Time-dependent ROC analysis for censored biomarker data due to limit of detection

Receiver operating characteristic (ROC) curve is a well-established analysis method to evaluate biomarker's discrimination accuracy for binary outcomes. When the endpoint of interest is time to event outcome such as time to cancer recurrence, a biomarker's time-varying discriminatory performance is often assessed by time-dependent ROC analysis. In practice, biomarkers are often imprecisely measured due to the limitation of assay sensitivity. The values below the limit of detection are not detectable. Ignorance of such data characteristic may lead to inaccurate estimation of marker's potential discriminatory power. The objective of this article is to extend time-dependent ROC method to censored biomarker data by using parameter estimates from the Cox regression model that accommodates censored biomarker measurements. In the simulation study, the proposed methods are shown to outperform the simple substitution method that has been conventionally adopted for handling censored data. Application data are also given to illustrate our methods.