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.