Optimal survival time-related cut-point with censored data

In biomedical research and practice, continuous biomarkers are often used for diagnosis and prognosis, with a cut-point being established on the measurement to aid binary classification. When survival time is examined for the purposes of disease prognostication and is found to be related to the baseline measure of a biomarker, employing a single cut-point on the biomarker may not be very informative. Using survival time-dependent sensitivity and specificity, we extend a concordance probability-based objective function to select survival time-related cut-points. To estimate the objective function with censored survival data, we adopt a non-parametric procedure for time-dependent receiver operational characteristics curves, which uses nearest neighbor estimation techniques. In a simulation study, the proposed method, when used to select a cut-point to optimally predict survival at a given time within a specified range, yields satisfactory results. We apply the procedure to estimate survival time-dependent cut-point on the prognostic biomarker of serum bilirubin among patients with primary biliary cirrhosis.