Relative risk

[1] Relative risk is used in the statistical analysis of the data of ecological, cohort, medical and intervention studies, to estimate the strength of the association between exposures (treatments or risk factors) and outcomes.

Relative risk is commonly used to present the results of randomized controlled trials.

[6] In cases where the base rate of the outcome is low, large or small values of relative risk may not translate to significant effects, and the importance of the effects to the public health can be overestimated.

[9] In regression models, the exposure is typically included as an indicator variable along with other factors that may affect risk.

The relative risk is usually reported as calculated for the mean of the sample values of the explanatory variables.

[citation needed] The relative risk is different from the odds ratio, although the odds ratio asymptotically approaches the relative risk for small probabilities of outcomes.

Thus, under the rare disease assumption In practice the odds ratio is commonly used for case-control studies, as the relative risk cannot be estimated.

Because the (natural log of the) odds of a record is estimated as a linear function of the explanatory variables, the estimated odds ratio for 70-year-olds and 60-year-olds associated with the type of treatment would be the same in logistic regression models where the outcome is associated with drug and age, although the relative risk might be significantly different.

[citation needed] Since relative risk is a more intuitive measure of effectiveness, the distinction is important especially in cases of medium to high probabilities.

[citation needed] In statistical modelling, approaches like Poisson regression (for counts of events per unit exposure) have relative risk interpretations: the estimated effect of an explanatory variable is multiplicative on the rate and thus leads to a relative risk.

Logistic regression (for binary outcomes, or counts of successes out of a number of trials) must be interpreted in odds-ratio terms: the effect of an explanatory variable is multiplicative on the odds and thus leads to an odds ratio.

The relative risk can be written as This way the relative risk can be interpreted in Bayesian terms as the posterior ratio of the exposure (i.e. after seeing the disease) normalized by the prior ratio of exposure.

If on the other hand, the posterior ratio of exposure is smaller or higher than that of the prior ratio, then the disease has changed the view of the exposure danger, and the magnitude of this change is the relative risk.