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:
= ( a / (a + b)) + (d / (c + d)) - 1 =
= ((a * d) - (b * c)) / ((a + b) * (c + d))
• 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)
• minimum index: -1
• maximum index: +1
• A perfect test would have a Youden index of +1.
• 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)))
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