title: 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.
authors.affiliation: Department of Health Sciences, Centre of Biostatistics for Clinical Epidemiology, University of Milan-Bicocca, Monza, Italy. matteo.rota@unimib.it.
authors.forename: Matteo
authors.initials: M
authors.lastname: Rota
authors.affiliation: Department of Health Sciences, Centre of Biostatistics for Clinical Epidemiology, University of Milan-Bicocca, Monza, Italy. laura.antolini@unimib.it.
authors.forename: Laura
authors.initials: L
authors.lastname: Antolini
authors.affiliation: Department of Health Sciences, Centre of Biostatistics for Clinical Epidemiology, University of Milan-Bicocca, Monza, Italy. grazia.valsecchi@unimib.it.
authors.forename: Maria Grazia
authors.initials: MG
authors.lastname: Valsecchi
mesh_terms: D000465:Algorithms; D015415:Biomarkers / Q000032:analysis*; D003198:Computer Simulation; D006801:Humans; D054198:Precursor Cell Lymphoblastic Leukemia-Lymphoma / Q000175:diagnosis / Q000378:metabolism; D011379:Prognosis; D012372:ROC Curve; D018121:Receptors, Cytokine / Q000032:analysis
chemical_list: D015415:Biomarkers; C498762:CRLF2 protein, human; D018121:Receptors, Cytokine