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Biostatistics Advance Access originally published online on January 20, 2006
Biostatistics 2006 7(3):456-468; doi:10.1093/biostatistics/kxj018
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

The optimal ratio of cases to controls for estimating the classification accuracy of a biomarker

Holly Janes*,{dagger}

Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, 615 North Wolfe Street, Baltimore, MD 21205, USA hjanes{at}jhsph.edu

Margaret Pepe

Department of Biostatistics, University of Washington, and Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue North, Seattle, WA 98195, USA

* To whom correspondence should be addressed.

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.

Keywords: Case–control design; Efficiency; Power; ROC curve; Sample size; Sensitivity; Specificity


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