Signature
NNT = 1 / ARR; NNT_L = 1 / ARR_U; NNT_U = 1 / ARR_L
| Inputs | Definition | Unit |
|---|---|---|
ARR | Absolute risk reduction over the stated period, expressed as a proportion, not a percentage | probability difference, not equal to 0 |
ARR_U | Upper limit of the confidence interval for the ARR | probability difference |
ARR_L | Lower limit of the confidence interval for the ARR, greater than zero for this form | probability difference |
NNT | Expected number of people treated with the intervention rather than the comparator for one additional person to avoid the event over the period | people, before rounding up |
|---|---|---|
NNT_L | Lower limit of the confidence interval for the NNT | people |
NNT_U | Upper limit of the confidence interval for the NNT | people |
Function
Absolute risk reduction function
Maps the risks of an adverse event with the comparator and with the intervention, over the same period, to their difference, oriented so that a benefit is positive. The difference converts a relative treatment effect into events avoided per person treated, the quantity that costs and QALYs in an economic evaluation are built from.
Try this function
Implementations
Excel
Reported NNT and limits
Excel rounds the reciprocal of the absolute ARR up to the next whole number and labels it from the sign of the ARR; the limits are returned only when the ARR interval lies wholly above zero.
=IF(ARR=0,NA(),ROUNDUP(1/ABS(ARR),0)); =IF(ARR>0,"NNTB","NNTH"); =IF(ARRLower>0,1/ARRUpper,NA()); =IF(ARRLower>0,1/ARRLower,NA())
Assumptions
Benefit direction and an interval that excludes zero
A positive ARR gives the number needed to treat for an additional beneficial outcome (NNTB); a negative ARR gives, in absolute value, the number needed to treat for an additional harmful outcome (NNTH). The limits apply directly when both ARR limits are positive. When the ARR interval includes zero, the NNT interval passes through infinity and is reported as running from NNTH through infinity to NNTB.
Period and comparator risk attached to the NNT
The NNT refers to the follow-up period of the ARR. Limits derived from a pooled relative effect and an assumed comparator risk do not include uncertainty in that comparator risk.
Worked examples
Altman example with an ARR of 10 per cent
An ARR of 0.10 with a 95% confidence interval of 0.05 to 0.15 gives an NNT of 10 with a 95% confidence interval of about 6.67 to 20, as in Altman (1998).
ARR = 0.10; ARR_L = 0.05; ARR_U = 0.15; NNT = 10; NNT_L = 6.67; NNT_U = 20
OSIRIS trial NNT and interval
An ARR of 0.06267 with a 95% confidence interval of 0.027 to 0.099, from the CONSORT 2010 example, gives about 15.96, reported as 16 infants treated early to prevent one death or case of oxygen dependence, with an interval of about 10.10 to 37.04.
ARR = 0.06267; ARR_L = 0.027; ARR_U = 0.099; NNT = 15.96; NNT_L = 10.10; NNT_U = 37.04
Common errors
Rounding the NNT down or to the nearest whole number
A risk difference of minus 0.12 gives 8.33, which the Cochrane convention reports as 9. Reporting 8 overstates the benefit per person treated. An ARR entered as a percentage, 5 rather than 0.05, gives an NNT of 0.2.
Reporting an incomplete interval when the ARR interval spans zero
Altman cites a reported NNT of minus 12.5 (minus 3.7 to infinity) for an ARR of minus 0.08 (minus 0.27 to 0.11). The complete interval is NNTH 12.5 (NNTH 3.7 to infinity to NNTB 9.1).
Sources
Confidence intervals for the number needed to treat
Altman DG. Confidence intervals for the number needed to treat. BMJ. 1998;317(7168):1309-1312. The NNT is the reciprocal of the absolute risk reduction, 1/ARR or 100/ARR for percentages; its confidence limits are the reciprocals of the ARR limits, with the example of an ARR of 10% (5% to 15%); intervals that include zero, and the labels NNTB and NNTH.
Cochrane convention for rounding and limits of the NNT
Schünemann HJ, Vist GE, Higgins JPT, Santesso N, Deeks JJ, Glasziou P, Akl EA, Guyatt GH. Chapter 15: Interpreting results and drawing conclusions (last updated August 2023). In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.5. Cochrane; 2024. Section 15.4.2 (definition of the NNT, NNTB and NNTH), section 15.4.4 (NNTs are by convention rounded up to the next whole number), section 15.4.4.1 (a risk difference of minus 0.12 gives an NNT of 9) and section 15.4.4.5 (confidence limits from the limits of the summary statistic).
Canonical Identity
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