Relative Risk Calculator

Relative risk (RR) is the ratio of the probability of an event occurring in an exposed group versus a non-exposed control group. First, the incidence in the exposed group is computed as Exposed Disease / (Exposed Disease + Exposed No Disease). Next, the incidence in the control group is computed as Control Disease / (Control Disease + Control No Disease). Dividing the exposed incidence by the control incidence yields the relative risk. To determine statistical precision, the natural logarithm of the relative risk is adjusted using the standard error and a z-score corresponding to your chosen confidence level, producing lower and upper confidence limits when exponentiated back.

Imagine a clinical study evaluating a new dietary supplement to prevent a specific condition. Out of 200 individuals in the exposed group, 40 developed the condition (and 160 did not). In the control group of 200 unexposed individuals, 80 developed the condition (and 120 did not). First, find the exposed incidence: 40 / 200 = 0.20 (20%). Next, find the control incidence: 80 / 200 = 0.40 (40%). Dividing these gives a relative risk of 0.20 / 0.40 = 0.50. This indicates that the exposed group has half the risk of developing the condition compared to the control group, suggesting a protective effect.

When analyzing your results, always examine the confidence interval alongside the point estimate. If the confidence interval crosses 1.0, the association may not be statistically significant at your chosen alpha level. Furthermore, ensure your sample sizes in both cohorts are robust enough to minimize random sampling error before drawing definitive clinical or operational conclusions.