In longitudinal studies, the marker is measured several times within a fixed follow-up. If a marker measurement has ability to signify a pending change in the clinical status of a patient, then a time-dependent ROC curve on a time-varying marker can be used to guide key medical decisions.

the disease status of an individual is observed and updated at each time point in time-dependent ROC curve analysis. With additional information of time of disease onset for each individual, a ROC curve can be constructed at several time points and the marker’s predictive ability can be compared. Thus, time-dependent ROC curve is an efficient tool in measuring the performance of a candidate marker given the true disease status of individuals at certain time points.

the receiver operating characteristic (ROC) curve is a tool that simply describes the range of trade-offs achieved by a diagnostic test.

The performance of a marker is evaluated by the area under the ROC curve (AUC) in which a higher AUC value indicates a better marker performance. The AUC is also equal to the probability of a diseased individual having a higher marker value than a healthy individual [8].

For the purpose of estimating the time‐dependent AUC and IAUC, the “indirect” methods have some drawbacks. For example, most ROC‐estimation procedures rely on strong parametric assumptions such as proportional hazards, which may lead to potential bias due to the misspecification of the time‐to‐event model. In addition, because these methods are “indirect,” they are not particularly efficient and require unnecessary intensive computation.

everal time‐dependent measures have been proposed in the literature, including time‐dependent sensitivity, specificity, ROC and AUC (Heagerty, Lumley, and Pepe, 2005; Heagerty and Zheng, 2005).