The Relative Risk (RR) is used to compare the probability of an event between two different groups. It is simply the ratio of the probability of the event occurring in two, mutually exclusive groups:
RR = π1 / π2
A RR 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 π2. A RR of > 1 means the event is more likely to occur in π1
Example: You might calculate the relative risk of PONV between men and women.
Odds Ration (OR) is also used to compare the odds of an event occurring in one group to the odds of it occurring in another group. It is a measure of effect size.
OR = π1(1 – π1) / π2(1 – π2)
An OR of 1 means that an event is equally like in both groups two groups. An OR of < 1 means the event is less likely to occur in π2. An OR of > 1 means the event is more likely to occur in π1
Which is appropriate for my study?
Briefly, the RR is favored in cohort studies, randomized, controlled trials, and other prospective studies. The OR is favored in case-control studies, in studies employing logistic regression, and in retrospective studies.