Calculate relative risk, absolute risk difference, and number needed to treat from a 2×2 contingency table. Essential for epidemiology, clinical trials, and risk assessment studies.
Last updated: March 2026
Exposed Group:
Control Group:
| Event | No Event | |
|---|---|---|
| Exposed | 15 | 85 |
| Control | 5 | 95 |
Relative Risk (RR) is a measure of the probability of an outcome occurring in an exposed group compared to an unexposed (control) group. It quantifies how many times more (or less) likely an event is to occur in the exposed group relative to the control group. RR is fundamental to epidemiology and clinical research for assessing the strength of associations between exposures and health outcomes.
An RR of 1.0 means equal risk in both groups (no association). An RR greater than 1 indicates increased risk in the exposed group (the exposure is a risk factor). An RR less than 1 indicates decreased risk in the exposed group (the exposure is protective). For example, an RR of 2.5 means the exposed group is 2.5 times more likely to experience the event compared to the control group.
The Absolute Risk Difference (ARD) shows the percentage point difference in risk between groups, while the Number Needed to Treat (NNT) indicates how many people would need to receive an intervention to prevent one event. The 95% Confidence Interval provides a range where we're 95% confident the true RR lies. If the CI crosses 1.0, the result is not statistically significant.
A study examines smoking and lung disease. Among 100 smokers, 15 developed lung disease. Among 100 non-smokers, 5 developed lung disease. Calculate relative risk.
RR compares probabilities (risk) of an outcome in exposed vs control groups. Odds Ratio compares odds instead of risks. Both measure associations but are calculated differently. RR is more intuitive for prospective studies; OR is preferable for case-control studies.
RR = 1 means equal risk in both groups—there's no association between exposure and outcome. The exposure neither increases nor decreases risk. This is the null hypothesis in most studies.
Yes! An RR of 0.5 means the exposed group has half the risk of the control group. This indicates a protective effect. For example, vaccinated people having 0.5× the infection risk as unvaccinated people.
If the 95% confidence interval includes 1.0, the RR is not statistically significant—we cannot confidently say the result differs from chance. Larger sample sizes help narrow the CI and increase precision.
The 95% CI is a range where we're 95% confident the true RR lies. If CI = [1.2, 3.5], the true RR is likely between 1.2 and 3.5. If it includes 1.0, results aren't statistically significant at the 0.05 level.
NNT (Number Needed to Treat) indicates how many people need to receive an intervention to prevent one adverse event. A lower NNT means more people benefit from treatment. It's useful for communicating clinical significance.
No. RR must be positive since it's a ratio of two probabilities (both positive). An RR of 0 would mean the event never occurs in the exposed group, which is rare in practice.
Use RR to show relative difference and strength of association. Use ARD to communicate absolute impact—how many percentage points lower (or higher) the risk is. ARD is often more clinically meaningful for decision-making.
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