Number needed to treat

Why do we ask a hundred people to take a daily tablet that will help perhaps one of them?

A preventive tablet is described as "reducing risk by twenty per cent", which sounds like it does something for one person in five. Then someone converts the same trial into a number needed to treat and says fifty people must take it for five years for one event to be avoided. Both statements are drawn from the identical result, and they feel like descriptions of different drugs.

The interesting question is not which is honest — both are — but why a genuinely effective treatment necessarily helps so few of the people who take it. That turns out to follow from the structure of prevention itself, not from any weakness of the drug.

Start by asking who could possibly be helped. Divide everyone who takes the tablet into three groups, and note that the division is exhaustive.

Some were never going to have the event during the period in question. The tablet cannot prevent what was not coming, so for them it delivers nothing but its cost. Some will have the event regardless — their trajectory was not close enough to the line for this intervention to change it. For them too, nothing. Only the third group remains: people whose event was marginal enough that this particular push averted it. Prevention can only ever operate on that thin slice.

Now put arithmetic on it. I will use an explicitly hypothetical drug, because real published figures for real drugs vary by population and follow-up length and I do not want to smuggle in a number that would not survive its context.

Suppose that without treatment, ten per cent of a group has the event over five years, and the treatment cuts that by a relative twenty per cent — so eight per cent have it with treatment. Take a hundred people. Untreated, ten events. Treated, eight. The absolute risk reduction is two percentage points, and the number needed to treat is one divided by that: 1/0.02 = 50.

Look at where the hundred people went. Ninety were never going to have the event at all. Eight had it despite the tablet. Two were spared. The "twenty per cent reduction" is entirely true — ten fell to eight — and it describes a two-in-a-hundred change in outcome, because it is twenty per cent of a ten per cent risk.

Which suggests the single most useful relation in preventive medicine. Relative risk reduction tends to stay roughly stable as baseline risk changes — an empirical regularity across many drug classes rather than a law, and one that does fail in places. Absolute benefit does not: it scales with the baseline. Take the same drug, same twenty per cent, and give it to a group whose five-year risk is one per cent. Now one per cent falls to 0.8 per cent, the absolute reduction is 0.2 percentage points, and the number needed to treat is 1/0.002 = 500.

Nothing about the drug changed. The tenfold difference in how many people must be exposed to help one came entirely from who was standing in front of it. That is why preventive medicine spends so much of its effort on estimating baseline risk: the pharmacology is fixed, so the only lever left is selection.

What would refute this? The claim is that absolute benefit scales with baseline risk while relative benefit does not. If a drug's absolute risk reduction were found to be constant across groups of very different baseline risk — so that a very low-risk population saw just as many events averted per hundred treated — the framework would be wrong and risk stratification pointless. Trials enrolling across a wide risk range show the opposite: reductions per hundred treated shrink as the population gets healthier.

Three refinements, and the third is the one most often missed.

First, a number needed to treat is meaningless without its time horizon and its comparator. Fifty over five years is not fifty "ever"; the same trial run for ten years would report a different number. Two NNTs from trials of different durations, in different populations, against different controls, cannot be compared as if they were properties of the drugs.

Second, the same arithmetic runs the other way: divide one by the absolute increase in some harm and you get a number needed to harm. A decision rests on the pair, computed over the same horizon — not the benefit alone.

Third, and most important: an NNT of fifty does not mean that one person in fifty is a responder and forty-nine are not. That is a natural reading and it is unsupported. The same trial result is equally consistent with every treated person having their event pushed slightly later in time, so that two fewer land inside the five-year window. A trial that counts events by a deadline cannot distinguish "two people fully protected" from "a hundred people slightly delayed". Survival curves that keep diverging as follow-up lengthens, rather than separating once and then running parallel, are more consistent with the second picture — but for most treatments this is genuinely unresolved, and stating the NNT does not resolve it.

Finally, a boundary worth naming clearly. Whether an NNT of fifty is worth taking is not a fact contained in the number. It depends on how severe the event is, how burdensome the daily cost is, and what the person weighs — which is a decision for that person together with a clinician who can examine them and knows their actual baseline risk. The arithmetic here explains why the number takes the shape it does; it settles nothing about anyone's treatment.

Every term the collection defines is gathered in the glossary.