title: Smooth ROC curves and surfaces for markers subject to a limit of detection using monotone natural cubic splines.
abstract: The use of ROC curves in evaluating a continuous or ordinal biomarker for the discrimination of two populations is commonplace. However, in many settings, marker measurements above or below a certain value cannot be obtained. In this paper, we study the construction of a smooth ROC curve (or surface in the case of three populations) when there is a lower or upper limit of detection. We propose the use of spline models that incorporate monotonicity constraints for the cumulative hazard function of the marker distribution. The proposed technique is computationally stable and simulation results showed a satisfactory performance. Other observed covariates can be also accommodated by this spline-based approach.
authors.affiliation: Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Samos 83200, Greece.
authors.forename: Leonidas E
authors.initials: LE
authors.lastname: Bantis
authors.forename: John V
authors.initials: JV
authors.lastname: Tsimikas
authors.forename: Stelios D
authors.initials: SD
authors.lastname: Georgiou
mesh_terms: D019540:Area Under Curve; D015415:Biomarkers / Q000378:metabolism; D001699:Biometry / Q000379:methods*; D006801:Humans; D057230:Limit of Detection; D008113:Liver Neoplasms / Q000175:diagnosis; D012372:ROC Curve; D016019:Survival Analysis
chemical_list: D015415:Biomarkers
keywords: Censoring; Constrained least squares; Diagnostic accuracy; Smooth distribution function; Smooth survival estimation