# Absolute risk reduction

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In clinical epidemiology and evidence-based medicine, the absolute risk reduction is a measure that compares the frequency of a clinical outcome in group of patients exposed to a factor compared to a control group of patients.[1] This measure should be contrasted with the relative risk reduction.

Most scientific journal articles fail to report absolute measures which may lead to exaggerated perceptions of results.[2]

## Calculations

Two-by-two table for a randomized-controlled trial or cohort study
Outcome
Present Absent
Experimental group Cell A Cell B Total in the experimental group
Control group Cell C Cell D Total in the control group
Total with the outcome Total without the outcome
${\displaystyle {\mbox{Experimental event rate EER)}}=\left({\frac {\mbox{ Cell A}}{{\mbox{Total in the }}experimental{\mbox{ group}}}}\right)}$
${\displaystyle {\mbox{Control event rate (CER)}}=\left({\frac {\mbox{Cell C}}{{\mbox{Total in the }}control{\mbox{ group}}}}\right)}$
${\displaystyle {\mbox{Absolute risk reduction}}=\left({\mbox{CER - EER}}\right)}$

### Confidence intervals

The confidence intervals can be calculated using the method of Daly:[3]

${\displaystyle {\mbox{Standard error}}={\sqrt {\left(R_{1}\times {\frac {1-R_{1}}{N_{1}}}\right)+\left(R_{2}\times {\frac {1-R_{2}}{N_{2}}}\right)}}}$
${\displaystyle {\mbox{Confidence intervals}}={\mbox{Absolute risk reduction}}\pm 1.96\times {\mbox{Standard error}}}$

## References

1. Barratt A, Wyer PC, Hatala R, et al (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. DOI:10.1503/cmaj.1021197. PMID 15313996. Research Blogging.
2. Welch HG et al.Ratio measures in leading medical journals: structured review of accessibility of underlying absolute risks.BMJ. 2006 Dec 16;333(7581):1248. Epub 2006 Oct 23. PMID 17060338
3. Daly LE (1998). "Confidence limits made easy: interval estimation using a substitution method.". Am J Epidemiol 147 (8): 783-90. PMID 9554420.