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# Overall accuracy and Youden index

- Measure

Accuracy counts correct results over the total; the Youden index adds sensitivity and specificity and subtracts 1.

Updated Nov 5, 2026

## Key points

- Accuracy = (TP + TN) / total.
- At low prevalence, accuracy mostly reflects specificity and can be high for a useless test.
- Youden index J = Se + Sp − 1; it runs from 0 (useless) to 1 (perfect).
- The Youden index does not depend on prevalence.
- The cutoff with the highest J is the point on the ROC curve furthest from the diagonal.

On this page

- The basics Key points
- What it is
- Formula and reading
- Worked example
- The two tests in the example (prevalence 1%)
- Markers
- How to read it
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## 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.

## Memory aid

Accuracy is fooled by the healthy: when almost everyone is well, always saying negative looks like a winning bet.

## 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.

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## Connections

## Related 5

- [ROC curve](https://durgical.com/en/epidemiology/roc-curve/)
- [Choosing a cutoff: sensitivity vs specificity](https://durgical.com/en/epidemiology/choosing-a-cutoff-sensitivity-vs-specificity/)
- [Sensitivity](https://durgical.com/en/epidemiology/sensitivity/)
- [Specificity](https://durgical.com/en/epidemiology/specificity/)
- [Validity and reliability](https://durgical.com/en/epidemiology/validity-and-reliability/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

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](https://ekja.org/journal/view.php?doi=10.4097/kja.21209) (Korean Journal of Anesthesiology, 2022); [Measures of Diagnostic Accuracy: Basic Definitions](https://europepmc.org/article/PMC/PMC4975285/) (EJIFCC, 2009); [Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests - Guidance for Industry and FDA Staff](https://www.fda.gov/regulatory-information/search-fda-guidance-documents/statistical-guidance-reporting-results-studies-evaluating-diagnostic-tests-guidance-industry-and-fda) (U.S. Food and Drug Administration, 2007).

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Representative model, for educational purposes only.

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License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/overall-accuracy-and-youden-index/