Attributable risk in the population (ARpop)
The second type of question we may ask relates to the excess risk of disease in the total population that is attributable to exposure. This is the attributable risk in the population (ARpop) or the population attributable risk. It is the proportion of cases in the general population that can be attributed to the exposure.
Ipop = incidence in population
Iu = incidence among unexposed
It represents the reduction in risk we would achieve if the entire population was not exposed. It helps to identify which exposures are most relevant in the community and will yield most benefit from public health interventions [1] [2].
Attributable fraction in the population (AFpop)
The population attributable risk can also be expressed as a percentage of the total risk in the population.
This is known as the attributable fraction in the population (AFpop):
Ipop = incidence in the population
Iu = incidence among the exposed
Table. Risk of death from speeding, Anystate, 2010
Speeding

Total drivers

No. of deaths

Risk of death per 1,000

Attributable risk (population)

Yes

2,000

100

50


No

8,000

80

10


Total

10,000

180

18

18  10 = 8/1,000

Speeding
This means that (if speeding causes driving related deaths) 44% of driving related deaths in the population can be attributed to speeding.
Table. Risk of death from drunk driving, Anystate, 2010
Drunk driving

Total drivers

No. of deaths

Risk of death per 1,000

Attributable risk (population)

Yes

300

45

150


No

9,700

135

14


Total

10,000

180

18

18  14 = 4/1,000

Drunk driving
This means that (if drunk driving causes driving related deaths) 22% of driving related deaths in the population can be attributed to drunk driving.
AFpop can also be expressed as:
The above formula is not valid if the RR is adjusted for confounders, as is often the case. In this situation one of the following alternatives is preferable:
Pe = proportion of the population exposed
PCe = proportion of cases exposed
Ie = incidence in exposed
Iu = incidence in unexposed
RR = risk ratio
ARe = attributable risk among exposed
If the risk factor is causal, then the population attributable risk depends on:
 the strength of the association (RR)
 the frequency of the exposure (Pe)
To have a large impact on the population, the exposure must be common.
Methods are also available for dealing with multiple exposure categories for a single risk factor [3], and for diseases caused by multiple risk factors [2] [4].
Sometimes, diseases are the result of complex interactions between risk factors. Methods to conceptualise and clarify these interactions have been developed. These include sequential attributable fractions [5] [6], and causal pies [7] [8].
Synopsis
Attributable risk in the population (ARpop)
Synonyms:
Attributable fraction in the population (AFpop)
Synonyms:

Attributable fraction (population)

Population attributable fraction

Attributable proportion (population)

Aetiological fraction / Preventable fraction (population)

Population attributable risk percent
References
 Rockhill B, Newman B, Weiberg C. Use and misuse of population attributable fractions. Am J Public Health 1998;88:1519.
 Coughlin SS, Benichou J, Weed DL. Attributable risk estimation in casecontrol studies. Epidemiol Rev 1994;16:5164.
 Hanley JA. A heuristic approach to the formulas for population attributable fraction. J Epidemiol Community Health 2001;55:50814.
 Bruzzi P, Green SB, Dyer DP, Brinton LA, Schairer C. Estimating the population attributable risk for multiple risk factors using casecontrol data. Am J Epidemiol 1985;122:90414.
 Eide GE, Gefeller O. Sequential and average attributable fractions as aids in the selection of prevention strategies. J Clin Epidemiol 1995;48:64555.
 Rowe A, Powell KE, Flanders WD. Why population attributable fractions can sum to more than one. Am J Prev Med 2004;26:2439.
 Hoffmann K, Flanders WD. Estimating the proportion of disease due to classes of sufficient causes. Am J Epidemiol 2006;164:12535.
 Liao SF, Lee WC. Weighing the causal pies in casecontrol studies. Ann Epidemiol 2010;20:56873.