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# 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.

Updated Nov 5, 2026

## Key points

- PAR = risk in the total population − risk in the unexposed.
- PAF = PAR / risk in the total population.
- Levin's formula: PAF = Pe(RR − 1) / [1 + Pe(RR − 1)], with Pe = prevalence of exposure.
- A common exposure with a modest RR can have a larger PAF than a rare one with a high RR.
- It assumes causation and no confounding, like the attributable risk.

On this page

- The basics Key points
- What it is
- Formula and reading
- Worked example
- Attributable fraction in the exposed versus in the population
- Markers
- How to read it
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## 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.

## Memory aid

Strength times spread: what counts for a population is how much a factor harms multiplied by how many people have it.

## 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.

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## Connections

## Related 5

- [Attributable risk and attributable fraction](https://durgical.com/en/epidemiology/attributable-risk-and-attributable-fraction/)
- [Relative risk](https://durgical.com/en/epidemiology/relative-risk/)
- [Prevalence](https://durgical.com/en/epidemiology/prevalence/)
- [Levels of prevention](https://durgical.com/en/epidemiology/levels-of-prevention/)
- [Disability-adjusted life years (DALYs)](https://durgical.com/en/epidemiology/disability-adjusted-life-years/)

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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).

## **Spotted a mistake?** We are always improving for the community. Tell us what is wrong and our team will review it. Report a mistake

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/population-attributable-risk/