Measures of effect - odds ratio

Definition

Odds ratio compares the odds of an outcome in an exposed/treated group versus a comparison group - odds (probability of an event divided by probability of it not occurring) are conceptually distinct from risk/probability itself, and odds ratio approximates relative risk reasonably well only when the outcome is relatively rare, diverging meaningfully from relative risk as outcome frequency increases
The standard, and often only calculable, effect measure from case-control studies and logistic regression analyses, given these methods' structural inability to directly calculate relative risk

As an outcome becomes more common (higher baseline probability), odds and probability diverge increasingly (odds always exceeds probability for events occurring more than half the time, with the gap widening as probability increases toward 1), meaning odds ratio increasingly overestimates the magnitude of relative risk as outcome frequency rises - this divergence is why odds ratio should not be casually interpreted as if it were relative risk, particularly for common outcomes

Odds ratio is the natural output of logistic regression analyses (commonly used to adjust for multiple confounding variables simultaneously) and of case-control study designs, explaining its frequent appearance in the epidemiological and clinical research literature despite being less intuitively interpretable than relative risk
The "rare disease assumption" (outcome prevalence below approximately 10%) is the rough threshold below which odds ratio and relative risk are considered close enough to be practically interchangeable for interpretation purposes

Odds ratios for common outcomes should be interpreted with the awareness that they likely overstate the true relative risk magnitude, particularly relevant when odds ratios exceeding 2-3 are reported for outcomes occurring in a substantial proportion of the study population
Should not be casually equated with relative risk in clinical communication, particularly for common conditions, given the risk of overstating the actual magnitude of effect to a patient or in published summaries

Rare disease assumption threshold for OR-RR interchangeability, logistic regression's natural production of odds ratios, case-control study odds ratio as the necessary effect measure, overestimation of relative risk magnitude for common outcomes
Odds ratio only approximates relative risk reasonably well when the outcome being studied is relatively rare (roughly below 10% prevalence) - for more common outcomes, odds ratio increasingly overstates the true relative risk, meaning a reported odds ratio for a common condition should not be casually communicated or interpreted as if it were an equivalent relative risk figure

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