Odds Ratio to Risk Ratio Converter

This calculator converts an odds ratio (OR) to a risk ratio (RR, also called relative risk) using the baseline risk in the control group. This conversion is essential for interpreting case-control studies and meta-analyses in clinical terms.

Enter the odds ratio and baseline risk
Odds Ratio (OR) From the study or meta-analysis
Baseline Risk in Control Group (%) Event rate in the unexposed/control group

Formula

OR to RR Conversion

\( RR = \frac{OR}{1 - p_0 + p_0 \times OR} \)

where \( p_0 \) is the baseline risk (event rate in the control group).

Treatment Group Risk

\( p_1 = p_0 \times RR \)

Absolute Risk Difference

\( ARD = p_1 - p_0 \)

Why Convert OR to RR?

Odds ratios are commonly reported in:

  • Case-control studies (where RR cannot be directly calculated)
  • Logistic regression analyses
  • Meta-analyses of observational studies

However, risk ratios are more intuitive for clinical interpretation. An RR of 2.0 means "twice the risk," while an OR of 2.0 means "twice the odds" — these are not the same when the outcome is common.

When OR ≈ RR

The odds ratio approximates the risk ratio when:

  • The outcome is rare (baseline risk < 10%)
  • The effect size is modest (OR close to 1)

When baseline risk is high, OR can substantially overestimate RR for harmful exposures and underestimate RR for protective exposures.

Specific Examples

Example 1: A meta-analysis reports OR = 2.5 for a treatment effect. If baseline risk is 5%, RR ≈ 2.38. If baseline risk is 30%, RR ≈ 1.79. The same OR implies very different relative risks.

Example 2: A case-control study finds OR = 0.5 for a protective factor. With 20% baseline risk, RR ≈ 0.56, meaning a 44% relative risk reduction.

Assumptions & Limitations

  • Requires knowledge of the baseline risk in the target population
  • Assumes the OR is valid and unbiased
  • Does not account for confounding or effect modification
  • Confidence intervals for RR require more complex calculations
  • The formula assumes a cohort-type interpretation of risk

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