NNT is the reciprocal of the absolute risk reduction
Mnemonic
“NNT is one over the absolute risk reduction”, and the absolute reduction is what matters:
- Absolute risk reduction = control event rate - treated event rate
- NNT = 1 / ARR
- Relative risk reduction = ARR / control event rate
“Relative sells the drug, absolute treats the patient.” A fall from 2 per cent to 1 per cent is a 50 per cent relative reduction but a 1 per cent absolute one, giving an NNT of 100.
Because relative risk reduction is roughly constant across risk groups, the benefit of any treatment depends almost entirely on the patient’s baseline risk, which is why the same statin has an NNT of 5 in secondary prevention and 100 or more in low risk primary prevention.
Always quote the NNT with a timeframe and an outcome, and always alongside the number needed to harm.
Expansion
Definitions, where the control event rate is CER and the experimental event rate EER
- Absolute risk reduction = CER - EER
- Relative risk = EER / CER
- Relative risk reduction = (CER - EER) / CER
- Number needed to treat = 1 / absolute risk reduction
- Number needed to harm = 1 / absolute risk increase
A worked example: a drug reduces events from 2 per cent to 1 per cent.
- Relative risk reduction: 50 per cent, which sounds substantial
- Absolute risk reduction: 1 per cent
- NNT = 100, so 100 people are treated for one to benefit
The same drug in a high risk group where events fall from 40 to 20 per cent has the same 50 per cent relative reduction, but an absolute reduction of 20 per cent and an NNT of 5.
This is the key insight: relative risk reduction is usually constant across risk groups, so the benefit of a treatment depends almost entirely on the patient’s baseline risk. The same drug is excellent value in secondary prevention and poor value in low risk primary prevention.
Interpreting an NNT: it must always be quoted with the timeframe and the outcome. “NNT 50” is meaningless; “NNT 50 over 5 years to prevent one myocardial infarction” is not.
Always pair it with the NNH. A treatment with an NNT of 30 for benefit and an NNH of 20 for a serious harm is not a good treatment, however impressive the relative risk reduction.
Odds ratios approximate relative risk only when the outcome is rare, and they exaggerate the effect when it is common, which is a frequent source of misreading.