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Regional confidence bands for ROC curves
Author(s) -
Jensen Katrin,
Müller HansHelge,
Schäfer Helmut
Publication year - 2000
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(20000229)19:4<493::aid-sim352>3.0.co;2-w
Subject(s) - receiver operating characteristic , nonparametric statistics , confidence interval , statistics , range (aeronautics) , quantile , sensitivity (control systems) , cut point , mathematics , sample size determination , coverage probability , sample (material) , materials science , chemistry , chromatography , electronic engineering , engineering , composite material
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. Copyright © 2000 John Wiley & Sons, Ltd.