Relative risk

In statisticsand mathematical epidemiology, relative risk (RR) is the risk of an event (or of developing a disease) relative to exposure. Relative risk is a ratioof the probabilityof the event occurring in the exposed group versus the control (non-exposed) group.

<math>RR= \frac {p_\mathrm{exposed}}{p_\mathrm{control}}. </math>

For example, if the probabilityof developing lung cancer among smokers was 20% and among non-smokers 10%, then the relative risk of cancer associated with smoking would be 2. Smokers would be twice as likely as non-smokers to develop lung cancer.

Statistical use and meaning

Relative risk is used frequently in the statistical analysis of clinical trialdata. It is used to compare the risk of developing a disease, in people receiving a new medical treatment versus people receiving an established (standard of care) treatment or a placebo. Relative risk is typically given with a confidence interval.

• A relative risk of 1 means there is no difference in risk between the two groups.
• A RR of < 1 means the event is less likely to occur in the experimental group than in the control group.
• A RR of > 1 means the event is more likely to occur in the experimental group than in the control group.

Association with odds ratio

Relative risk is different from odds ratio, although asymptotically approaches odds ratio for small probabilities. In fact, odds ratio has much wider use in statistics, since logistic regression, often associated with clinical trials, works with odds ratio, not relative risk. For example, in logistic regression model where the treatment outcome is associated with drug and age, and odds ratio for 70-year-olds and 60-year-olds associated with type of treatment would be the same, although the relative risk might be significantly different.

Since relative risk is a more intuitive measure of effectiveness, the distinction is important especially in cases of medium to high probabilities. If action A carries a risk of 99.9% and action B a risk of 99.0% then the relative risk is just over 1, while the odds associated with action A are almost 10 times higher than the odds with B.

The odds ratiois used in case-control studiesand retrospective studies. Relative risk is used in randomized controlled trialsand cohort studies.^{[{{fullurl:Template:FULLPAGENAME}}#endnote_musc_edu]}

See also

• Confidence interval
• Odds ratio
• Number needed to treat(NNT)
• Number needed to harm(NNH)

Reference

1. ^ Medical University of South Carolina, Odds ratio versus relative risk, Accessed on: September 8, 2005.

External link

• Relative risk
• EBM glossary

This article is licensed under the GNU Free Documentation License.
It uses material from the http://en.wikipedia.org/wiki/Relative+risk Wikipedia article Relative risk.