YoudenIndex

YoudenIndex, or Youden's J statistic, is a summary measure used to evaluate the discriminatory ability of a binary diagnostic test. It combines sensitivity and specificity into a single statistic to compare tests or to select an optimal threshold for classification.

Formally, sensitivity is the true positive rate and specificity is the true negative rate. Youden's index J is defined as J = sensitivity + specificity − 1. Because sensitivity and specificity lie in the interval [0, 1], J lies in [−1, 1]. A value of 1 indicates perfect discrimination, 0 indicates a test with no diagnostic value relative to random guessing, and negative values indicate performance worse than random.

Youden's index is equivalent to TPR − FPR, since FPR = 1 − specificity. In the ROC space, maximizing J corresponds to choosing the point on the ROC curve that is farthest from the diagonal line of no discrimination; the threshold achieving the maximum J is often selected as the optimal cut-off. J is independent of disease prevalence because it relies on sensitivity and specificity rather than predictive values.

Practical use and limitations: J is computed across possible thresholds using sample data to identify the threshold with the largest J. Confidence intervals can be estimated via bootstrapping. As with any single-number metric, J should be interpreted in the clinical context, considering costs of misclassification and prevalence, and it should be used alongside other measures such as predictive values and decision-analytic considerations.