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# ROC curve

- Concept

A plot of sensitivity against 1 − specificity across all cutoffs; its area sums up how well the test discriminates.

Updated Nov 5, 2026

## Key points

- Y axis: sensitivity; X axis: 1 − specificity (false positive rate).
- Each point on the curve is a different cutoff.
- AUC = 0.5: no discrimination (the diagonal); AUC = 1: perfect discrimination.
- An AUC of 0.8 or more is usually considered acceptable.
- The curve closest to the top-left corner (largest AUC) belongs to the better test.
- The Youden index (Se + Sp − 1) helps choose the most balanced cutoff.

## What it is

The ROC (receiver operating characteristic) curve plots, for every possible cutoff, sensitivity on the vertical axis and 1 − specificity on the horizontal axis. A useless test follows the diagonal; a perfect test rises to the top-left corner. The area under the curve (AUC) sums up the ability to tell diseased from healthy people in a single number, and lets two tests be compared without fixing a cutoff.

## Worked example

- Data: a marker is evaluated at four cutoffs: 30, 40, 50 and 60 points.
- Sensitivity and 1 − specificity: 30 → (0.98, 0.60), 40 → (0.95, 0.30), 50 → (0.88, 0.15), 60 → (0.80, 0.08).
- Plot the four points and join them from (0, 0) to (1, 1): that is the ROC curve.
- Youden at each cutoff: 0.98 − 0.60 = 0.38; 0.95 − 0.30 = 0.65; 0.88 − 0.15 = 0.73; 0.80 − 0.08 = 0.72.
- The highest index is at 50 points (0.73), with 60 very close behind (0.72).
- Reading: if a second marker had an AUC of 0.75 and this one 0.90, this one would discriminate better overall.

## Rough guide to reading the area under the curve

| AUC | Discrimination |
| --- | --- |
| 0.5 | None (like tossing a coin) |
| 0.6 to 0.7 | Poor |
| 0.7 to 0.8 | Acceptable with reservations |
| 0.8 to 0.9 | Good |
| Above 0.9 | Excellent |

## Markers

- ROC
- AUC
- Youden

## In practice

- Studies of new biomarkers report the AUC to compare them with existing markers.
- Two tests with the same AUC can behave differently in the region that matters (for example, at high specificity) if their curves cross.

## Common pitfalls

- Reading the AUC as the probability of a correct diagnosis in a particular patient.
- Comparing AUCs without a confidence interval or a statistical test.
- Always choosing the Youden cutoff without considering the cost of each type of error.

## Memory aid

Up and to the left is the goal: the curve that hugs that corner separates the ill from the well best.

## Test yourself

Think of the answer, then tap the question to see it.

## What do the axes of an ROC curve show?

The vertical axis is sensitivity and the horizontal axis is 1 − specificity, the false positive rate.

## A test has an AUC of 0.5. What does it mean?

It discriminates no better than chance: its curve lies on the diagonal.

## What does the area under the curve mean in terms of pairs of patients?

The probability that, taking one diseased and one healthy person at random, the diseased one has the value more suggestive of disease.

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## Connections

## Related 5

- [Choosing a cutoff: sensitivity vs specificity](https://durgical.com/en/epidemiology/choosing-a-cutoff-sensitivity-vs-specificity/)
- [Overall accuracy and Youden index](https://durgical.com/en/epidemiology/overall-accuracy-and-youden-index/)
- [Sensitivity](https://durgical.com/en/epidemiology/sensitivity/)
- [Specificity](https://durgical.com/en/epidemiology/specificity/)
- [Likelihood ratios](https://durgical.com/en/epidemiology/likelihood-ratios/)

[← 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).

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Representative model, for educational purposes only.

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Source: https://durgical.com/en/epidemiology/roc-curve/
License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/roc-curve/