Calculate Youden Index from sensitivity and specificity, derive it from a confusion matrix, or find the cutoff threshold that maximizes J.

J gives sensitivity and specificity equal weight. Maximizing it among entered thresholds does not establish a clinically appropriate cutoff; consider validation, prevalence and error consequences.

Related Calculators

Youden Index Formula

The following formula is used to calculate the Youden Index.

YI = Sensitivity + Specificity - 1

Variables:

  • YI is the Youden Index
  • Sensitivity is the true positive rate
  • Specificity is the true negative rate

At a fixed threshold, Youden J = sensitivity + specificity − 1. Its range is −1 to 1: 1 means perfect sensitivity and specificity, −1 means both are zero, and 0 means sensitivity equals the false-positive rate at that threshold. A zero value at one threshold does not prove that the entire test is useless.

What is a Youden Index?

Youden J at a fixed threshold is the vertical difference between its ROC point and the diagonal. Maximizing J selects the largest difference among the thresholds considered, giving sensitivity and specificity equal weight. The calculator compares only the candidate rows supplied. This statistical criterion alone does not establish an appropriate clinical cutoff; validation, prevalence and the consequences of errors also matter.

How to Calculate Youden Index?

The following steps outline how to calculate the Youden Index.

  1. First, determine the Sensitivity (true positive rate).
  2. Next, determine the Specificity (true negative rate).
  3. Next, use the formula YI = Sensitivity + Specificity – 1 to calculate the Youden Index.
  4. Finally, calculate the Youden Index.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Sensitivity (true positive rate) = 0.85

Specificity (true negative rate) = 0.75