The risk difference (RD), excess risk, or attributable risk is the difference between the risk of an outcome in the exposed group and the unexposed group. It is computed as

I_e - I_u

, where

I_e

is the incidence in the exposed group, and

I_u

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

I_e - I_u

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

I_u - I_e

. 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.

Usage in reporting

It is recommended to use absolute measurements, such as risk difference, alongside the relative measurements, when presenting the results of randomized controlled trials. Their utility can be illustrated by the following example of a hypothetical drug which reduces the risk of

colon cancer Colorectal cancer (CRC), also known as bowel cancer, colon cancer, or rectal cancer, is the development of cancer from the colon or rectum (parts of the large intestine). Signs and symptoms may include blood in the stool, a change in bowel mo ...

from 1 case in 5000 to 1 case in 10,000 over one year. The relative risk reduction is 0.5 (50%), while the absolute risk reduction is 0.0001 (0.01%). 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. 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.

Inference

Risk difference can be estimated from a 2x2

contingency table In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. They are heavily used in survey research, business i ...

: The point estimate of the risk difference is :

RD = \frac - \frac.

The sampling distribution of RD is approximately normal, with standard error :

SE(RD) = \sqrt.

The

1 - \alpha

confidence interval for the RD is then :

CI_(RD) = RD\pm SE(RD)\cdot z_\alpha,

where

z_\alpha

is the

standard score In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the mean ...

Usage in reporting

Inference

Numerical examples

Risk reduction

Risk increase

See also

References