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Performance Metrics: Youden’s Index

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What is Youden’s Index?

Youden’s Index (also known as Youden’s J Statistic or J) is a performance metric that evaluates the performance of a binary classification model. Its value ranges from 0 to 1. When the value is at its minimum of zero, the model is useless. When its value is 1, there are no false negatives or false positives and the predictions are perfect.

Youden’s Index can be calculated as follows:

J = \frac{\text{true positives}}{\text{true positives}+\text{false negatives}}+\frac{\text{true negatives}}{\text{true negatives}+\text{false positives}}-1

 

It can also be expressed in terms of sensitivity and specificity:

J = \text{sensitivity} + \text{specificity} -1

 

From this last expression, one can easily grasp how J is particularly useful for evaluating a model when sensitivity and specificity are equally important. The cutoff point that optimizes the vertical distance between the ROC-curve and the equal line will optimize a model with sensitivity and specificity being equal.

Youden's Index on the ROC Curve