Relative Risk vs Odds Ratio

Relative risk (RR) is the ratio of the probability of an outcome in the exposed group to that in the unexposed group; the odds ratio (OR) is the ratio of the odds of the outcome in the two groups. They are similar when the outcome is rare but diverge when it is common, and the OR then exaggerates the apparent effect.

Definitions

• Risk = events / total in the group.
• Odds = events / non-events.
• RR = risk in exposed / risk in unexposed.
• OR = odds in exposed / odds in unexposed.

Illustrative example with worked numbers

Invented for teaching. Outcome in 100 exposed and 100 unexposed people: 30 events with exposure and 20 without. Risk exposed 30/100 = 0.30; risk unexposed 20/100 = 0.20; RR = 1.5. Odds exposed = 30/70 = 0.429; odds unexposed = 20/80 = 0.25; OR = 1.71. If events were rare (3 versus 2 per 100), RR = 1.5 and OR = 1.52, almost the same.

Which design uses which

• Cohort studies and trials: can estimate risks, so RR can be reported (or risk difference).
• Case-control studies: cannot estimate risk directly, so the OR is the usual measure.
• Logistic regression gives odds ratios; if the outcome is common, convert or use methods that estimate risk ratios directly, with statistical advice.

Interpretation

An RR of 1.5 means the risk is 50% higher in the exposed group. An OR of 1.71 does not mean a 71% higher risk when the outcome is common: it refers to the odds. Describing ORs as "risk" in a common outcome overstates the effect. Always present absolute risks as well.

Common pitfalls

• Reading odds ratios as risk ratios.
• Reporting only relative measures without baseline risk.

Key takeaways

• RR compares risks; OR compares odds; they converge for rare outcomes.
• Report absolute risks, with confidence intervals.

This page is general educational information about research methods. It is not medical, legal or regulatory advice; follow your institution's ethics board and your target journal's instructions.