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.
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.
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.
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: Principles of Epidemiology | Lesson 3 - Section 6 (Centers for Disease Control and Prevention, 2012); Principles of Epidemiology | Lesson 3 - Section 5 (Centers for Disease Control and Prevention, 2012).
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Representative model, for educational purposes only.