[Dictionary] Odds Ratio (OR)

An odds ratio (OR) is the ratio of the odds of an outcome occurring in one group to the odds of it occurring in another group, where odds is the probability of the event divided by the probability of the event not occurring (p / (1−p)), not the probability itself. OR = 1 indicates no association; OR > 1 indicates higher odds in the first (numerator) group; OR < 1 indicates lower odds. What makes a ratio genuinely an odds ratio, rather than a relative risk described loosely as 'odds,' is that it is built from odds (a ratio of two probabilities) rather than from a risk (a single probability of the event among everyone at risk) — the calculation OR = (A×D)/(B×C) from a 2×2 table is mathematically identical whether the underlying study is a cohort, a cross-sectional survey, or a case-control study, which is precisely why OR (unlike relative risk) is calculable from a case-control design that samples on outcome status rather than on exposure and follows no defined population forward in time.