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# Relative risk reduction

- Measure

What share of the original risk a treatment removes; it always sounds bigger than the absolute reduction.

Updated Nov 5, 2026

## Key points

- RRR = (CER − EER) / CER = ARR / CER = 1 − RR.
- It is given as a percentage: RR 0.75 → RRR 25%.
- The same RRR can correspond to very different absolute reductions.
- It tends to be similar across populations; the ARR changes with baseline risk.
- Reporting only the RRR makes benefits look bigger.

On this page

- The basics Key points
- What it is
- Formula and reading
- Worked example
- Absolute versus relative
- Markers
- How to read it
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## What it is

The relative risk reduction (RRR) expresses the absolute reduction as a fraction of the control group's risk. It equals 1 minus the relative risk. It stays fairly stable across populations with different baseline risk, which is why trials often report it, but it can impress: an RRR of 50% may mean going from 2 to 1 per 1,000. Always read it next to the absolute reduction.

## Formula and reading

- RRR = 1 − RR, with RR = EER / CER.
- RRR = 0: no effect; positive RRR: treatment lowers risk; negative: it raises it.
- To get back to absolute terms: ARR = RRR × CER.

## Worked example

- Data: a drug is tested in two populations. A: control risk 20%, treated 15%. B: control risk 0.8%, treated 0.6%.
- A: RR = 15 / 20 = 0.75, RRR = 1 − 0.75 = 25%; ARR = 20 − 15 = 5 points.
- B: RR = 0.6 / 0.8 = 0.75, RRR = 25%; ARR = 0.8 − 0.6 = 0.2 points.
- NNT A = 1 / 0.05 = 20; NNT B = 1 / 0.002 = 500.
- Reading: the same 25% RRR means treating 20 people per event prevented in A and 500 in B.

## Absolute versus relative

| Measure | Formula | Depends on baseline risk | What it answers |
| --- | --- | --- | --- |
| Absolute reduction (ARR) | CER − EER | Yes | How many events do I prevent per 100? |
| Relative reduction (RRR) | (CER − EER) / CER | Little | What fraction of the risk do I remove? |
| NNT | 1 / ARR | Yes | How many must I treat to prevent one? |

## Markers

- RRR
- 1 − RR

## How to read it

- A claim that something halves the risk needs the baseline risk to judge how much it matters.
- For vaccines, vaccine efficacy is an RRR: 1 − (risk in the vaccinated / risk in the unvaccinated).

## Common pitfalls

- Using the RRR instead of the ARR when calculating the NNT.
- Comparing treatments by their RRR without looking at each study's baseline risk.

## Memory aid

Relative boasts, absolute informs: 25% sounds the same everywhere, but the events prevented do not.

## Test yourself

Think of the answer, then tap the question to see it.

## A trial reports RR = 0.60. What is the RRR?

RRR = 1 − 0.60 = 0.40, that is 40%.

## Control risk is 10% and the RRR is 30%. What is the ARR?

ARR = 0.30 × 10% = 3 percentage points.

## Why can the RRR give an exaggerated impression of benefit?

It hides the baseline risk: 50% less may mean going from 2 to 1 per 1,000.

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## Connections

## Related 4

- [Absolute risk reduction](https://durgical.com/en/epidemiology/absolute-risk-reduction/)
- [Relative risk](https://durgical.com/en/epidemiology/relative-risk/)
- [Number needed to treat](https://durgical.com/en/epidemiology/number-needed-to-treat/)
- [Statistical vs clinical significance](https://durgical.com/en/epidemiology/statistical-vs-clinical-significance/)

[← 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); [Principles of Epidemiology | Lesson 3 - Section 6](https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section6.html) (Centers for Disease Control and Prevention, 2012).

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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/relative-risk-reduction/