Table of Contents
What Is Relative Risk?
Relative risk (RR), also called the risk ratio, is a measure of association used in epidemiology and clinical research. It compares the probability of an outcome (e.g., disease) in an exposed group to the probability in an unexposed (control) group. RR is calculated from prospective (cohort) studies where subjects are followed over time.
An RR of 1.0 means no difference in risk between groups. An RR greater than 1.0 indicates increased risk in the exposed group, while an RR less than 1.0 indicates decreased risk (a protective effect). The further the RR is from 1.0, the stronger the association.
Formula
SE = √(1/a - 1/(a+b) + 1/c - 1/(c+d))
Where a = exposed with outcome, b = exposed without outcome, c = unexposed with outcome, and d = unexposed without outcome. The 95% confidence interval uses the log-transformed RR and its standard error.
Interpreting Relative Risk
| RR Value | Interpretation | Example |
|---|---|---|
| RR = 1.0 | No association | Exposure has no effect on outcome |
| RR > 1.0 | Positive association (risk factor) | Smoking and lung cancer (RR ≈ 15-30) |
| RR < 1.0 | Negative association (protective) | Vaccination and disease (RR ≈ 0.1) |
| RR = 2.0 | Double the risk | Exposed group has 2x the risk |
| RR = 0.5 | Half the risk | Exposed group has 50% lower risk |
Frequently Asked Questions
What is the difference between relative risk and odds ratio?
Relative risk compares probabilities (risks) directly: P(event|exposed) / P(event|unexposed). The odds ratio compares odds: [a/b] / [c/d] = (a*d) / (b*c). The odds ratio is used in case-control studies where true risk cannot be calculated. When the outcome is rare (less than 10%), the odds ratio approximates the relative risk.
When is the 95% confidence interval important?
The 95% CI tells you the range of plausible values for the true relative risk. If the interval includes 1.0, the result is not statistically significant at the 5% level -- meaning you cannot conclude that the exposure is associated with the outcome. A narrow CI indicates a precise estimate, while a wide CI suggests more uncertainty.