# 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 ${\displaystyle AF_{p}=(I_{p}-I_{u})/I_{p}}$, where ${\displaystyle I_{p}}$ is the incidence in the population, and ${\displaystyle I_{u}}$ is the incidence in the unexposed group.[1]

Equivalently it can be calculated as ${\displaystyle AF_{p}={\frac {P_{e}(RR-1)}{1+P_{e}(RR-1)}}}$, where ${\displaystyle P_{e}}$is the exposed proportion of the population and ${\displaystyle RR}$ 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 AFp 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 AFp 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

${\displaystyle AF_{p}={\frac {\sum _{i}P_{i}RR_{i}-\sum _{i}P_{i}'RR_{i}}{\sum _{i}P_{i}RR_{i}}}}$where ${\displaystyle P_{i}}$is the proportion of the population exposed to the level ${\displaystyle i}$, ${\displaystyle P_{i}'}$is the desired (ideal) proportion of the population exposed to the level ${\displaystyle i}$, and ${\displaystyle RR_{i}}$is the relative risk at exposure level ${\displaystyle i}$.[4]