# Number needed to treat

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The number needed to treat (NNT) is a way of summarizing the benefit of an intervention to improve health care.[1][2] The NNT has been proposed to improve quantitative literacy.[1] The calculations are derived from the results of a randomized controlled trial of an intervention.

Two-by-two table for a screening program
Outcome
Present Absent
Experimental (intervention) group Cell A Cell B Total in experimental group
Control group Cell C Cell D Total in control group
Total with outcome Total without outcome

## Calculations

### Event rates

${\displaystyle {\mbox{Experimental event rate}}=\left({\frac {\mbox{Cell A}}{\mbox{Cell A + Cell B}}}\right)}$
${\displaystyle {\mbox{Control event rate}}=\left({\frac {\mbox{Cell C}}{\mbox{Cell C + Cell D}}}\right)}$

### Measures of efficacy

${\displaystyle {\mbox{Absolute risk reduction}}=\left({\mbox{Experimental event rate}}-{\mbox{Control event rate}}\right)}$
${\displaystyle {\mbox{Number need to treat}}=\left({\frac {100}{\mbox{Absolute risk reduction}}}\right)}$

### Deriving the NNT from the odds or risk ratios

The odds ratio may be used to derive the number needed to treat:[3][4]

For odds ratios less than 1:[4]

${\displaystyle NNT={\frac {1-CER*(1-OR)}{CER*(1-OR)*(1-CER)}}{\mbox{, where CER is control event rate and OR is odds ratio}}}$

For odds ratios greater than 1:[4]

${\displaystyle NNT={\frac {1+CER*(OR-1)}{CER*(OR-1)*(1-CER)}}{\mbox{, where CER is control event rate and OR is odds ratio}}}$

The relative risk ratio may be used to derive the number needed to treat:[3][5]

${\displaystyle NNT={\frac {1}{CER*(1-RRR)}}{\mbox{, where CER is control event rate and RRR is relative risk ratio}}}$

The relative risk reduction may be used to derive the number needed to treat:[3][5]

${\displaystyle NNT={\frac {1}{CER*(RRR)}}{\mbox{, where CER is control event rate and RRR is relative risk reduction}}}$

## Variations

Years-needed-to-treat to add 1 year of life is proposed to estimate treatment effects.[6]

## References

1. Laupacis A, Sackett DL, Roberts RS (1988). "An assessment of clinically useful measures of the consequences of treatment". N. Engl. J. Med. 318 (26): 1728–33. PMID 3374545[e]
2. Wen L, Badgett R, Cornell J (2005). "Number needed to treat: a descriptor for weighing therapeutic options". Am J Health Syst Pharm 62 (19): 2031–6. DOI:10.2146/ajhp040558. PMID 16174840. Research Blogging.
3. Furukawa TA, Guyatt GH, Griffith LE (February 2002). "Can we individualize the 'number needed to treat'? An empirical study of summary effect measures in meta-analyses". Int J Epidemiol 31 (1): 72–6. PMID 11914297[e]
4. McQuay HJ, Moore RA (May 1997). "Using numerical results from systematic reviews in clinical practice". Ann. Intern. Med. 126 (9): 712–20. PMID 9139558[e]
5. Chatellier G, Zapletal E, Lemaitre D, Menard J, Degoulet P (February 1996). "The number needed to treat: a clinically useful nomogram in its proper context". BMJ 312 (7028): 426–9. PMID 8601116. PMC 2350093[e]
6. Levy WC, Mozaffarian D, Linker DT, et al. (March 2009). "Years-needed-to-treat to add 1 year of life: a new metric to estimate treatment effects in randomized trials". Eur. J. Heart Fail. 11 (3): 256–63. DOI:10.1093/eurjhf/hfn048. PMID 19164422. Research Blogging.