In statistics and mathematical epidemiology, relative risk (RR) of an event associated with the exposure is a ratio of probability of outcome of interest in exposed group versus treatment group. Statistics is a type of data analysis which practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. ... Epidemiology is the study of the distribution and determinants of health-related states or events in specified populations, and the application of this study to control of health problems (Last 2001). ... The word probability derives from the Latin probare (to prove, or to test). ...

An intuitive example would be that if a probablility of lung cancer among smokers would be 0.2 and among non-smokers 0.1, then the relative risk of cancer associated with smoking is 2.

Statistical use and meaning

Relative risk is used in hypothesis testing for difference in exposures (predictors) in an influence of outcome. Relative risk is typically given with a confidence interval. Prediction of future events is an ancient human wish. ... In statistics, confidence intervals are the most prevalent form of interval estimation. ...

• A relative risk of 1 means there is not difference between the two groups.
• A RR of < 1 means the event is less likely than the control event.
• A RR of > 1 means the event is more likely than the control event.

A typical example where relative risk would matter is wheter a new drug is better than the old drug in double-blind trial. Double-blind describes an especially stringent way of conducting an experiment, usually on human subjects, in such as way as to attempt to eliminate subjective bias on the part of both experimental subjects and the experimenters. ...

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. Therefore, since relative risk is a more intuitive measure of effectiveness, it is important to remember to keep track of what you're using. The odds-ratio is a statistical measure, particularly important in Bayesian statistics and logistic regression. ... The logit (pronounced with a long o and a soft g, SAMPA /loUdZIt/) of a number p between 0 and 1 is Plot of logit in the range 0 to 1, base is e (The base of the logarithm function used here is of little importance in the present article... In medicine, a clinical trial (synonyms: clinical studies, research protocols, medical research) is a research study. ...

The odds ratio is used in case-control studies and retrospecitve studies. The relative risk is used in randomized controlled trials and cohort studies.^[1] The odds-ratio is a statistical measure, particularly important in Bayesian statistics and logistic regression. ... Case-control studies are one type of epidemiological study design. ... A randomized controlled trial (RCT) is a form of clinical trial, or scientific procedure used in the testing of the efficacy of medicines or medical procedures. ... A cohort study is a form of longitudinal study used in medicine and social science. ...

Also see

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

In statistics, confidence intervals are the most prevalent form of interval estimation. ... The odds-ratio is a statistical measure, particularly important in Bayesian statistics and logistic regression. ... The number needed to treat (NNT) is an epidemiological measure that indicates how many patients would require treatment with a form of medication to reduce the expected number of cases of a defined endpoint by one. ... The number needed to harm (NNH) is an epidemiological measure that indicates how many patients would require a specific treatment to cause harm in one patient. ...

Reference

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

External link

• Relative risk
• EBM glossary