Optimal cut-point definition in biomarkers: The case of censored failure time outcome

Abstract

Background: Cut-point finding is a crucial step for clinical decision making when dealing with diagnostic (or prognostic) biomarkers. The extension of ROC-based cut-point finding methods to the case of censored failure time outcome is of interest when we are in the presence of a biomarker, measured at baseline, used to identify whether there will be the development, or not, of some disease condition within a given time point τ of clinical interest. Methods: Three widely used cut-point finding methods, namely the Youden index, the concordance probability and the point closest to-(0,1) corner in the ROC plane, are extended to the case of censored failure time outcome resorting to non-parametric estimators of the sensitivity and specificity that account for censoring. The performance of these methods in finding the optimal cut-point is compared under Normal and Gamma distributions of the biomarker (in subjects developing or not the disease condition). Normality ensures that estimators point theoretically to the same cut-point. Two motivating examples are provided in the paper. Results: The point closest-to-(0,1) corner approach has the best performance from simulations in terms of mean square error and relative bias. Conclusions: We discuss the use of the Youden index or concordance probability associated to the cut-point identified through the closest-to-(0,1) corner approach to ease interpretability of the classification performance of the dichotomized biomarker. In addition, the achieved performance of the dichotomized biomarker classification associated to the estimated cut-point can be represented through a confidence interval of the point on the ROC curve.