NNT, ARR, RRR — Treatment-Effect Statistics

Definitions

For a trial comparing a treatment to control:

• Control event rate (CER): % of control group with the event.
• Experimental event rate (EER): % of treated group with the event.
• Absolute risk reduction (ARR) = CER − EER.
• Relative risk reduction (RRR) = ARR / CER × 100%.
• Number needed to treat (NNT) = 1 / ARR (with ARR as a decimal).

Why all three

Headlines almost always cite RRR ("aspirin reduces heart attacks by 20%!") because it sounds biggest. The same trial in absolute terms ("treats 1,000 people for 5 years to prevent ~10 events" — NNT 100) sounds far less impressive but is more clinically actionable.

Worked example

A primary-prevention statin trial:

• Control group: 4% MI rate over 5 years.
• Treatment group: 3% MI rate.
• ARR = 1%.
• RRR = 25%.
• NNT = 100 over 5 years.

So 100 people take the statin for 5 years to prevent 1 MI.

Why ARR/NNT matter for longevity decisions

• Low-baseline-risk populations: even big RRRs translate to large NNTs — treatment effort/risk may not be worth it.
• High-baseline-risk populations: the same RRR translates to small NNTs — same drug is much more valuable.
• Always ask: what was the baseline rate? what was the absolute reduction?

NNH

Number needed to harm: 1 / absolute risk increase of the most significant adverse effect. NNT-vs-NNH comparison is the framework for deciding whether a treatment is net beneficial.

Related entries

Hazard ratio, Bradford-Hill criteria, Mendelian randomization.