How to Calculate Relative Risk
Relative risk (RR) is calculated as the ratio of the proportion of individuals who develop disease in the exposed group divided by the proportion who develop disease in the unexposed group. 1
Basic Formula
The fundamental calculation is straightforward:
- RR = Risk in Exposed Group / Risk in Unexposed Group 1, 2
- Where risk = (number of affected individuals / total number of individuals in that group) 2
For example, if 20 out of 100 exposed individuals develop disease (risk = 0.20) and 10 out of 100 unexposed individuals develop disease (risk = 0.10), then RR = 0.20/0.10 = 2.0 1
Key Interpretation Points
- An RR of 1.0 indicates no association between exposure and outcome 1
- An RR far from 1.0 (either >1 or <1) suggests the association is less likely due to confounding 1
- RR > 1.0 indicates increased risk with exposure 2
- RR < 1.0 indicates decreased risk (protective effect) with exposure 2
Statistical Considerations
Confidence Intervals
Always report the 95% confidence interval (CI) alongside the RR to assess statistical uncertainty. 1, 3 When relative risks are not directly reported in studies, you can calculate them from raw data and then compute the 95% CI using published formulas 1. If only a p-value is provided, the CI can be calculated using standard conversion formulas 1.
Meta-Analysis Applications
When pooling multiple studies:
- Use inverse-variance weighting with a random-effects model to compute pooled RR 1
- Assess heterogeneity using the I² statistic 1
- The pooled relative effects can then be applied to various baseline risks to compute absolute risk differences 1
Important Distinctions and Caveats
RR vs Odds Ratio (OR)
The OR approximates the RR only when the outcome is rare (<10% in the unexposed population). 4 When outcomes are common (≥10%), the OR will exaggerate the RR 4. This is critical because:
- Case-control studies typically report ORs, not RRs 2, 4
- Cohort studies can directly calculate RR 4
- In meta-analyses where both ORs and RRs are pooled, the OR closely approximates RR when baseline risk is low 1
Relative vs Absolute Risk
RR should always be interpreted alongside absolute risk measures, as relative measures alone can be misleading. 3 For example:
- An RR of 2.0 could represent an increase from 0.1% to 0.2% (minimal clinical impact) 3
- Or an increase from 10% to 20% (substantial clinical impact) 3
- Both the relative risk and absolute risk with 95% CIs should be reported together to provide complete clinical context 3
Consistency Across Populations
Relative effects tend to be more consistent across different populations and studies than absolute measures. 1 This property makes RR particularly useful for:
- Comparing effects across diverse geographic populations 1
- Applying pooled estimates from meta-analyses to different baseline risk groups 1
- However, this is not universal—some associations show constant rate differences rather than constant rate ratios 1
Common Pitfalls
Misclassification Bias
Exposure misclassification causes the RR to be biased toward the null value (RR = 1.0). 5 The degree of bias depends on:
- Sensitivity and specificity of exposure measurement 5
- True prevalence of exposure in the population 5
- The true underlying relative risk 5
Study Design Limitations
- In case-control studies, you cannot directly calculate RR—only OR 2, 4
- Cross-sectional studies may provide prevalence ratios rather than true risk ratios 1
- Retrospective studies require careful consideration of the relationship between OR and RR 6
Practical Application in Research
When abstracting data for systematic reviews:
- Record the RR and its 95% CI directly when reported 1
- If not reported, abstract raw data to calculate RR as the ratio of proportions 1
- For multiple exposure levels within categories, select the highest exposure measure to avoid overweighting single studies 1
- Consider both ratio measures (RR) and difference measures (risk difference) as they may show different patterns 1