Youden Index

J Statistic (Youden Index) Explained

The Youden Index represents a summary measurement of the receiver operating characteristic (ROC) curve for the accuracy of a diagnostic test with ordinal or continuous endpoints.

It originates from the work of Youden WJ. back in 1950 and gives equal weight to false positive and false negative values, so it can be concluded that when two tests have the same index, it means they have the same proportion of total misclassified results.

• J Statistic Youden Index = Sensitivity + Specificity – 1

OR

• J Statistic Youden Index = [TP / (TP + FN)] + [TN / (FP + TN)] - 1

Where:

TP = True Positives

TN = True Negatives

FP = False Positives

FN = False Negatives

Youden Index ranges between 0 and 1, with 0 values indicating that a diagnostic test gives the same proportion of positive results for groups with and without the disease. A value of 1 indicates that there are no false positives or false negatives.

The J Statistic can be used in conjunction with receiver operating characteristic (ROC) analysis, where the index is defined for all points of the ROC curve. The maxim value of the index can then be used as a cut-off for numerical diagnostic tests.

References

Original reference

Youden WJ. Index for rating diagnostic tests. Cancer. 1950; 3(1):32-35.

Other references

Ruopp MD, Perkins NJ, Whitcomb BW, Schisterman EF. Youden Index and optimal cut-point estimated from observations affected by a lower limit of detection. Biom J. 2008; 50(3):419-30.

Shan G. Improved Confidence Intervals for the Youden Index. PLoS One. 2015; 10(7):e0127272.

Nakas CT, Alonzo TA, Yiannoutsos CT. Accuracy and cut-off point selection in three-class classification problems using a generalization of the Youden index. Stat Med. 2010; 29(28):2946-55.