[Durgical](https://durgical.com/en/) › [DurgiPedia](https://durgical.com/en/durgipedia/) › [Epidemiology](https://durgical.com/en/epidemiology/) › [Measures of frequency and association](https://durgical.com/en/epidemiology/areas/measures/) › Absolute risk reduction

# Absolute risk reduction

- Measure

The difference in risk between the control and treated groups: how many events are prevented per 100 people treated.

Updated Nov 5, 2026

## Key points

- ARR = risk in controls − risk in the treated (CER − EER).
- It is given in percentage points with its period: 3 points fewer over 3 years.
- It depends on baseline risk: the same treatment gives a larger ARR in high-risk patients.
- NNT = 1 / ARR.
- For treatment decisions, the ARR tells more than the relative reduction.

On this page

- The basics Key points
- What it is
- Formula and reading
- Worked example
- The same relative effect at different baseline risks
- Markers
- How to read it
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## 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.

## Memory aid

Absolute subtracts, relative divides: for the ARR you only take one risk away from the other.

## 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.

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## Connections

## Related 5

- [Relative risk reduction](https://durgical.com/en/epidemiology/relative-risk-reduction/)
- [Number needed to treat](https://durgical.com/en/epidemiology/number-needed-to-treat/)
- [Relative risk](https://durgical.com/en/epidemiology/relative-risk/)
- [Attributable risk and attributable fraction](https://durgical.com/en/epidemiology/attributable-risk-and-attributable-fraction/)
- [Number needed to harm](https://durgical.com/en/epidemiology/number-needed-to-harm/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

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](https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-15) (Cochrane, 2024); [Chapter 6: Choosing effect measures and computing estimates of effect](https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-06) (Cochrane, 2024).

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Representative model, for educational purposes only.

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License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/absolute-risk-reduction/