Youden's J Index Calculator — Diagnostic Test Performance

Formula

How this is calculated

Youden's J statistic, proposed by W.J. Youden in 1950, provides a single summary measure of the performance of a diagnostic test across its entire range. It equals sensitivity plus specificity minus one, giving a value between 0 (test performs at chance level) and 1 (perfect discrimination). It is equivalent to the vertical distance from the chance diagonal to the point on the ROC curve corresponding to the chosen cut-off, which makes it the optimal cut-off criterion under equal misclassification costs.

The positive likelihood ratio (LR+) describes how much more likely a positive test result is in a diseased individual compared to a healthy one. An LR+ above 10 provides strong evidence of disease. The negative likelihood ratio (LR−) describes how much less likely a positive test result is in a diseased individual; an LR− below 0.1 provides strong evidence against disease. These ratios are more clinically useful than sensitivity and specificity alone because they can be combined with pre-test probability via Bayes' theorem.

Limitations: J assumes equal costs of false positives and false negatives. If missing a disease (false negative) is far more dangerous than a false alarm, the optimal cut-off shifts toward higher sensitivity at the cost of specificity. In practice, always report J alongside the raw sensitivity, specificity and the AUC of the full ROC curve.