# Attributable fraction among the exposed

In epidemiology, attributable fraction among the exposed (AFe) is the proportion of incidents in the exposed group that are attributable to the risk factor. Term attributable risk percent among exposed is used if the fraction is expressed as a percentage.[1] It is calculated as ${\displaystyle AF_{e}=(I_{e}-I_{u})/I_{e}=(RR-1)/RR}$, where ${\displaystyle I_{e}}$ is the incidence in the exposed group, ${\displaystyle I_{u}}$ is the incidence in the unexposed group, and ${\displaystyle RR}$ is the relative risk.[2]

Group exposed to a risk factor (left) has increased risk of an adverse outcome (black) compared to the unexposed group (right). In the exposed group, one third of the adverse outcomes can be attributed to the exposure (AFe = 1/3).

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

## Synonyms

Multiple synonyms of AFe are in use: attributable fraction,[1][3] relative attributable risk,[1] attributable proportion among the exposed,[1] attributable risk among the exposed.[4]

Similarly, attributable risk percent (ARP) is used as a synonym for the attributable risk percent among the exposed.[3]

In climatology, fraction of attributable risk (FAR) is used to denote a proportion of adverse event risk attributable to the human influence on climate or other forcing factor.[5]

## Numerical example

Example of risk increase
Experimental group (E) Control group (C) Total
Events (E) EE = 75 CE = 100 115
Non-events (N) EN = 75 CN = 150 285
Total subjects (S) ES = EE + EN = 150 CS = CE + CN = 250 400
Event rate (ER) EER = EE / ES = 0.5, or 50% CER = CE / CS = 0.4, or 40%
Equation Variable Abbr. Value
EER − CER absolute risk increase ARI 0.1, or 10%
(EER − CER) / CER relative risk increase RRI 0.25, or 25%
1 / (EER − CER) number needed to harm NNH 10
EER / CER risk ratio RR 1.25
(EE / EN) / (CE / CN) odds ratio OR 1.5
(EER − CER) / EER attributable fraction among the exposed AFe 0.2

## References

1. ^ a b c d "Dictionary of Epidemiology - Oxford Reference". doi:10.1093/acref/9780199976720.001.0001. Retrieved 2018-05-09.
2. ^ Cole P, MacMahon B (November 1971). "Attributable risk percent in case-control studies". Br J Prev Soc Med. 25 (4): 242–4. PMC 478665. PMID 5160433.
3. ^ a b J., Rothman, Kenneth (2012). Epidemiology : an introduction (2nd ed.). New York, NY: Oxford University Press. p. 66. ISBN 9780199754557. OCLC 750986180.
4. ^ P., Armitage, (2002). Statistical methods in medical research. Berry, G. (Geoffrey), Matthews, J. N. S. (4th ed.). Oxford: Blackwell Scientific Publications. p. 683. ISBN 9780470773666. OCLC 646751070.
5. ^ Peter A. Stott; et. al. (2013). "Attribution of Weather and Climate-Related Events". In Asrar, Ghassem; Hurrell, James W. Climate science for serving society : research, modeling and prediction priorities. Dordrecht: Springer. p. 315. ISBN 9789400766921. OCLC 851370783.