Measures of impact among the exposed

Attributable risk among the exposed (ARe)

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 exposure.

EXAMPLE: Reducing automobile related deaths

Let us suppose that we are in charge of a prevention program and that our goal is to reduce automobile-related deaths. However, we have a limited budget and 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) from exposure in both groups (drunk drivers and speeding drivers). This means that in each exposed group, we are aiming to measure how many deaths occur due to drunk driving and 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:

Table. Risk of death from speeding or drunk driving, Anystate, 2010 Speeding

Speeding	Total drivers	No. of deaths	Risk of death	Attributable risk (exposed)
Yes	2,000	100	50	50 - 10 = 40/1,000
No	8,000	80	10
Drunk driving	Total drivers	No. of deaths	Risk of death per 1,000	Attributable risk (exposed)
Yes	300	45	150	150 - 14 = 136/1,000
No	9,700	135	14

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:

• be attributed to the exposure
• be avoided by eliminating the exposure.

Attributable fraction in cohort studies

In a cohort study, the attributable fraction among the exposed (AFe) is:

Ie = incidence among exposed

Iu = incidence among unexposed

RR = risk ratio

In the example of speeding and drunk driving, we therefore have:

Speeding

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.

Drunk driving

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 the 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:

Ie = incidence among exposed

Iu = incidence among unexposed

RR = risk ratio

Table. Vaccine effectiveness in the population of Anystate, 2010

No. of cases	Cases per 1,000	Risk ratio (RR)
Population
Vaccinated	306,045	150	0.49	0.28
Unvaccinated	298,655	515	1.72	Reference
Total	604,700	665	1.1

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 prevented 72% of these cases (the preventable fraction).

The estimated number of cases that were prevented by the vaccination program is therefore:

526 x 0.72 = 379 cases

Attributable fraction in case-control studies

AFe = attributable fraction among the exposed

PFe = preventable fraction among the exposed

OR = odds ratio

Two assumptions are made in substituting OR for RR:

• controls represent the general population
• the prevalence of exposure is low.

Methods are also available for calculating attributable fractions for matched case-control studies.

Synopsis

Attributable risk among the exposed (ARe)

• 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

Synonyms:

• Attributable risk (exposed)
• Attributable benefit (exposed)
• Risk difference / Excess risk
• Rate difference / Excess rate
• Absolute risk reduction

Attributable fraction among the exposed (AFe)

• 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?

Synonyms:

• Attributable fraction (exposed)
• Attributable proportion / Attributable risk percent (exposed)
• Aetiological fraction / Preventable fraction (exposed)
• Relative risk reduction

credits

FEM Editor 2007

• Meirion Evans

Original Authors

• Alain Moren
• Marta Valenciano
• Thomas Grein

FEM Contributors

• Lisa Lazareck
• Meirion Evans