Absolute Risk Reduction Calculator: ARR, RRR, NNT and Confidence Intervals
Calculate absolute risk reduction (ARR), relative risk reduction (RRR), relative risk and the number needed to treat or harm from event rates or a 2 × 2 table, with 90%, 95% or 99% confidence intervals (Wald or Newcombe).
How it works
ARR = CER − EER · RRR = ARR ÷ CER = 1 − RR · RR = EER ÷ CER · NNT = 1 ÷ ARR (rounded up) · SE(ARR) = √(CER(1 − CER)/n₁ + EER(1 − EER)/n₂) · 95% CI = ARR ± 1.96 × SE (Wald) or Newcombe hybrid score limits
Absolute risk reduction is the plain difference between the event rate in the control group (CER) and in the treated group (EER): the drop in probability that a patient like those in the study actually experiences. Relative risk reduction divides that difference by the control rate, which can make a small absolute change sound large: halving a 2% risk is a 50% RRR but only a 1-point ARR. The reciprocal of the ARR is the number needed to treat, rounded up to a whole patient by convention. A negative ARR means the treatment raises the risk (an absolute risk increase), and the reciprocal becomes the number needed to harm. With Event counts the calculator also gives the confidence interval for the ARR, by the Wald formula used by Altman (1998), MedCalc and most calculators, or by Newcombe's hybrid score method, which behaves better with small groups or rates near 0% or 100%. It converts the interval into an NNT interval, and adds relative risk with its log-method interval, the odds ratio and a two-proportion z-test P value. If you count a good outcome (cure, response), set it under More options: the result is then the absolute benefit increase, EER − CER.
Worked example
With the default rates, 20% of the control group and 12% of the treated group have the event. ARR = 20.00% − 12.00% = 8.00%. RRR = 8 ÷ 20 = 40.00% and RR = 0.600. NNT = 1 ÷ 0.08 = 12.50, rounded up to 13. Out of 1,000 patients, 80 events are prevented. Entered as counts, 40 of 200 versus 24 of 200, the Wald 95% CI for the ARR is 0.86% to 15.14%, the NNT interval is NNTB 6.6 to 116.6, and the RR interval is 0.376 to 0.957.
Sources: Cochrane Handbook, Chapter 15: risk differences, NNTB and NNTH · MedCalc: Relative risk, NNT and confidence intervals · ClinCalc: Number Needed to Treat calculator · CMAJ: Tips for learners of evidence-based medicine (NNT and its CI) · Newcombe hybrid score interval for a difference of proportions (McGill) · MetricGate: How to calculate NNT with a confidence interval
Frequently asked questions
Why is absolute risk reduction more useful than relative risk reduction?
Relative reduction ignores the starting risk, so a drug that lowers a risk from 0.02% to 0.01% can advertise a 50% relative reduction while helping almost nobody. The absolute reduction, 0.01 percentage points, shows the real size of the benefit. Good reporting gives both.
How do I calculate absolute risk reduction?
Subtract the event rate in the treated group from the event rate in the control group. If 26% of control patients and 16% of treated patients have the event, the ARR is 10 percentage points and the NNT is 1 ÷ 0.10 = 10.
How is the confidence interval for ARR calculated?
The usual (Wald) method is ARR ± 1.96 × √(CER(1 − CER)/n₁ + EER(1 − EER)/n₂). For 80 of 500 versus 45 of 500 events the ARR is 7.00% with a 95% CI of 2.92% to 11.08%. With small groups or rates close to 0% or 100%, the Newcombe hybrid score method is more reliable; you can choose it under More options.
What is the relationship between ARR and NNT?
They are reciprocals: NNT = 1 ÷ ARR. An 8% absolute reduction means 1 ÷ 0.08 = 12.5, so about 13 people must be treated for one to benefit. The NNT interval is made from the reciprocals of the ARR interval limits.
What if the treatment increases risk?
Then the ARR is negative, an absolute risk increase, and its reciprocal is the number needed to harm: how many patients must be treated for one extra bad outcome. The calculator switches the label automatically.
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Educational statistics tool, not medical advice. Treatment decisions should be made with a clinician who knows the patient.