Attributable fraction among the exposed

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).

In epidemiology, attributable fraction among the exposed (AF_e) is the proportion of incidents in the exposed group that are attributable to the risk factor. The term attributable risk percent among the 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] 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 AF_e are in use: attributable fraction,^[1][3] relative attributable risk,^[1] attributable proportion among the exposed,^[1] and 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

Quantity	Experimental group (E)	Control group (C)	Total
Events (E)	EE = 75	CE = 100	175
Non-events (N)	EN = 75	CN = 150	225
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%	—

Variable	Abbr.	Formula	Value
Absolute risk increase	ARI	EER − CER	0.1, or 10%
Number needed to harm	NNH	1 / (EER − CER)	10
Relative risk (risk ratio)	RR	EER / CER	1.25
Relative risk increase	RRI	(EER − CER) / CER, or RR − 1	0.25, or 25%
Attributable fraction among the exposed	AFe	(EER − CER) / EER	0.2
Odds ratio	OR	(EE / EN) / (CE / CN)	1.5

See also

• Population Impact Measures
• Attributable fraction for the population

References

1. Porta, Miquel, ed. (2014). "A Dictionary of Epidemiology". Dictionary of Epidemiology - Oxford Reference. Oxford University Press. doi:10.1093/acref/9780199976720.001.0001. ISBN 9780199976720. 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. doi:10.1136/jech.25.4.242. PMC 478665. PMID 5160433.
3. 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. (eds.). Climate science for serving society : research, modeling and prediction priorities. Dordrecht: Springer. p. 315. ISBN 9789400766921. OCLC 851370783.