Number needed to treat

The number needed to treat (NNT) is a way of summarizing the benefit of an intervention to improve health care. The NNT has been proposed to improve quantitative literacy. 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

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

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

Measures of efficacy

${\mbox{Absolute risk reduction}}=\left({\mbox{Experimental event rate}}-{\mbox{Control event rate}}\right)$

${\mbox{Number need to treat}}=\left({\frac {100}{\mbox{Absolute risk reduction}}}\right)$

Deriving the NNT from the odds or risk ratios

The odds ratio may be used to derive the number needed to treat:

For odds ratios less than 1:

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

For odds ratios greater than 1:

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

The relative risk ratio may be used to derive the number needed to treat:

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

The relative risk reduction may be used to derive the number needed to treat:

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

Variations

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

See also

• Randomized controlled trial
• Absolute risk reduction
• Relative risk reduction

External links

Tables of NNTs for various treatments:

• Bandolier
• University of Toronto Centre for Evidence-Based Medicine