Odds Ratio to Relative Risk Conversion

Converts an odds ratio (OR) into a relative risk (RR) — important because ORs from logistic regression are frequently misinterpreted as RRs, especially when the outcome is common.

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Inputs

• Odds Ratio (with optional 95% CI)
• Baseline risk (P0) — incidence in the control group

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Method (Zhang & Yu, 1998)

RR = OR / (1 - P0 + (P0 * OR))

CI bounds converted with the same formula:

RR_lower = OR_lower / (1 - P0 + (P0 * OR_lower))
RR_upper = OR_upper / (1 - P0 + (P0 * OR_upper))

This correction matters most when the outcome is common (baseline risk > 10%) — the OR substantially overstates the RR. When the outcome is rare, OR approximates RR and the correction has little effect.

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