2
1.1294
3.5416
0.2
0.1
2
1.1294
3.5416
0.2
0.1
The Relative Risk Calculator computes the risk ratio (RR) comparing the probability of an event between an exposed and an unexposed group, along with a 95% confidence interval. Relative risk is the most intuitive measure of association in cohort studies and randomized controlled trials.
A relative risk of 1 means both groups have equal risk. RR > 1 indicates increased risk with exposure, while RR < 1 indicates a protective effect. Unlike the odds ratio, relative risk directly compares probabilities, making it easier to interpret for clinicians and patients.
From a 2×2 table with cells a, b, c, d:
Risk in Exposed Group:
$$R_e = \frac{a}{a + b}$$
Risk in Unexposed Group:
$$R_u = \frac{c}{c + d}$$
Relative Risk:
$$RR = \frac{R_e}{R_u} = \frac{a/(a+b)}{c/(c+d)}$$
95% Confidence Interval:
The log of the relative risk is approximately normal, so:
$$SE(\ln RR) = \sqrt{\frac{1}{a} - \frac{1}{a+b} + \frac{1}{c} - \frac{1}{c+d}}$$
$$CI = \exp\left(\ln(RR) \pm 1.96 \cdot SE(\ln RR)\right)$$
This method (Katz logarithmic method) is the standard for large-sample relative risk inference. It assumes independent samples and non-zero event counts in both groups.
RR = 1: No difference in risk between groups — the exposure has no effect on the outcome.
RR > 1: The exposed group has higher risk. RR = 2.0 means the exposed group is twice as likely to experience the event.
RR < 1: The exposure is protective. RR = 0.5 means 50% lower risk in the exposed group.
If the 95% CI includes 1, the difference is not statistically significant at the 5% level.
Inputs
Results
RR = 2.0: the exposed group has double the risk. The 95% CI (1.22, 3.28) excludes 1, so this is statistically significant.
Inputs
Results
RR = 0.33: the treatment group has one-third the risk of adverse events compared to control.
Use relative risk in cohort studies and RCTs where you can calculate incidence rates directly. Use odds ratio in case-control studies or logistic regression. For rare outcomes (< 10%), OR approximates RR closely.
No. In case-control studies, you sample based on outcome status, so you cannot estimate incidence directly. The odds ratio is the appropriate measure for case-control designs.
It means the exposed group has 50% higher risk of the event compared to the unexposed group. If the baseline risk is 10%, the exposed group has approximately 15% risk.
Relative risk is a ratio (dimensionless), while absolute risk difference (ARD) is the subtraction of the two risks. RR = 2.0 sounds dramatic, but if risks are 0.002 vs. 0.001, the absolute difference is tiny (0.001).
If a = 0 or c = 0, the RR equals 0 or is undefined, and the log method fails. Continuity corrections (adding 0.5) or exact methods should be used in these cases.
No. RR for increased risk ranges from 1 to ∞, but for protective effects ranges from 0 to 1. This asymmetry means RR = 2.0 (doubling) and RR = 0.5 (halving) represent the same magnitude of association in opposite directions.
Roboculator Team
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