# Attributable risk

In epidemiology, attributable risk or excess risk is the difference in rate of a condition between an exposed population and an unexposed population.[1] Attributable risk is mostly calculated in cohort studies, where individuals are assembled on exposure status and followed over a period of time. Investigators count the occurrence of the diseases. The cohort is then subdivided by the level of exposure and the frequency of disease is compared between subgroups. One is considered exposed and another unexposed. The formula commonly used in Epidemiology books for attributable risk is ${\displaystyle AR=I_{e}-I_{u}}$, where ${\displaystyle I_{e}}$ = incidence in exposed and ${\displaystyle I_{u}}$ = incidence in unexposed. Once the AR is calculated, then the AR percent can be determined, which is calculated as ${\displaystyle 100*(I_{e}-I_{u})/I_{e}}$.

Population attributable risk (PAR) is the reduction in incidence that would be observed if the population were entirely unexposed, compared with its current (actual) exposure pattern.[2] The concept was first proposed by Levin in 1953.[3][4]

## Diversity of interpretation

Greenland and Robins distinguished between excess fraction and etiologic fraction in 1988.[5]

• Etiologic fraction is the proportion of cases in the exposed population in which the exposure has played a causal role in disease development.
• Excess fraction, however, is the proportion of cases occurring during some period of time among the exposed population that is in excess in comparison with the unexposed.

All excess cases are etiologic cases, but not vice versa. The example given by Greenland and Robins is that if one is studying cases of leukemia among soldiers in the 20 years after they were exposed to radiation from a nuclear bomb test, there may be cases that were caused by the radiation, but even if they hadn't been exposed they would have gotten leukemia anyway during the 20 years.

From the standpoint of both law and biology it is important to measure the etiology fraction. In most epidemiological studies, PAR measures only the excess fraction. (Larger than etiologic fraction)

## Uses

Another measure, known as the population attributable fraction (PAF), can be calculated to help guide policymakers in planning public health interventions.[6] In practical terms, the population attributable fraction provides an indication of what the percentage reduction in the incidence rate of a disease could be in a given population if the exposure were eliminated altogether.[7] As a hypothetical example, if all radon exposure in a community were removed, and everything else were left unchanged, the number of lung cancer cases would decrease. The population attributable fraction provides an indication of the relative reduction in new cases of the disease in the event that this could be done. In other words, it indicates the proportion of new cases of a disease within a population that can be said to be due to (i.e. attributable to) a particular exposure.[8]

## Combined PAR

The PAR for a combination of risk factors is the proportion of the disease that can be attributed to any of the risk factors studied. The combined PAR is usually lower than the sum of individual PARs since a diseased case can simultaneously be attributed to more than one risk factor and so be counted twice.

Assuming a multiplicative model with no interaction (i.e. no departure from multiplicative scale), combined PAR can be manually calculated by this formula:

${\displaystyle {\text{Combined PAR}}=1-(1-{\text{PAR}}_{1})(1-{\text{PAR}}_{2})(1-{\text{PAR}}_{3})\cdots .\,}$