Number needed to treat:
formula and worked example

One prevented event, counted in people

Number needed to treat (NNT) restates a benefit as a headcount: how many people must receive the intervention for one additional person to avoid the outcome. It is the reciprocal of the absolute risk reduction, so a bigger benefit produces a smaller NNT.

The appeal is that it ties effort to payoff. A health service, a safety team or a retention programme can multiply the NNT by the unit cost of the intervention and see the cost of one prevented event, which a percentage difference alone does not reveal.

The mirror image is the number needed to harm, which counts how many people must be treated for one extra adverse effect. Weighing the two side by side is a standard way to frame a benefit-risk trade-off.

Because the NNT is a reciprocal, it is unstable when the benefit is small. A risk difference of 0.5 percentage points gives an NNT of 200, and a difference of 0.25 points doubles that to 400. This is why statisticians prefer to report the absolute risk reduction with its interval and treat the NNT as a translation of it, not as a primary result.

The formula, step by step

• Control risk: proportion of the comparison group that had the event over the follow-up period.
• Treatment risk: proportion of the treated group that had the event over the same period.

Subtract the treatment risk from the control risk to get the absolute risk reduction as a proportion, take its reciprocal, and round up to the next whole person. Rounding up is the usual convention because you cannot treat a fraction of a person and you would not want to understate the effort required.

Worked example: 12% against 8%

A trial records the event in 12 of 100 control participants and in 8 of 100 treated participants.

1. 1Take the risk difference: 0.12 - 0.08 = 0.04.
2. 2Take the reciprocal: 1 / 0.04 = 25.
3. 3The value is already a whole number, so rounding up leaves it at 25.
4. 4Interpret: treat 25 people over the follow-up period to prevent one event.

What an NNT of 25 implies

An NNT of 25 means that for every 25 people treated, one avoids the event and 24 get no additional benefit in terms of this outcome. That sounds poor until you remember that the figure is an average and that preventing a serious event can justify wide treatment. A low NNT is not automatically good, and a high NNT is not automatically bad.

Compare it with what the intervention costs, what harm it can cause and how severe the prevented event is. Preventive measures for common problems often carry NNTs in the tens or hundreds and are still considered worthwhile when they are cheap and safe. Where to draw the line varies by field and by health system.

Always quote the follow-up period. An NNT of 25 over one year is a stronger statement than the same value over ten years.

It also helps to flip the sentence. An NNT of 25 can be read as 'each treated person has a 4% chance of being the one who benefits'. Said that way, patients and managers often find the figure easier to weigh against inconvenience, because it sounds like a personal chance, not a crowd count.

How baseline risk moves the NNT

A modest rise in control risk, from 0.12 to 0.132, shrinks the risk difference from 0.040 to 0.052 and the NNT from 25 to 20, since 1 / 0.052 is about 19.2 and rounds up. This is the central lesson of the measure: because it is a reciprocal, small shifts in the difference make large shifts in the NNT, and as the difference approaches zero the NNT climbs without limit.

Traps in using NNT

• Leaving out the time horizon, which makes NNTs from different trials look comparable when they are not.
• Carrying a trial's NNT to a population with a different baseline risk. The relative effect might transfer, but the NNT will not.
• Computing it when the difference is not statistically distinguishable from zero. The interval around an NNT can stretch to infinity, and a point estimate then misleads.
• Rounding down. A result of 19.2 is reported as 20, not 19.
• Comparing NNTs for different outcomes as though a prevented headache and a prevented death were equal units.

Using it in practice

Imagine a workplace programme that costs 1,500 rupees per employee and has an NNT of 25 for avoiding a certain injury over a year. The cost of preventing one injury is about 25 x 1,500 = 37,500 rupees. If an injury typically costs far more in treatment and lost work, the programme pays for itself; if it costs less, the case rests on welfare grounds alone.