The attributable risk among the exposed (risk difference or excess risk) is the proportion of cases among exposed individuals that can be attributed to the exposure. It provides information about the absolute effects of the exposure .
Let us suppose that we are in charge of a prevention programme and that our goal is to reduce automobile-related deaths. However, we have a limited budget and we want to have the maximum impact on reducing deaths.
We decide to conduct a cohort study of 10,000 drivers to examine risk factors for automobile-related deaths. We are particularly interested in factors like drunk driving and speeding since we believe interventions are feasible.
We would like to quantify the disease burden (deaths) due to the exposure in each of the two groups (drunk drivers and speeding drivers). This means that in each exposed group we are aiming to measure how many of the deaths that occur are due to drunk driving and to speeding respectively.
First, we calculate the risk difference between the exposed and unexposed. This is known as the attributable risk among the exposed (ARe):
The study gives the following results:
No. of deaths
Risk of death
Attributable risk (exposed)
50 - 10 = 40/1,000
Risk of death per 1,000
150 - 14 = 136/1,000
We can also express attributable risk as the percentage of all deaths among the exposed that can be attributed to the exposure. .This is known as the attributable fraction among the exposed (AFe):
Ie = incidence among exposed
Iu = incidence among unexposed
If the risk factor is causal, then the attributable fraction among the exposed corresponds to the proportion of disease among the exposed that can:
In a cohort study, the attributable fraction among the exposed (AFe) is:
RR = risk ratio
In the example of speeding and drunk driving we therefore have:
This means that (if speeding causes driving related deaths) 80% of driving related deaths among speeding drivers can be attributed to speeding. They could be avoided if speeding did not occur.
This means that (if drunk driving causes driving related deaths) 91% of driving related deaths among drunk drivers can be attributed to drunk driving. They could be avoided if drunk driving did not occur.
These examples illustrate what happens if exposure increases risk of disease. If exposure prevents disease (e.g. vaccination), the attributable risk is often called the preventable fraction among the exposed (PFe).
We would then have the following:
No. of cases
Cases per 1,000
Risk ratio (RR)
To calculate the preventable fraction:
The expected number of cases among the vaccinated population, if they were unvaccinated, is:
306,045 x (1.72/1,000) = 526 cases
We have calculated that the vaccine was able to prevent 72% of these cases (the preventable fraction).
The estimated number of cases that were prevented by the vaccination programme is therefore:
526 x 0.72 = 379 cases
AFe = attributable fraction among the exposed
PFe = preventable fraction among the exposed
OR = odds ratio
Two assumptions are made in substituting OR for RR:
that controls are representative of the general population
that the prevalence of exposure is low .
Methods are also available for calculating attributable fractions for matched case-control studies .
The number of cases (amount of disease) among the exposed that can be attributed to the exposure
What is the risk among the exposed that is due to the exposure?
This is calculated as the absolute difference between risk in the exposed and risk in the unexposed
It assumes that the causal effect is entirely due to the risk factor
Attributable benefit (exposed)
Risk difference / Excess risk
Rate difference / Excess rate
Absolute risk reduction
The proportion of cases (percentage of disease) among the exposed that can be attributed to the exposure
Attributable risk expressed as a proportion of the risk in the exposed
What is the proportion of disease among the exposed that:
can be attributed to the exposure?
can be prevented if the exposure is eliminated?
Attributable fraction (exposed)
Attributable proportion / Attributable risk percent (exposed)
Aetiological fraction / Preventable fraction (exposed)
Relative risk reduction
1. Greenland S, Robins JM. Conceptual problems in the definition and interpretation of attributable fractions. Am J Epidemiol 1988;128:1185-97.2. Cole P, MacMahon B. Attributable risk percent in case-control studies. Br J Prev Soc Med 1971;25:242-4.3. Kuritz SJ, Landis JR. Attributable risk ratio estimation from matched-pairs case-control data. Am J Epidemiol 1987;125:324-8.