Absolute risk reduction
- Measure
The difference in risk between the control and treated groups: how many events are prevented per 100 people treated.
What it is
The absolute risk reduction (ARR) is the control group's risk minus the treated group's risk, over a defined period. Unlike relative measures, it keeps the real scale: it says how many events are prevented per 100 or 1,000 people. It is the most useful measure for decisions, because a large relative benefit can be tiny in absolute terms when baseline risk is low, and the number needed to treat comes from it.
Formula and reading
- ARR = CER − EER, with CER = c/(c+d) and EER = a/(a+b) when the treated are in the first row.
- ARR = 0: no effect; positive ARR: treatment prevents events; negative: it causes them (absolute risk increase).
- It is the risk difference of meta-analysis handbooks, with the sign set by the order of subtraction.
Worked example
- Data: a 3-year trial with 2,000 patients. Control (1,000): 80 strokes. Treated (1,000): 50 strokes.
- Risk in controls = 80 / 1,000 = 0.08 (8%).
- Risk in the treated = 50 / 1,000 = 0.05 (5%).
- ARR = 0.08 − 0.05 = 0.03, that is 3 percentage points over 3 years.
- Per 1,000 treated for 3 years, 30 events are prevented; NNT = 1 / 0.03 ≈ 33.3, rounded up to 34.
- Reading: treatment prevents 3 events per 100 patients treated over 3 years.
The same relative effect at different baseline risks
| Group | Control risk | Treated risk | ARR | NNT |
|---|---|---|---|---|
| High risk | 20% | 15% | 5 points | 20 |
| Low risk | 2% | 1.5% | 0.5 points | 200 |
Markers
- ARR
- RD
How to read it
- When comparing two treatments, ask for the ARR or the NNT with its time period.
- In primary prevention baseline risk is usually low, so the ARR is low too.
Common pitfalls
- Reporting the ARR without the follow-up period.
- Subtracting in the wrong order and getting the wrong sign.
- Presenting only the relative reduction, which inflates the impression of benefit.
Test yourself
Think of the answer, then tap the question to see it.
Risk is 12% in controls and 9% in the treated. What is the ARR?
ARR = 12% − 9% = 3 percentage points.
Why is the ARR more useful than the relative reduction for decisions?
It keeps the real scale: it says how many events are prevented per 100 treated, which depends on baseline risk.
How do you go from the ARR to the NNT?
NNT = 1 / ARR (with the ARR as a proportion), rounded up.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Chapter 15: Interpreting results and drawing conclusions (Cochrane, 2024); Chapter 6: Choosing effect measures and computing estimates of effect (Cochrane, 2024).
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Representative model, for educational purposes only.