The attributable risk of a disease given an exposure is simply the rate of disease (incidence) in the exposed people minus the rate in the unexposed people. So the attributable risk for lung cancer in smokers is, in essence, simply the rate of lung cancer amongst smokers minus the rate of lung cancer amongst non-smokers. In fact AR shows which proportion of the disease in exposed subjects is due to exposure. This is also frequently referred to as the "risk difference" when dealing with risk data or "rate difference" with rate or person-time data.
Definition: Population attributable risk is the reduction in incidence that would be observed if the population were entirely unexposed, compared with its current (actual) exposure pattern.
In 1953, Levin first proposed the concept of population attributable risk. However, PAR refers to a family of concepts, not a single quantity. Greenland and Robins distinguished between excess fraction and etiologic fraction in 1988. Etiologic fraction is the proportion of the cases that the exposure had played a causal role in its development. Excess fraction, however, is the proportion of the cases that occurs among exposed population that is in excess in comparison with the unexposed . All excess cases are etiologic cases, but not vice versa. 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. (Smaller than etiologic fraction)
Population attributable fraction estimates can help guide policymakers in planning public health interventions. Population attributable fraction (PAF), population attributable risk proportion, and population attributable risk percent are all the same as PAR.
It is possible to imagine what would happen in a community if, say, you removed all the radon, and left everything else unchanged. The number of lung cancer cases would fall. This fall is the population attributable risk for lung cancer from radon. Please note that this isn't actually possible, so this is a thought experiment, but for all that it's a useful one.
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.
When there is no multiplicative interaction (no departure from multiplicative scale), combined PAR can be manually calculated by this formula: