Relative risk reduction

The relative risk reduction is a measure used in epidemiology. It is calculated by dividing the absolute risk reduction by the control event rate.^[1]^[2]^[3]^[4]

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The relative risk reduction can be more useful than the absolute risk reduction in determining an appropriate treatment plan, because it accounts not only for the effectiveness of a proposed treatment, but also for the relative likelihood of an incident (positive or negative) occurring in the absence of treatment.

Like many other epidemiological measures, the same equations can be used to measure a benefit or a harm (although the signs may need to be adjusted, depending upon how the data was collected.)

Worked example

Abbreviation	Variable	Equation	Value
-	subjects in control group	-	250
-	subjects in experimental group	-	150
-	events in control group	-	100
-	events in experimental group	-	15
CER	control event rate	= events / subjects in control group	0.4, or 40%
EER	experimental event rate	= events / subjects in experimental group	0.1, or 10%
ARR	absolute risk reduction (or increase)	= CER - EER	0.3, or 30%
RRR	relative risk reduction (or increase)	= (CER - EER) / CER	0.75
NNT	number needed to treat/number needed to harm	= 1 / ARR	3.33
OR, RR	odds ratio, relative risk (not really identical, but similar -- see articles for details)	= CER / EER	4

References

^ Barratt A, Wyer P, Hatala R, McGinn T, Dans A, Keitz S, Moyer V, For G (2004). "Tips for learners of evidence-based medicine: 1. Relative risk reduction, absolute risk reduction and number needed to treat". CMAJ 171 (4): 353-8. PMID 15313996.
^ http://evidence.ahc.umn.edu/arr-s5.htm
^ http://www.jr2.ox.ac.uk/bandolier/booth/glossary/Rrisk.html
^ http://gim.unmc.edu/dxtests/Effect1.htm