youden

Youden's index, also known as Youden's J statistic, is a summary measure used to evaluate the performance of diagnostic tests and biomarkers. It was introduced by American statistician W. J. Youden in 1950 as a simple way to quantify the trade-off between sensitivity and specificity.

Definition and calculation: For a chosen threshold on a diagnostic marker, sensitivity (true positive rate) and specificity (true negative rate) are computed. Youden's index is J = sensitivity + specificity − 1. Equivalently, J = (TP/(TP+FN)) + (TN/(TN+FP)) − 1, and it ranges from -1 to +1, with +1 representing a perfect test and 0 indicating no diagnostic value (equivalent to random guessing).

Usage: The optimal threshold is often taken as the value that maximizes J, providing the best balance between correctly identifying cases and controls. Because J depends only on sensitivity and specificity, it is independent of disease prevalence and can be used to compare tests or biomarkers across studies.

Limitations: Youden's index assumes equal costs of false positives and false negatives and does not incorporate prevalence, clinical consequences, or asymmetric misclassification costs. In imbalanced datasets, maximizing J may not align with clinical priorities; confidence intervals and bootstrap methods are used to assess uncertainty.