The Youden Index and the Optimal Cut‐Point Corrected for Measurement Error

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Abstract
Random measurement error can attenuate a biomarker's ability to discriminate between diseased and non‐diseased populations. A global measure of biomarker effectiveness is the Youden index, the maximum difference between sensitivity, the probability of correctly classifying diseased individuals, and 1‐specificity, the probability of incorrectly classifying health individuals. We present an approach for estimating the Youden index and associated optimal cut‐point for a normally distributed biomarker that corrects for normally distributed random measurement error. We also provide confidence intervals for these corrected estimates using the delta method and coverage probability through simulation over a variety of situations. Applying these techniques to the biomarker thiobarbituric acid reaction substance (TBARS), a measure of sub‐products of lipid peroxidation that has been proposed as a discriminating measurement for cardiovascular disease, yields a 50% increase in diagnostic effectiveness at the optimal cut‐point. This result may lead to biomarkers that were once naively considered ineffective becoming useful diagnostic devices.