Relative risk

Relative risk is the ratio of the probability of the event occurring in one group versus another group.

Medical statistics uses categorical data analysis extensively to describe the association between the occurrence of a disease and exposure to a risk factor. In this application, the terminology is often used to frame the statistics in terms of risk. Risk difference is equivalent to a difference between proportions, and a risk ratio is equivalent to a ratio of proportions.

The term relative risk is the ratio of the probability of the event occurring in the exposed group versus a non-exposed group. It is the same as the risk ratio. Although a relative risk is different from odds ratio, in some circumstances, such as the low prevalence of the disease, the odds ratio asymptotically approaches the relative risk and is, therefore, an estimate of the relative risk. It is better to avoid confusion and use the terms risk ratio and odds ratio for the effect size estimates and use the term relative risk for the population parameter.

A prospective cohort study or a clinical trial can estimate the risk ratio or the odds ratio of the occurrence of a disease given exposure to a risk factor. Whereas, a retrospective case-control study can estimate the odds ratio of the risk factor given the disease, which is equivalent to the odds ratio of the occurrence of the disease given the risk factor. A risk ratio is not useful because it refers to the risk factor given the disease, which is not normally of interest. However, as stated above the odds ratio can be used as an estimate of the relative risk in most circumstances.

Practitioners often prefer the risk ratio due to its more direct interpretation. Statisticians tend to prefer the odds ratio as it applies to a wide range of study designs, allowing comparison between different studies and meta-analysis based on many studies.  It also forms the basis of logistic regression.