Optimal cutoffs for continuous biomarkers for survival data under competing risks

Identifying an optimal cutoff value for a continuous biomarker is often useful for medical applications. For binary outcome, commonly used cutoff finding criteria include Youden's index, classification accuracy, and the Euclidean distance to the upper left corner on the ROC curve. We extend these three criteria to accommodate censored survival time that subjected to competing risks. We provide various definitions of time-dependent true positive rate and false positive rate and estimate those quantities using nonparametric methods. In simulation studies, the Euclidean distance to the upper left corner on the ROC curve shows the best overall performance.