Relative Risk - Statistical Use and Meaning

Statistical Use and Meaning

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:

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

As a consequence of the Delta method, the log of the relative risk has a sampling distribution that is approximately normal with variance that can be estimated by a formula involving the number of subjects in each group and the event rates in each group (see Delta method). This permits the construction of a confidence interval (CI) which is symmetric around log(RR), i.e.,

where is the standard score for the chosen level of significance and SE the standard error. The antilog can be taken of the two bounds of the log-CI, giving the high and low bounds for an asymmetric confidence interval around the relative risk.

In regression models, the treatment is typically included as a dummy variable along with other factors that may affect risk. The relative risk is normally reported as calculated for the mean of the sample values of the explanatory variables.