The risk difference (RD), excess risk, or attributable risk is the difference between the

risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environ ...

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 The number needed to treat (NNT) or number needed to treat for an additional beneficial outcome (NNTB) is an epidemiology, epidemiological measure used in communicating the effectiveness of a health-care intervention, typically a treatment with me ...

, and the inverse of the absolute risk increase is the

number needed to harm In medicine, the number needed to harm (NNH) is an epidemiology, epidemiological measure that indicates how many persons on average need to be exposed to a risk-factor, risk factor over a specific period to cause harm in an average of one person ...

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 ...

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 Ben Michael Goldacre (born 20 May 1974) is a British physician, academic and science writer. He is the first Bennett Professor of Evidence-Based Medicine and director of the Bennett Institute for Applied Data Science at the University of Oxford ...

believe that the risk difference is best presented as a

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

- 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 int ...

: The

point estimate In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown popu ...

of the risk difference is :

RD = \frac - \frac.

The

sampling distribution In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic. For an arbitrarily large number of samples where each sample, involving multiple observations (data poi ...

of RD is approximately normal, with

standard error The standard error (SE) of a statistic (usually an estimator of a parameter, like the average or mean) is the standard deviation of its sampling distribution or an estimate of that standard deviation. In other words, it is the standard deviati ...

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 or ''z''-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 ...

for the chosen level of significance

Bayesian interpretation

We could assume a disease noted by

D

, and no disease noted by

\neg D

, exposure noted by

E

, and no exposure noted by

\neg E

. The risk difference can be written as :

RD = P(D\mid E)-P(D\mid \neg E).

Usage in reporting

Inference

Bayesian interpretation

Numerical examples

Risk reduction

Risk increase

See also

References