Absolute Risk Reduction (ARR) and NNT Calculator

Understanding Risk Reduction Metrics

When evaluating a treatment or intervention, doctors and researchers use several measures to describe how much benefit is provided.
Each tells a different part of the story.

The Four Key Measures

Control Event Rate (CER): the event rate in the control (untreated) group.
Experimental Event Rate (EER): the event rate in the treated group.

Absolute Risk Reduction (ARR)

ARR = CER − EER

This is the most honest measure. It tells you the actual percentage point difference.

Relative Risk Reduction (RRR)

RRR = ARR ÷ CER × 100%

This compares the reduction relative to the baseline risk. Drug advertising often highlights RRR because it sounds impressive.

Relative Risk (RR)

RR = EER ÷ CER

If RR < 1, treatment reduces the event rate.

Number Needed to Treat (NNT)

NNT = 1 ÷ ARR (when using decimals, not percentages)

NNT tells you how many patients must be treated to prevent one additional event. It is rounded up to a whole person, by convention, so the claim is never more generous than the data.

Worked Example

A cholesterol drug trial: CER = 10%, EER = 6%

• ARR = 10% − 6% = 4%
• RRR = 4% ÷ 10% = 40% (sounds great in ads!)
• RR = 6% ÷ 10% = 0.60
• NNT = 1 ÷ 0.04 = 25 (25 people treated to prevent 1 event)

An NNT always has a time attached

An NNT of 25 means nothing until you know over how long. If that trial ran five years, it is 25 people taking the drug for five years to spare one of them the event. The same drug over one year would have a much larger NNT. That is why the calculator asks how long the trial ran, and why two NNTs from trials of different lengths cannot be compared directly.

How sure is the number?

A trial is a sample, so its NNT comes with uncertainty. With the group sizes, the calculator gives a 95% confidence interval for the absolute difference (the Wald interval) and turns it into an interval for the NNT, as Douglas Altman set out in the BMJ in 1998. When the interval for the difference crosses zero, the NNT interval runs from a benefit, through infinity, to a harm: the trial cannot tell whether the treatment helps at all.

NNT Interpretation Guide

There is no universal scale. A good NNT for preventing a death is very different from a good NNT for easing a headache, and a rough guide like the one below only makes sense alongside the outcome, the time frame and the side effects.

When the treatment makes things worse

If the treated group has the higher event rate, every one of these measures flips. ARR becomes Absolute Risk Increase (ARI), RRR becomes Relative Risk Increase (RRI), and RR comes out above 1. The NNT becomes the Number Needed to Harm (NNH), and the whole interpretation table above reverses with it: a low NNT is excellent, while a low NNH is alarming. An NNH of 4 means one extra person is harmed for every four treated, which is the sort of number that stops a trial.

The calculator detects this from the two rates you enter and relabels every row, so read the labels rather than assuming the direction.