Relative Risk Calculator
Calculate relative risk (risk ratio) and confidence intervals for epidemiological studies
Calculate Relative Risk
Statistical Parameters
2×2 Contingency Table
| Disease | No Disease | Total | |
|---|---|---|---|
| Exposed Group | a | b | 0 |
| Control Group | c | d | 0 |
| Total | 0 | 0 | 0 |
Table explanation:
- a: Number in exposed group who developed disease
- b: Number in exposed group who did not develop disease
- c: Number in control group who developed disease
- d: Number in control group who did not develop disease
Example: Heavy Drinking and Liver Failure
Study Design
Exposed Group: Heavy drinkers (>2 drinks/day) - 100 people
Control Group: Light drinkers (≤2 drinks/day) - 100 people
Outcome: Liver failure development over 5 years
Results: 8 liver failures in heavy drinkers, 1 in light drinkers
Calculation
Risk in heavy drinkers = 8/100 = 8.0%
Risk in light drinkers = 1/100 = 1.0%
Relative Risk = 8.0% / 1.0% = 8.0
Interpretation: Heavy drinking increases liver failure risk by 8 times
Relative Risk Interpretation
Increased Risk
Exposure increases disease risk
RR = 2.0 means 2× higher risk
No Association
No effect of exposure
Risk same in both groups
Protective Effect
Exposure reduces disease risk
RR = 0.5 means 50% lower risk
Statistical Tips
Larger sample sizes give narrower confidence intervals
CI not including 1.0 indicates statistical significance
RR is best for cohort studies and clinical trials
Consider confounding variables in interpretation
Understanding Relative Risk
What is Relative Risk?
Relative risk (risk ratio) compares the probability of an event occurring in an exposed group to the probability of the same event in a control group. It's a fundamental measure in epidemiology used to assess the strength of association between exposure and outcome.
When to Use Relative Risk
- •Cohort studies (prospective or retrospective)
- •Randomized controlled trials
- •Cross-sectional studies with known incidence
- •Intervention effectiveness assessment
Formula and Confidence Interval
RR = [a / (a + b)] / [c / (c + d)]
CI = exp[ln(RR) ± Z × √(1/a + 1/c - 1/(a+b) - 1/(c+d))]
Clinical Significance
RR = 2.0: Exposure doubles the risk
RR = 0.5: Exposure reduces risk by 50%
RR = 1.0: No association with exposure
Attributable Risk
The difference in risk between exposed and unexposed groups. Shows the excess risk due to exposure.
Confidence Intervals
Range of plausible values for the true relative risk. Narrower intervals indicate more precision.
Statistical Significance
When confidence interval doesn't include 1.0, the association is statistically significant.