Overall accuracy and Youden index
- Measure
Accuracy counts correct results over the total; the Youden index adds sensitivity and specificity and subtracts 1.
What it is
Overall accuracy (the proportion of correct results) looks like the most intuitive measure, but it misleads when the disease is rare: a test that calls everyone negative is right almost every time. The Youden index, J = sensitivity + specificity − 1, does not depend on prevalence and is 0 for a useless test and 1 for a perfect one. It is also used to choose the cutoff that best balances both errors.
Formula and reading
- Accuracy = (TP + TN) / (TP + FP + FN + TN).
- J = Se + Sp − 1 = Se − (1 − Sp).
- Reading: J of 0.80 = the test achieves 80% of the separation a perfect test would.
- Accuracy depends on prevalence; J does not.
Worked example
- Data: 10,000 people are screened; prevalence is 1%, so 100 are diseased and 9,900 healthy.
- A useless test that always says negative gets all 9,900 healthy right; accuracy = 9,900 / 10,000 = 99%; J = 0 + 1 − 1 = 0.
- A real test with 85% sensitivity and 95% specificity: TP 85, FN 15, TN 9,405, FP 495.
- Accuracy = (85 + 9,405) / 10,000 = 9,490 / 10,000 = 94.9%.
- J = 0.85 + 0.95 − 1 = 0.80.
- Reading: the useful test is less accurate than the useless one (94.9% versus 99%), but its J is 0.80 versus 0.
The two tests in the example (prevalence 1%)
| Test | Sensitivity | Specificity | Accuracy | Youden |
|---|---|---|---|---|
| Always negative | 0% | 100% | 99% | 0 |
| Real test | 85% | 95% | 94.9% | 0.80 |
Markers
- accuracy
- J
- Youden
How to read it
- When a study reports only accuracy, look for sensitivity and specificity separately.
- The Youden index appears in cutoff studies, but the chosen cutoff can be adjusted to the cost of each error.
Common pitfalls
- Judging a test only by its overall accuracy in rare diseases.
- Forgetting the − 1 in the Youden index.
- Using the Youden cutoff in screening when not missing cases matters more.
Test yourself
Think of the answer, then tap the question to see it.
Sensitivity 70% and specificity 90%. What is the Youden index?
J = 0.70 + 0.90 − 1 = 0.60.
Why does overall accuracy mislead when prevalence is low?
Healthy people make up almost the whole total, so accuracy mostly reflects specificity, even if the test finds no diseased people.
What is the Youden index of a test that does not discriminate?
0, because its sensitivity equals 1 − specificity.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Receiver operating characteristic curve: overview and practical use for clinicians (Korean Journal of Anesthesiology, 2022); Measures of Diagnostic Accuracy: Basic Definitions (EJIFCC, 2009); Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests - Guidance for Industry and FDA Staff (U.S. Food and Drug Administration, 2007).
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Representative model, for educational purposes only.