Relative risk
In statistics and epidemiology, relative risk or risk ratio (RR) is the ratio of the probability of an event occurring (for example, developing a disease, being injured) in an exposed group to the probability of the event occurring in a comparison, non-exposed group. Relative risk includes two important features: (i) a comparison of risk between two "exposures" puts risks in context, and (ii) "exposure" is ensured by having proper denominators for each group representing the exposure
Consider an example where the probability of developing lung cancer among smokers was 20% and among non-smokers 1%. This situation is expressed in the 2 × 2 table to the right.
Here, a = 20, b = 80, c = 1, and d = 99. Then the relative risk of cancer associated with smoking would be
Smokers would be twenty times as likely as non-smokers to develop lung cancer.
The alternative term risk ratio is sometimes used because it is the ratio of the risk in the exposed divided by the risk in the unexposed.
Relative risk contrasts with the actual or absolute risk, and may be confused with it in the media or elsewhere.
Relative risk is used frequently in the statistical analysis of binary outcomes where the outcome of interest has relatively low probability. It is thus often suited to clinical trial data, where it is used to compare the risk of developing a disease, in people not receiving the new medical treatment (or receiving a placebo) versus people who are receiving an established (standard of care) treatment. Alternatively, it is used to compare the risk of developing a side effect in people receiving a drug as compared to the people who are not receiving the treatment (or receiving a placebo). It is particularly attractive because it can be calculated by hand in the simple case, but is also amenable to regression modelling, typically in a Poisson regression framework.
In a simple comparison between an experimental group and a control group:
When the event is not necessarily an adverse one, the term relative probability may be used instead.
We could assume a disease noted by , and no disease noted by , exposure noted by , and no exposure noted by . Relative risk can be written as
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