Construction of confidence regions in the ROC space after the estimation of the optimal Youden index-based cut-off point

Leonidas E. Bantis, Christos T. Nakas, Benjamin Reiser

Research output: Contribution to journalArticlepeer-review

Abstract

After establishing the utility of a continuous diagnostic marker investigators will typically address the question of determining a cut-off point which will be used for diagnostic purposes in clinical decision making. The most commonly used optimality criterion for cut-off point selection in the context of ROC curve analysis is the maximum of the Youden index. The pair of sensitivity and specificity proportions that correspond to the Youden index-based cut-off point characterize the performance of the diagnostic marker. Confidence intervals for sensitivity and specificity are routinely estimated based on the assumption that sensitivity and specificity are independent binomial proportions as they arise from the independent populations of diseased and healthy subjects, respectively. The Youden index-based cut-off point is estimated from the data and as such the resulting sensitivity and specificity proportions are in fact correlated. This correlation needs to be taken into account in order to calculate confidence intervals that result in the anticipated coverage. In this article we study parametric and non-parametric approaches for the construction of confidence intervals for the pair of sensitivity and specificity proportions that correspond to the Youden index-based optimal cut-off point. These approaches result in the anticipated coverage under different scenarios for the distributions of the healthy and diseased subjects. We find that a parametric approach based on a Box-Cox transformation to normality often works well. For biomarkers following more complex distributions a non-parametric procedure using logspline density estimation can be used.

Original languageEnglish
Pages (from-to)212-223
Number of pages12
JournalBiometrics
Volume70
Issue number1
DOIs
StatePublished - Mar 2014

Keywords

  • Delta method
  • Logspline
  • ROC curve
  • Sensitivity
  • Specificity
  • Youden index

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • Applied Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • Statistics and Probability

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