# Attributable fraction for the population

In epidemiology, **attributable fraction for the population (AFp)** is the proportion of incidents in the population that are attributable to the risk factor. Term **attributable risk percent for the population** is used if the fraction is expressed as a percentage.[1] It is calculated as , where is the incidence in the population, and is the incidence in the unexposed group.[1]

Equivalently it can be calculated as , where is the exposed proportion of the population and is the relative risk not adjusted for confounders.[1][2]

It is used when an exposure increases the risk, as opposed to reducing it, in which case its symmetrical notion is preventable fraction for the population.

## Synonyms

Multiple synonyms of the attributable fraction for the population are in use: attributable proportion for the population,[1] population attributable proportion,[1] Levin's attributable risk,[1] population attributable risk,[2] and population attributable fraction.[3][4]

Similarly, population attributable risk percent (PAR) is used as a synonym for the attributable risk percent for the population.[1][2][5]

## Interpretation

Attributable fraction for the population combines both the relative risk of an incident with respect to the factor, as well as the prevalence of the factor in the population. Values of AF_{p} close to 1 indicate that both the relative risk is high, and that the risk factor is prevalent. In such case, removal of the risk factor will greatly reduce the number of the incidents in the population. The values of AF_{p} close to 0, on the other hand, indicate that either the relative risk is low, or that the factor is not prevalent (or both). Removal of such factor from the population will have little effect. Because of this interpretation, the AFp is well suited for the public policy making.[6]

For example, in 1953 Levin's paper it was estimated that lung cancer has relative risk of 3.6 - 13.4 in smokers compared to non-smokers, and that the proportion of the population exposed to smoking was 0.5 - 0.96, resulting in the high value of attributable fraction for the population 0.56 - 0.92.[6]

## Generalizations

Attributable fraction for the population can be generalized to the case where the multilevel exposure to the risk factor. In such case

where is the proportion of the population exposed to the level , is the desired (ideal) proportion of the population exposed to the level , and is the relative risk at exposure level .[4]

## References

- "Dictionary of Epidemiology - Oxford Reference". doi:10.1093/acref/9780199976720.001.0001. Retrieved 2018-05-09.
- Armitage P, Berry G, Matthews JN (2002).
*Statistical methods in medical research*(4th ed.). Oxford: Blackwell Scientific Publications. p. 682. ISBN 978-0-470-77366-6. OCLC 646751070. - Rockhill B, Newman B, Weinberg C (January 1998). "Use and misuse of population attributable fractions".
*American Journal of Public Health*.**88**(1): 15–9. doi:10.2105/ajph.88.1.15. PMC 1508384. PMID 9584027. - "Metrics: Population Attributable Fraction (PAF)". World Health Organization. Retrieved 2018-05-09.
- Cole P, MacMahon B (November 1971). "Attributable risk percent in case-control studies".
*British Journal of Preventive & Social Medicine*.**25**(4): 242–4. doi:10.1136/jech.25.4.242. PMC 478665. PMID 5160433. - Northridge ME (September 1995). "Public health methods--attributable risk as a link between causality and public health action".
*American Journal of Public Health*.**85**(9): 1202–4. doi:10.2105/ajph.85.9.1202. PMC 1615585. PMID 7661224.