# Number Needed to Treat (NNT)

## Richard Goldstein, Ph.D.

An easy way to compare the benefits and risks of various treatment options is highly desirable. The NNT has been proposed for this purpose. But what is the NNT? Say a study compares two groups with respect to treating an acute condition (e.g., bacterial infection or a flu vaccine). Let's say that with option A, 10% of subjects get the flu while with option B, 20% get the flu. That is, risk is reduced from 0.2 to 0.1 (i.e., the absolute risk reduction (ARR) is 0.1 (0.2 - 0.1). The NNT is the inverse, or reciprocal, of this (i.e., 1/0.1) and is equal to 10, meaning we need, on average, to treat 10 people to achieve a benefit for one person. If the calculated NNT is not an integer, round up to the nearest integer. This sounds good, but
1. What is the comparator (option B)? If it is a placebo, is this NNT of interest in a situation where a placebo would not be used in a clinical encounter? The NNT should be relative to whatever would commonly be prescribed. Similarly, if B is a real treatment but at an unrealistic dose, do we care about the NNT?
2. What if we have two studies, each against placebo; can we then compare the two NNTs? Only if the placebo rate is the same in the two studies. Further complications loom if the two studies have non-placebo comparators but these alternatives differ.
3. The NNT would be the same if the risks were 90% and 80% instead of 20% and 10%  but would the decision by either patient or doctor be the same? Often the baseline matters.
4. Many people, as shown in the literature, misinterpret the NNT. One mis-interpretation is to treat the NNT as a within-person measure (e.g., I will do 10 times better if I use treatment A).
5. While the NNT may make some sense for acute conditions, what if we are talking about a chronic condition (e.g., hypertension and risk of stroke). In this case, the NNT will differ by follow-up time even if the relative risk does not change over time. For example, suppose a study with 10,000 subjects: after 6 months 50 on B have a stroke v. 5 on A; after one year, 100 on B have had stroke v. 10 on A; the NNT is 112 at 6 months and 56 at 12 months. How do we choose the most appropriate follow-up time? One suggestion is to use annualized rates; however, this assumes a constant hazard (often untrue) and also only works if the hazard rate is low; also, this changes the interpretation from people to person-years which is even harder to interpret.
6. The situation is even more complex in time-to-event (survival, or duration, analysis) studies. This is particularly true if there are multiple studies with different lengths of follow-up.
7. The NNT by itself can be misleading (even if the baseline risk is also presented) and should be supplemented with adverse event information (possibly including the number needed to harm (NNH) and its baseline).
8. There are a number of statistical complexities, generally stemming from the fact that the NNT is a reciprocal, including:
• if the ARR is 0, the NNT is undefined.
• This means that if a confidence interval (CI) for the NNT crosses 0, there is a discontinuity and we have two pieces, unconnected, for the CI.
• The CI is hard to calculate in virtually any situation.
• The NNT is unstable in a technical sense and shows a great deal of variation, more than one would expect based on the variation in the observed risks.
• Calculating an NNT in a meta-analysis involves a lot of, generally incorrect and sometimes untestable, assumptions.

Richard Goldstein last updated this on 7 Mar 2011. Thanks to Mel Glenn, M.D. for comments.
Topic revision: r1 - 18 Jun 2011, FrankHarrell

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