Risk difference

If the risk of an outcome is increased by the exposure, the term absolute risk increase (ARI) is used, and computed as

Equivalently, if the risk of an outcome is decreased by the exposure, the term absolute risk reduction (ARR) is used, and computed as

[2][3] The inverse of the absolute risk reduction is the number needed to treat, and the inverse of the absolute risk increase is the number needed to harm.

[2] It is recommended to use absolute measurements, such as risk difference, alongside the relative measurements, when presenting the results of randomized controlled trials.

[4] Their utility can be illustrated by the following example of a hypothetical drug which reduces the risk of colon cancer from 1 case in 5000 to 1 case in 10,000 over one year.

The absolute risk reduction reflects the low probability of getting colon cancer in the first place, while reporting only relative risk reduction, would run into risk of readers exaggerating the effectiveness of the drug.

[5] Authors such as Ben Goldacre believe that the risk difference is best presented as a natural number - drug reduces 2 cases of colon cancer to 1 case if you treat 10,000 people.

Natural numbers, which are used in the number needed to treat approach, are easily understood by non-experts.

[6] Risk difference can be estimated from a 2x2 contingency table: The point estimate of the risk difference is The sampling distribution of RD is approximately normal, with standard error The

is the standard score for the chosen level of significance[3] We could assume a disease noted by

Illustration of two groups: one exposed to a risk factor, and one unexposed. Exposed group has smaller risk of adverse outcome (RD = −0.25, ARR = 0.25).
The adverse outcome (black) risk difference between the group exposed to the treatment (left) and the group unexposed to the treatment (right) is −0.25 (RD = −0.25, ARR = 0.25).