Time-dependent receiver operating characteristic curve estimator for correlated right-censored time-to-event data

In clinical trials, evaluating the accuracy of risk scores (markers) derived from prognostic models for prediction of survival outcomes is of major concern. The time-dependent receiver operating characteristic curve and the corresponding area under the receiver operating characteristic curve are appealing measures to evaluate the predictive accuracy. Several estimation methods have been proposed in the context of classical right-censored data which assumes the event time of individuals are independent. In many applications, however, this may not hold true if, for example, individuals belong to clusters or experience recurrent events. Estimates may be biased if this correlated nature is not taken into account. This paper is then aimed to fill this knowledge gap to introduce a time-dependent receiver operating characteristic curve and the corresponding area under the receiver operating characteristic curve estimation method for right-censored data that take the correlated nature into account. In the proposed method, the unknown status of censored subjects is imputed using conditional survival functions given the marker and frailty of the subjects. An extensive simulation study is conducted to evaluate and demonstrate the finite sample performance of the proposed method. Finally, the proposed method is illustrated using two real-world examples of lung cancer and kidney disease.