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

• Published in: Biometrics Vol. 70; no. 1; pp. 212 - 223
• Main Authors: Bantis, Leonidas E, Nakas, Christos T, Reiser, Benjamin
• Format: Journal Article
• Language: English
• Published: United States Blackwell Publishers 01.03.2014; Blackwell Publishing Ltd; International Biometric Society
• Subjects: Bioinformatics; biomarkers; Biomarkers - analysis; BIOMETRIC PRACTICE; Biometrics; biometry; Brucella - isolation & purification; Brucellosis; Brucellosis - blood; Brucellosis - microbiology; CA-125 Antigen - blood; CD3 Complex - blood; Computer Simulation; Confidence interval; Confidence Intervals; Covariance matrices; Data Interpretation, Statistical; decision making; Delta method; Diagnostic Tests, Routine - methods; Gaussian distributions; Humans; Logspline; Maximum likelihood estimation; Pancreatic Neoplasms - blood; Parameter estimation; Rectangles; ROC Curve; Sample size; Sensitivity; Sensitivity and Specificity; Simulations; Specificity; Statistical discrepancies; T-Lymphocytes - microbiology; Youden index; Sensitivity; Specificity; Youden index; Logspline; ROC curve; Delta method
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/biom.12107

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.