Attributable risk

Overview
The attributable risk of 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.

The population attributable risk is an estimate of the proportion of disease or other outcomes in a community due to exposure to a specific factor.

For example, Tobacco smoking is the main cause of lung cancer, but a small proportion of cases of lung cancer in almost all communities are due to other exposures, for example, radon, indoor air pollution, outdoor air pollution, arsenic, unfortunate genetics and so on.

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.