In the last episode I said that “compared to not taking the drug, about 150 people will need to take it to prevent one additional death in 4.1 years.”

This statistic is called the Number Needed to Treat (NNT).

I quite like it and wish that more clinical studies would report this number. I think it can be more intuitive and informative than the relative risk reduction and the absolute risk difference.

The NNT is defined as the average of the number of subjects who need to take the drug to prevent one more event from occurring.

For example, in the case of the statin study, discussed in the previous post, this means that 150 people need to take the drug to prevent one more death (all cause mortality).

And remember, this too is a time-sensitive measure, so that really means that 150 people need to take the drug to prevent one more death in 4.1 years.

NNT Calculation

The calculation for the NNT is relatively simple, especially if we have already calculated the absolute risk difference. In most cases, the NNT is just the inverse of the absolute risk difference. Here’s the full formula:

Let’s try it out:

From the last post we know that the risk difference of the statin group versus control group was 0.00578. Therefore:

Well, that’s not exactly 150 like I said before. What’s up?

The Meta-analysis

Because of the fact we are using a meta-analysis, researchers have determined that “the NNT derived from pooled absolute risk differences (from a meta-analysis) is not very informative and may be misleading if used to assess the benefit of a given intervention for an individual patient.”

So we must use a different, more complicated formula. The Cochrane Collaboration, a global independent network of researchers, professionals, patients, carers, and people interested in health, which does a lot of work in meta-analyses, gives the following formula for calculating NNTs from meta-analyses:

where ACR = risk in the control group (event incidence rate)

and OR = Odds Ratio

We have those two values from the last post: ACR = 0.005751682 (just the CI_c), and the OR is 0.88. Put them in the equation:

That’s it! That is what I called ‘about 150 people.’

We interpret that as: the average of the number of subjects who need to take the drug to prevent one more death from occurring, in 4.1 years, is 154.

Would you take the drug? Sure…it depends…

Problems with the NNT

While the NNT has many benefits, it also has some problems. I won’t go much into that here, but one of the main problems is the calculation of confidence intervals. You will find lots of different opinions regarding the calculations of confidence intervals of the NNT. Some sources just state a simple formula, some say that it is only possible in certain situations, some say plainly that, “The NNT statistic is biased, and reliable confidence intervals cannot be provided.”

In some situations, confidence intervals are clearly unreliable, actually, you usually see the NNT reported without confidence intervals.

I would advocate something similar to what I did in the previous post, which can be summed up by the quote here:

When numbers needed to treat are presented for an intervention, the setting in which it occurred, the time period, the outcome, and the baseline risk of the patients for whom the number needed to treat is thought to be applicable should be described.

Conclusion

Number Needed to Treat

The NNT can be an intuitive and informative statistic which aids in interpreting the results of some clinical trials.

The NNT is  the average of the number of subjects who need to take the drug to prevent one more event from occurring.

The NNT also has its problems, especially the calculation of confidence intervals.

I will reiterate what I said from the last post, but now for the NNT:

To make an informed decision, you need the context of the NNT, the setting, the time period, the outcome, the baseline risk, and who the subjects are.

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R

It’s been a while since I’ve had a post with R-code so here is a simple function that returns the three measures we have been talking about recently: the absolute risk difference, the relative risk reduction, and the NNT. You enter the number of events for the control group, the number of subjects in the control group, the number of events for the treatment group, and the number of subjects in the treatment group. It returns the three measures.

measures_of_risk= function(events_control,subjects_control,events_treat,subjects_treat){

risk_diff = abs((events_treat/subjects_treat)-(events_control/subjects_control))
rel_risk = risk_diff/(events_control/subjects_control)
NNT = 1/risk_diff

cat("The Absolute Risk Difference is", risk_diff,"\n")
cat("The Relative Risk Reduction is", rel_risk,"\n")
cat("The Number Needed to Treat is", NNT)
}

measures_of_risk(1925,33793,1725,33683)

The Absolute Risk Difference is 0.005751682
The Relative Risk Reduction is 0.1009697
The Number Needed to Treat is 173.8622