The time-dependent Receiver Operating Characteristic (ROC) curve is often used to study the diagnostic accuracy of a single continuous biomarker, measured at baseline, on the onset of a disease condition when the disease onset may occur at different times during the follow-up and hence may be right censored. Due to censoring, the true disease onset status prior to the pre-specified time horizon may be unknown on some patients, which causes difficulty in calculating the time-dependent sensitivity and specificity. We study a simple method that adjusts for censoring by weighting the censored data by the conditional probability of disease onset prior to the time horizon given the biomarker and the observed censoring time. Our numerical study shows that the proposed method produces unbiased and efficient estimators of time-dependent sensitivity and specificity as well as area under the ROC curve, and outperforms several other published methods currently implemented in R packages.
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