Relative risk reduction
- Measure
What share of the original risk a treatment removes; it always sounds bigger than the absolute reduction.
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.
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.
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); Principles of Epidemiology | Lesson 3 - Section 6 (Centers for Disease Control and Prevention, 2012).
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Representative model, for educational purposes only.