Estimating time-dependent ROC curves using data under prevalent sampling

Prevalent sampling is frequently a convenient and economical sampling technique for the collection of time-to-event data and thus is commonly used in studies of the natural history of a disease. However, it is biased by design because it tends to recruit individuals with longer survival times. This paper considers estimation of time-dependent receiver operating characteristic curves when data are collected under prevalent sampling. To correct the sampling bias, we develop both nonparametric and semiparametric estimators using extended risk sets and the inverse probability weighting techniques. The proposed estimators are consistent and converge to Gaussian processes, while substantial bias may arise if standard estimators for right-censored data are used. To illustrate our method, we analyze data from an ovarian cancer study and estimate receiver operating characteristic curves that assess the accuracy of the composite markers in distinguishing subjects who died within 3-5 years from subjects who remained alive. Copyright © 2016 John Wiley & Sons, Ltd.