The 'timeROC' R package is provided to make the methodology easily usable.