Number Needed to Treat (NNT), Number Needed to Harm (NNH) and Likelihood to Help or Harm (LHH)
Number Needed to Treat (NNT)
The number needed to treat (NNT) is based on comparing one treatment, typically a new one, with another treatment (usually the standard treatment) or perhaps with nothing. That is, it is always relative to another situation. NNT says, “by treating this number of patients with the new treatment, one additional good outcome will be obtained compared to treating the same number in the usual manner.” A lower number is better.
In terms of a fake concrete example, it might go like this: suppose you are treating patients who have hypertension and your goal is to get blood pressure down to 120/80. A study recently showed that with drug B, the NNT is 20. Further suppose you previously used drug A, the usual choice, and 14 patients out of 20 would have achieved a blood pressure of 120/80. Now you switch to drug B and use it in 20 patients. The expected result is that 15 patients will achieve a blood pressure of 120/80.
If you’ve calculated the absolute risk difference (ARD), then the NNT is easy to find. It is simply one divided by the absolute risk difference, i.e.,
NNT = 1 / ARD
Using our fake example, suppose drug A typically results in 70% of patients achieving a blood pressure of 120/80. Now with drug B, 75% of patients achieve a blood pressure of 120/80.
Absolute risk difference = 75% – 70% = 5% (0.05) so NNT = 1 / 0.05 = 20
Notice that the NNT will be 20 if the ARD is 15% – 10% or 85% – 80% (or whatever 5% difference you select).
Number Needed to Harm (NNH)
The number needed to harm (NNH) looks at the other side of treatment and is also relative to another treatment or condition (usually the standard treatment or no treatment): “by treating this number of patients with the new treatment, one additional harmful outcome will occur than if they had been treated in the usual manner.”
Continuing with our fake example, suppose drug B, the new hypertension drug, causes an arrhythmia in two out of every 1,000 patients treated, while drug A causes the arrhythmia in five out of every 10,000 patients. The formula for calculating NNH is very similar to that for NNT, in that the formula is one divided by the absolute risk difference (ARD). Higher numbers are better.
NNH = 1 / ARD
In the fake example, NNH = 1 / (0.002-0.0005) = 1 / 0.0015 = 667 (rounding up to the next nearest integer)
So, for every 667 patients treated with drug B, one more patient will have an arrhythmia than if those 667 patients had been treated with drug A. As with NNT, as long as the difference in risks between new and old treatment is 0.0015, the NNH = 667. That is, a bad outcome that occurs in 25.0015% of patients on the new drug and 25.0% of patients on the old drug will have a NNH of 667.
Likelihood to Help or Harm (LHH)
This brings us to a third quantity: likelihood to help or harm (LHH), which is the ratio of NNH to NNT and is meant to summarize the risks vs. the benefits of one treatment related to another. Since it generally compares one negative outcome to one positive outcome, often the focus is on outcomes deemed “important.” Higher numbers are better, i.e., it will take more people to cause a harm than to reap a benefit.
Using our fake example of the hypertension drug, calculating LHH is as follows:
LHH = NNH / NNT = 667 / 20 = 33.35
Points to Consider
Although NNT, NNH and LHH are useful when comparing two possible treatment options, they need to be placed in context. Remember that risk is itself an estimate of the outcome with a certain amount of error on either side of it. Put two risks together and now you have even more uncertainty. So even though NNT gives you a nice integer like “20,” that’s just an approximation.
If you have the confidence interval for the absolute risk difference (ARD), you can get the confidence interval for the NNT by taking the reciprocals of the lower and upper boundaries of the ARD confidence interval. For example, suppose the 95% confidence interval for the difference in achieving blood pressure of 120/80 was 1% to 9%, then the 95% confidence interval for the NNT would be:
Lower bound = 1 / 0.09 = 12
Upper bound = 1 / 0.01 = 100
Note that even though the confidence interval for the ARD is relatively narrow, the confidence interval for NNT is fairly wide. With larger risk differences you won’t see a divergence this dramatic. For example, if the ARD is 20% with a 95% confidence interval of 16% to 24% (same width as above), the 95% confidence interval for the NNT is 5 to 7.
The ARD, NNT and NNH relate to the types of patients enrolled into the studies from where these quantities were obtained. If the ARD from our fake hypertension medication example involved the study of obese, middle-aged patients and you are considering treatment of a thin, elderly patient, the NNT may not be as relevant.