title: Regional confidence bands for ROC curves.
abstract: The performance of a diagnostic test is characterised by its specificity and sensitivity. For a quantitative diagnostic test these criteria depend on the selected cut-off point. The receiver operating characteristic (ROC) curve of a quantitative diagnostic test is generated by plotting sensitivity against specificity as the cut-off point runs through the whole range of possible test values. In practice, the ROC curve is estimated from clinical data. One important goal is to select an optimal cut-off point. For this purpose the sample variability has to be taken into account. Recently, Campbell has introduced nonparametric asymptotic simultaneous confidence bands that are valid for the whole ROC curve. In this paper a nonparametric asymptotic approach for the construction of regional confidence bands for ROC curves is proposed. It can be applied for any specificity interval of interest. Our approach is based on the asymptotic theory of empirical and quantile processes. To investigate the small sample properties of the different approaches, a Monte Carlo study was conducted using normal and log-normal data. A method for sample size calculation is presented. Finally, the approaches are applied to a tumour marker in the diagnosis of bone marrow metastases.
authors.affiliation: Institute of Medical Biometry and Epidemiology, Philipps-University of Marburg, Bunsenstrasse 3, 35037 Marburg, Germany. jensen@imbi.uni-heidelberg.de
authors.forename: K
authors.initials: K
authors.lastname: Jensen
authors.forename: H H
authors.initials: HH
authors.lastname: Müller
authors.forename: H
authors.initials: H
authors.lastname: Schäfer
mesh_terms: D019046:Bone Marrow Neoplasms / Q000175:diagnosis; D018288:Carcinoma, Small Cell / Q000188:drug therapy; D019937:Diagnostic Techniques and Procedures / Q000706:statistics & numerical data*; D006801:Humans; D007770:L-Lactate Dehydrogenase; D008175:Lung Neoplasms / Q000188:drug therapy; D009010:Monte Carlo Method; D015337:Multicenter Studies as Topic; D009362:Neoplasm Metastasis / Q000175:diagnosis; D012372:ROC Curve; D018401:Sample Size; D012680:Sensitivity and Specificity; D018709:Statistics, Nonparametric; D013269:Stochastic Processes
chemical_list: D007770:L-Lactate Dehydrogenase