Population attributable risk
- Measure
How many cases in the whole population are due to an exposure; it depends on its strength and on how many people are exposed.
What it is
The population attributable risk (PAR) is the risk in the whole population minus the risk in the unexposed. The population attributable fraction (PAF) expresses it as a share of all cases. Unlike the attributable fraction in the exposed, it depends on how common the exposure is: a factor with a moderate RR that many people have can cause more cases in a population than a strong but rare factor. That is why it guides public health priorities.
Formula and reading
- PAR = Rt − Ru; PAF = (Rt − Ru) / Rt.
- Levin: PAF = Pe(RR − 1) / [1 + Pe(RR − 1)].
- Reading: a PAF of 44% means that, if the link is causal, removing the exposure would prevent 44 of every 100 cases in the population.
Worked example
- Data: population of 10,000; 40% exposed (4,000). Yearly risk: 15 per 1,000 in the exposed and 5 per 1,000 in the unexposed.
- Cases: 4,000 × 0.015 = 60 exposed and 6,000 × 0.005 = 30 unexposed; total 90, overall risk 9 per 1,000.
- PAR = 9 − 5 = 4 per 1,000 per year; PAF = 4 / 9 ≈ 0.444, that is 44%.
- With Levin: 0.4 × (3 − 1) = 0.8; PAF = 0.8 / 1.8 ≈ 0.444. It matches.
- Rare exposure (1%) with RR = 10: PAF = 0.01 × 9 / (1 + 0.09) = 0.09 / 1.09 ≈ 8%.
- Reading: the common exposure with RR 3 explains 44% of cases; the rare one with RR 10, only about 8%.
Attributable fraction in the exposed versus in the population
| Feature | In the exposed | In the population |
|---|---|---|
| Formula | (RR − 1) / RR | Pe(RR − 1) / [1 + Pe(RR − 1)] |
| Depends on how many are exposed | No | Yes |
| Question | How many cases among the exposed are due to the exposure? | How many cases in the whole population would be prevented? |
| Use | Individual risk, occupational health | Public health priorities |
Markers
- PAR
- PAF
- Levin
How to read it
- It explains why smoking, hypertension and obesity dominate population strategies: they are very common.
- Burden-of-disease studies use population attributable fractions to share deaths and DALYs among risk factors.
Common pitfalls
- Confusing it with the attributable fraction in the exposed.
- Adding the PAFs of several factors and expecting 100%: they can exceed it because the factors overlap.
- Using a confounded RR, which biases the PAF.
Test yourself
Think of the answer, then tap the question to see it.
What does the population attributable fraction need that the fraction in the exposed does not?
The prevalence of the exposure in the population.
Pe = 50% and RR = 2. What is the PAF by Levin's formula?
0.5 × 1 = 0.5; PAF = 0.5 / 1.5 ≈ 0.33, that is 33%.
Why can a factor with RR 1.5 matter more for public health than one with RR 8?
If the first is very common and the second very rare, the first can explain more cases in the population.
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.