title: The optimal ratio of cases to controls for estimating the classification accuracy of a biomarker.
abstract: The case-control design is frequently used to study the discriminatory accuracy of a screening or diagnostic biomarker. Yet, the appropriate ratio in which to sample cases and controls has never been determined. It is common for researchers to sample equal numbers of cases and controls, a strategy that can be optimal for studies of association. However, considerations are quite different when the biomarker is to be used for classification. In this paper, we provide an expression for the optimal case-control ratio, when the accuracy of the biomarker is quantified by the receiver operating characteristic (ROC) curve. We show how it can be integrated with choosing the overall sample size to yield an efficient study design with specified power and type-I error. We also derive the optimal case-control ratios for estimating the area under the ROC curve and the area under part of the ROC curve. Our methods are applied to a study of a new marker for adenocarcinoma in patients with Barrett's esophagus.
authors.affiliation: Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, 615 North Wolfe Street, Baltimore, MD 21205, USA. hjanes@jhsph.edu
authors.forename: Holly
authors.initials: H
authors.lastname: Janes
authors.forename: Margaret
authors.initials: M
authors.lastname: Pepe
mesh_terms: D000230:Adenocarcinoma / Q000175:diagnosis / Q000209:etiology; D019540:Area Under Curve; D001471:Barrett Esophagus / Q000150:complications; D015415:Biomarkers / Q000032:analysis*; D016022:Case-Control Studies; D003627:Data Interpretation, Statistical; D004938:Esophageal Neoplasms / Q000209:etiology; D006801:Humans; D012372:ROC Curve; D012680:Sensitivity and Specificity
chemical_list: D015415:Biomarkers