title: Youden Index and optimal cut-point estimated from observations affected by a lower limit of detection.
abstract: The receiver operating characteristic (ROC) curve is used to evaluate a biomarker's ability for classifying disease status. The Youden Index (J), the maximum potential effectiveness of a biomarker, is a common summary measure of the ROC curve. In biomarker development, levels may be unquantifiable below a limit of detection (LOD) and missing from the overall dataset. Disregarding these observations may negatively bias the ROC curve and thus J. Several correction methods have been suggested for mean estimation and testing; however, little has been written about the ROC curve or its summary measures. We adapt non-parametric (empirical) and semi-parametric (ROC-GLM [generalized linear model]) methods and propose parametric methods (maximum likelihood (ML)) to estimate J and the optimal cut-point (c *) for a biomarker affected by a LOD. We develop unbiased estimators of J and c * via ML for normally and gamma distributed biomarkers. Alpha level confidence intervals are proposed using delta and bootstrap methods for the ML, semi-parametric, and non-parametric approaches respectively. Simulation studies are conducted over a range of distributional scenarios and sample sizes evaluating estimators' bias, root-mean square error, and coverage probability; the average bias was less than one percent for ML and GLM methods across scenarios and decreases with increased sample size. An example using polychlorinated biphenyl levels to classify women with and without endometriosis illustrates the potential benefits of these methods. We address the limitations and usefulness of each method in order to give researchers guidance in constructing appropriate estimates of biomarkers' true discriminating capabilities.
authors.affiliation: Division of Epidemiology, Statistics and Prevention Research, National Institute of Child Health and Human Development, National Institutes of Health, DHHS, 6100 Executive Blvd, 7B03, Rockville Bethesda, MD, USA.
authors.forename: Marcus D
authors.initials: MD
authors.lastname: Ruopp
authors.forename: Neil J
authors.initials: NJ
authors.lastname: Perkins
authors.forename: Brian W
authors.initials: BW
authors.lastname: Whitcomb
authors.forename: Enrique F
authors.initials: EF
authors.lastname: Schisterman
mesh_terms: D015415:Biomarkers / Q000032:analysis*; D003198:Computer Simulation; D004715:Endometriosis; D005260:Female; D006801:Humans; D015233:Models, Statistical; D011078:Polychlorinated Biphenyls / Q000032:analysis; D012372:ROC Curve; D018401:Sample Size
chemical_list: D015415:Biomarkers; D011078:Polychlorinated Biphenyls