Definition
Attributable risk is the disease rate in a group exposed to a risk factor minus the rate in a group that was not exposed. It tries to measure how much of the disease would not have happened without that factor. It assumes the two groups are alike in everything except that factor, so if that assumption wobbles, the number wobbles with it.
Risk that came along versus risk that was caused
Imagine stepping onto a scale while wearing wet clothes. The number on the dial mixes your real body weight with the weight of the water in the fabric. If you want to know only the weight added by the water, you have to subtract your weight from before you got wet.
Epidemiology, the study of health and disease in populations, asks the very same question. Suppose someone who lived near a risk factor gets sick. You can't assume the factor caused all of that illness. Everyone carries a baseline risk of getting the disease for other reasons, even without the factor.
That is why researchers carefully separate what merely showed up together from what the factor actually caused. When a disease appears, an event that was just tangled up in the story is very different from the pure risk that would not have happened without the factor, and the two have to be counted differently.
A share found by subtraction, and the assumption behind it
Counting this pure risk is simpler than you might expect. Take the rate of illness among people who were exposed to the risk, and subtract the rate among people who were not exposed.
Say 10 out of 1,000 people who smoke get lung cancer. Among 1,000 people who never smoke, 1 still gets lung cancer because of air pollution or genes. That means 1 of the 10 smokers' cases could have happened without tobacco anyway.
So the risk added by tobacco alone is 10 minus 1, or 9 cases' worth. Put the two groups' rates side by side and take the difference after subtracting the baseline rate. That value is the attributable risk.
There is one assumption hidden in this subtraction, though. You can call the difference tobacco's share only if the two groups are similar in everything except smoking. If the smokers were older to begin with, or carried other risks too, the subtracted number absorbs that share as well. Attributable risk is not a number that proves cause. It is a number that measures the effect once you assume cause.
A bit more precisely: a compass for public health
To be a bit more precise, attributable risk is one of the key compasses that governments and hospitals use when they set health policy. People tend to be more startled by relative risk, which tells you how many times higher the risk gets.
But even if a risk jumps 100 times, the number of people who actually get sick stays tiny if the disease started out at one in a hundred million. On the other hand, a risk that rises only 1.2 times can still matter a great deal if the disease is common and millions of people face it every day. Removing that factor could prevent a lot of illness.
Attributable risk shows exactly this point in numbers. It tells you how much risk was added for each exposed person. Multiply that by how many people in society are exposed to the factor, and you finally get the number of cases that would disappear if the factor were removed. That is why public health looks at these two numbers together, rather than at vague fear, to decide what to tackle first.
Common misconceptions
Every illness in a person exposed to a risk factor is caused by that factor.
Even without the factor, people can get sick for other reasons because a baseline risk exists. Assuming the two groups are alike except for that factor, you subtract the unexposed group's rate from the exposed group's rate to estimate the factor's share.
A risk factor with a large relative risk always does the most harm to society as a whole.
For a very rare disease, even a many-fold increase leaves the actual number of patients very small. By contrast, cutting a common risk factor that reaches a huge number of people can prevent more illness, even if the added risk for each person is modest.
Where you meet it
Subtracting the heart disease rate among nonsmokers from the rate among smokers to measure the effect of tobacco alone
Subtracting the respiratory disease rate in a clean-air rural village from the rate in a village near a factory to estimate the harm of air pollution (assuming the two villages are otherwise similar)
In one sentence
It is a measure that subtracts the baseline rate of an unexposed group from the rate of an exposed group, to estimate how much of the disease would not have happened without the factor.