The odds ratio (OR) and relative risk (RR) are both used to measure the association between exposure and an outcome in epidemiology.
Step 1: Odds Ratio (OR):
- The odds ratio is the ratio of the odds of an event occurring in the exposed group to the odds of the event occurring in the unexposed group.
- Formula:
\[
OR = \frac{(a/c)}{(b/d)}
\]
where \(a\), \(b\), \(c\), and \(d\) are values from a 2x2 table of exposure and outcome.
Step 2: Relative Risk (RR):
- The relative risk is the ratio of the probability of an event occurring in the exposed group to the probability in the unexposed group.
- Formula:
\[
RR = \frac{a/(a+b)}{c/(c+d)}
\]
where \(a\), \(b\), \(c\), and \(d\) are values from a 2x2 table of exposure and outcome.
Step 3: Key Differences:
- Odds Ratio: More commonly used in case-control studies, as it is easier to calculate from retrospective data.
- Relative Risk: Typically used in cohort studies where the incidence of the outcome in both exposed and unexposed groups can be directly compared.