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⚕️ Relative Risk Calculator

Calculate relative risk (RR), 95% confidence interval, absolute risk reduction (ARR), relative risk reduction (RRR), and number needed to treat (NNT) from a 2×2 contingency table.

Enter your 2×2 contingency table:

Event (outcome+) No Event (outcome−)
Exposed
Unexposed

a = exposed & event, b = exposed & no event, c = unexposed & event, d = unexposed & no event

Relative Risk Formulas

Risk_exposed = a / (a + b)
Risk_unexposed = c / (c + d)
RR = Risk_exposed / Risk_unexposed
ARR = Risk_unexposed − Risk_exposed
RRR = ARR / Risk_unexposed = 1 − RR
NNT = 1 / ARR
95% CI: exp(ln(RR) ± 1.96 × SE_ln(RR))
SE_ln(RR) = √(b/a(a+b) + d/c(c+d))
'What is NNT?', 'answer' => 'Number Needed to Treat (NNT) is the number of people who need to be treated to prevent one additional event. NNT = 1/ARR. A lower NNT indicates a more effective treatment.'], ['question' => 'When should I use RR vs odds ratio?', 'answer' => 'Relative risk is preferred for cohort studies (prospective). Odds ratio (OR) is used in case-control studies. For rare events (prevalence < 10%), OR approximates RR well. For common outcomes, OR overstates the association.'], ['question' => 'What is the 95% confidence interval for RR?', 'answer' => 'The 95% CI gives the range within which the true RR is likely to fall with 95% confidence. If the CI does not include 1.0, the result is statistically significant at α = 0.05.'], ]" />

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