 ### Description

Youden's index is one way to attempt summarizing test accuracy into a single numeric value.

Youden's index =

= 1 - ((false positive rate) + (false negative rate))

= 1 - ((1 - (sensitivity)) + (1 - (specificity)))

= (sensitivity) + (specificity) - 1

It may also be expressed as:

Youden's index =

= ( a / (a + b)) + (d / (c + d)) - 1 =

= ((a * d) - (b * c)) / ((a + b) * (c + d))

where:

• a + b = people with disease

• c + d = people without disease

• a = people with disease identified by test (true positive)

• b = people with disease not identified by test (false negatives)

• c = people without disease identified by test (false positives)

• d = people without disease not identified by test (true negatives)

Interpretation:

• minimum index: -1

• maximum index: +1

• A perfect test would have a Youden index of +1.

Limitation:

• The index by itself would not identify problems in sensitivity or specificity.

Baye's theorem can be expressed using the Youden index:

post-test probability given a positive test result =

= ((pretest probability) * S) / (((pretest probability) * (Youden index)) + (1 - E))

post-test probability given a negative test result =

= ((pretest probability) * (1 - S)) / (E - ((pretest probability) * (Youden index)))