## 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 the exposure .

#### EXAMPLE: Reducing automobile related deaths

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:

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

 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 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

 Population No. of cases Cases per 1,000 Risk ratio (RR) Vaccinated 306,045 150 0.49 0.28 Unvaccinated 298,655 515 1.72 Reference Total 604,700 665 1.10

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

### 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:

• 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 .

## 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

## References

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.