An odds ratio (OR) is a measure of association between an exposure and an outcome. It represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.
In simpler terms, an odds ratio is a statistic that quantifies the strength of the association between two events, A and B.
Odds ratios are used extensively in epidemiology. An OR is defined as the ratio of the odds of A occurring in the presence of B to the odds of A occurring in the absence of B.
For example, the odds of death occurring in the presence of smoking vs. the odds of death occurring in the absence of smoking.
The odds ratio is calculated by dividing the odds of an outcome in an exposed group by the odds of that outcome in an unexposed group:
$$ OR = (a/b)/(c/d) $$
where: a = exposed cases b = exposed non-cases c = unexposed cases d = unexposed non-cases