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# Attributable risk and attributable fraction

- Measure

How much of the risk in the exposed is due to the exposure, as cases per 1,000 and as a percentage.

Updated Nov 5, 2026

## Key points

- Attributable risk (AR) = risk in the exposed − risk in the unexposed.
- Attributable fraction in the exposed = AR / risk in the exposed = (RR − 1) / RR.
- It assumes the association is causal and unconfounded.
- With RR = 2, half the cases among the exposed are attributed to exposure; with RR = 3, two thirds.
- It is the risk difference seen from a harmful factor; the ARR is the same idea seen from a treatment.

On this page

- The basics Key points
- What it is
- Formula and reading
- Worked example
- From relative risk to attributable fraction
- Markers
- How to read it
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## What it is

The attributable risk in the exposed is the risk in the exposed minus the risk in the unexposed: the extra cases that appear because of exposure, if the link is causal. The attributable fraction among the exposed expresses that difference as a share of the risk in the exposed, and equals (RR − 1)/RR. Both answer the question: if the exposure were removed, how many cases among the exposed would be prevented?

## Formula and reading

- AR = Re − Ru, in units of risk (for example, per 1,000 over 10 years).
- AFe = (Re − Ru) / Re = (RR − 1) / RR, given as a percentage.
- Reading: AR = 0 means no excess risk; an AFe of 67% means two of every three cases among the exposed are due to exposure.

## Worked example

- Data: over 10 years, tuberculosis occurs in 30 per 1,000 miners exposed to silica and 10 per 1,000 unexposed.
- Attributable risk = 30 − 10 = 20 per 1,000 exposed over 10 years.
- RR = 30 / 10 = 3.
- Attributable fraction in the exposed = 20 / 30 ≈ 0.667, equal to (3 − 1) / 3; that is 67% (rounded).
- Reading: if the link is causal, about 2 of every 3 cases among exposed miners would be prevented without silica.

## From relative risk to attributable fraction

| RR | Attributable fraction in the exposed |
| --- | --- |
| 1.5 | 33% |
| 2 | 50% |
| 3 | 67% |
| 5 | 80% |
| 10 | 90% |

## Markers

- AR
- AFe
- (RR − 1)/RR

## How to read it

- Occupational health uses it to estimate how many cases among exposed workers are due to the workplace hazard.
- When the exposure protects, the same arithmetic gives vaccine efficacy (1 − RR).

## Common pitfalls

- Calculating it when the association is not causal or is confounded.
- Confusing the attributable fraction in the exposed with the population fraction, which depends on how many are exposed.
- Leaving out the risk period.

## Memory aid

The excess is the attributable part: whatever the exposed have on top of the unexposed is charged to the exposure.

## Test yourself

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

## Risk is 50 per 1,000 in the exposed and 20 per 1,000 in the unexposed. What is the attributable risk?

50 − 20 = 30 per 1,000 exposed over the period.

## With RR = 4, what is the attributable fraction in the exposed?

(4 − 1) / 4 = 0.75, that is 75%.

## What assumption is needed to read the attributable risk as preventable cases?

That the link is causal and not explained by bias or confounding.

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## Connections

## Related 4

- [Population attributable risk](https://durgical.com/en/epidemiology/population-attributable-risk/)
- [Relative risk](https://durgical.com/en/epidemiology/relative-risk/)
- [Absolute risk reduction](https://durgical.com/en/epidemiology/absolute-risk-reduction/)
- [Bradford Hill criteria for causation](https://durgical.com/en/epidemiology/bradford-hill-criteria-for-causation/)

[← 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: [Principles of Epidemiology | Lesson 3 - Section 6](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section6.html) (Centers for Disease Control and Prevention, 2012); [Principles of Epidemiology | Lesson 3 - Section 5](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section5.html) (Centers for Disease Control and Prevention, 2012).

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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/attributable-risk-and-attributable-fraction/