ARR / RRR / OR

The same treatment benefit can be reported as a 25% cut in risk or as 5 percentage points. Enter the raw numbers from a study and this calculator gives every standard effect measure, so you see both sides of the story.

How the calculation works

You enter the four numbers of a 2×2 table: the number of events (deaths, heart attacks, relapses) and the total number of participants in the control group and in the treatment group. From these the calculator derives the control event rate, CER = events / n, and the experimental event rate, EER = events / n.

It then applies the standard evidence-based medicine formulas: absolute risk reduction ARR = CER − EER; relative risk reduction RRR = ARR / CER; relative risk RR = EER / CER; odds ratio OR = [a / (n₁ − a)] / [c / (n₀ − c)], where a and c are events in the treatment and control groups; and number needed to treat NNT = 1 / ARR, rounded up as the Cochrane Handbook recommends.

If the treatment group has more events, ARR turns negative and the calculator shows NNH, the number needed to harm, instead of NNT. If every participant in a group had the event, the odds are undefined and OR is shown as ∞. Event counts larger than the group size are capped automatically.

Worked example

The control group has 20 events among 100 people (CER 20%) and the treatment group 15 among 100 (EER 15%). ARR = 20% − 15% = 5%, RRR = 5 / 20 = 25%, RR = 0.15 / 0.20 = 0.75. The odds are 15/85 = 0.176 and 20/80 = 0.25, so OR = 0.706. NNT = 1 / 0.05 = 20: you need to treat 20 people for the length of the trial to prevent one event.

Things to keep in mind

• RRR always sounds more impressive than ARR. When baseline risk is low, a 25% RRR can mean an ARR of 0.5% and an NNT of 200, so look at both.
• NNT is tied to a time frame: an NNT of 20 over five years is very different from an NNT of 20 over one year.
• OR approximates RR only when events are rare (roughly under 10%). With common outcomes the OR overstates the effect compared with the RR.
• No confidence intervals or p-values are calculated, so a point estimate alone can't tell you whether the difference is statistically significant.
• Applying trial results to an individual depends on that person's own baseline risk. Treatment decisions belong with a clinician.