Youden Index and Optimal Cut‐Point Estimated from Observations Affected by a Lower Limit of Detection
Open accessAbstract
The receiver operating characteristic (ROC) curve is used to evaluate a biomarker's ability for classifying disease status. The Youden Index (J), the maximum potential effectiveness of a biomarker, is a common summary measure of the ROC curve. In biomarker development, levels may be unquantifiable below a limit of detection (LOD) and missing from the overall dataset. Disregarding these observations may negatively bias the ROC curve and thus J. Several correction methods have been suggested for mean estimation and testing; however, little has been written about the ROC curve or its summary measures. We adapt non-parametric (empirical) and semi-parametric (ROC-GLM [generalized linear model]) methods and propose parametric methods (maximum likelihood (ML)) to estimate J and the optimal cut-point (c *) for a biomarker affected by a LOD. We develop unbiased estimators of J and c * via ML for normally and gamma distributed biomarkers. Alpha level confidence intervals are proposed using delta and bootstrap methods for the ML, semi-parametric, and non-parametric approaches respectively. Simulation studies are conducted over a range of distributional scenarios and sample sizes evaluating estimators' bias, root-mean square error, and coverage probability; the average bias was less than one percent for ML and GLM methods across scenarios and decreases with increased sample size. An example using polychlorinated biphenyl levels to classify women with and without endometriosis illustrates the potential benefits of these methods. We address the limitations and usefulness of each method in order to give researchers guidance in constructing appropriate estimates of biomarkers' true discriminating capabilities.
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For Qwen-2.5-1.5B-Instruct, Youden's J statistic reaches its highest value of 46.0% when τ=0.95.
“The overall discrimination ability of the estimator, quantified by Youden's J statistic (Ruopp et al., 2008) (TPR -FPR), reaches its highest value of 46.0% when the threshold τ is set to 0.95.”
From TT-SI: Self-Improving LLM Agents with Test-Time Training (2026) · cites this paper as Ruopp et al., 2008
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“The overall discrimination ability of the estimator, quantified by Youden’s J statistic (Ruopp et al., 2008) (TPR − FPR), reaches its highest value of 46.0% when the threshold τ is set to 0.95.”
InfluentialSelf-Improving LLM Agents at Test-Time
Acikgoz, E. C., Qian, C., Ji, H., Hakkani-Tür, D., & Tur, G. (2025) · arXiv
“The overall discrimination ability of the estimator, quantified by Youden’s J statistic (Ruopp et al., 2008) (TPR − FPR), reaches its highest value of 46.0% when the threshold τ is set to 0.95.”
Influential
- Authors
- Ruopp, M. D., Perkins, N. J., Whitcomb, B. W., & Schisterman, E. F.
- Affiliations
- United States Department of Health and Human Services (US)
- Corresponding author
- Schisterman, Enrique F.
- Venue
- Biometrical Journal
- Publisher
- Wiley
- Published
- 2008-06
- Volume
- 50
- Issue
- 3
- Pages
- 419-430
- ISSN
- 0323-3847 (ISSN-L)
- 1521-4036
- PMC
- PMC2515362
- OpenAlex
- W2009637031
- Cited by
- 1,320
- References
- 0
- Citations by year
- 2026: 129 · 2025: 161 · 2024: 157 · 2023: 127 · 2022: 149 · 2021: 143 · 2020: 111 · 2019: 89 · 2018: 68 · 2017: 55 · 2016: 34 · 2015: 32 · 2014: 19 · 2013: 13 · 2012: 22
- FWCI
- 3.16
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Biometrical Journal (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institutes of Health
- National Institute of Child Health and Human Development
- Eunice Kennedy Shriver National Institute of Child Health and Human Development (Z01HD008761)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Computer Science › Artificial Intelligence › Imbalanced Data Classification Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- Youden index, optimal cut-point, receiver operating characteristic, detection limit, biomarker discrimination, maximum likelihood estimation, confidence intervals, endometriosis, polychlorinated biphenyls
- MeSH terms
- Computer Simulation, Endometriosis, Female, Humans, Polychlorinated Biphenyls, ROC Curve, Models, Statistical, Biomarkers, Sample Size
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