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NNT Advanced Calculator (Cates Plot)
Turn a trial’s risk reduction into a number needed to treat and a visual Cates plot of 100 people — with confidence intervals and the exact R command behind the result. A full guide follows below. Validated against R 4.3.3.
In Simple Words
The number needed to treat (NNT) is how many patients must be treated for one extra person to benefit; it is the reciprocal of the absolute risk reduction. A Cates plot (a smiley-face or 100-person diagram) shows that benefit visually: out of 100 treated people, how many would have had the event anyway, how many are helped, and how many gain nothing.
The visual matters because percentages mislead. A “50% relative reduction” sounds dramatic but may correspond to helping only one or two people in a hundred. Plotting the absolute effect on a 100-person grid gives patients and clinicians an honest, intuitive sense of how much a treatment actually delivers.
When to Use an NNT With a Cates Plot
Use an NNT and Cates plot when communicating the size of a treatment’s benefit to patients, in shared decision-making, or in a paper where you want the absolute effect to be clear rather than hidden behind a relative measure.
Always attach the time horizon and the 95% confidence interval — an NNT means nothing without the period it refers to. For the basic reciprocal calculation, use our NNT calculator; to compare relative measures, see the odds ratio and relative risk tool. Unsure which to present? Our Test Selector can help.
e1 <- {e1}; n1 <- {n1}; e0 <- {e0}; n0 <- {n0}
pt <- e1/n1; pc <- e0/n0
arr <- pc - pt
se <- sqrt(pt*(1-pt)/n1 + pc*(1-pc)/n0)
ci <- arr + c(-1, 1) * qnorm(0.975) * se
c(ARR = arr, NNT = 1/arr)
1/rev(ci) # NNT 95% CI (valid when the ARR CI excludes 0)User guide
When to use. Report treatment effects as absolute risk reduction, relative risk, odds ratio and number needed to treat, each with a 95% CI, plus a Cates plot showing what happens to 100 treated people.
Assumptions. Binary outcome over a fixed follow-up; reasonably large counts for the Wald intervals.
Common mistakes. When the ARR interval includes zero, the NNT interval runs through infinity (NNTB to NNTH): do not quote it as a simple range. NNT is specific to the follow-up time.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Altman DG. Confidence intervals for the number needed to treat. BMJ. 1998;317:1309-1312.
- Laupacis A, Sackett DL, Roberts RS. An assessment of clinically useful measures of the consequences of treatment. N Engl J Med. 1988;318:1728-1733.
Worked Examples
Example 1 — From risk reduction to a picture
If the event rate falls from 30% to 20%, the absolute risk reduction is 10% and the NNT is 10. On a Cates plot of 100 people, about 20 would have the event despite treatment, about 10 are spared by it, and the rest were never going to have the event — making the modest real benefit visible.
Example 2 — Relative versus absolute
A treatment cutting risk from 2% to 1% is a 50% relative reduction but only a 1% absolute reduction, giving an NNT of 100. The Cates plot shows 99 of 100 unaffected and one helped, correcting the false impression created by the headline 50% figure.
Assumptions to Check
A defined time horizon. NNT depends on the follow-up period; an NNT of 20 over one year differs entirely from 20 over a decade, so the period must always be stated.
Comparable baseline risk. NNT applies to a population with the control event rate used; for patients at very different baseline risk, the NNT changes and should be recomputed.
Binary outcome. NNT and the Cates plot are for yes/no events. Continuous outcomes need a mean difference and effect size instead.
Common Mistakes
Quoting NNT without a time horizon
An NNT is meaningless without the period over which it applies. Always attach the follow-up time.
Letting a relative reduction stand alone
A large relative risk reduction can hide a tiny absolute benefit. The Cates plot exists precisely to prevent that misreading.
Ignoring the confidence interval
A point NNT hides uncertainty; report the 95% interval, noting that a non-significant effect produces an unusual interval spanning benefit and harm.
Applying one NNT to all patients
Because NNT depends on baseline risk, a single figure does not transfer to populations with very different underlying risk.
Frequently Asked Questions
What is a Cates plot?
It is a 100-person (often smiley-face) diagram showing how many people out of 100 are helped, harmed, or unaffected by a treatment, making the absolute benefit visual.
How is NNT related to risk reduction?
NNT is one divided by the absolute risk reduction; an ARR of 0.10 gives an NNT of 10.
Why show a visual instead of a percentage?
Percentages, especially relative ones, routinely overstate benefit; a 100-person picture conveys the true absolute effect intuitively.
Does the result match R?
Yes. The calculator uses the standard ARR and reciprocal formulas and shows the R command so you can reproduce the NNT and the plot data.
Related Calculators
References
- Veroniki AA, Bender R, Glasziou P, Straus SE, Tricco AC. The number needed to treat in pairwise and network meta-analysis and its graphical representation. J Clin Epidemiol. 2020;122:153–160. PMID 30905696.
- Citrome L, Ketter TA. When does a difference make a difference? Interpretation of number needed to treat, number needed to harm, and likelihood to be helped or harmed. Int J Clin Pract. 2013;67(5):407–411. PMID 23574101.
- Cook RJ, Sackett DL. The number needed to treat: a clinically useful measure of treatment effect. BMJ. 1995;310(6977):452–454.
Need This Analysis Done for Your Manuscript?
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