# Relative risk ratio

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In clinical epidemiology and evidence-based medicine, the relative risk ratio or more simply the relative risk, is a measure of the likelihood 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 absolute risk reduction.

## 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
${\displaystyle {\mbox{Experimental event rate EER)}}=\left({\frac {\mbox{ Cell A}}{{\mbox{Total in the }}experimental{\mbox{ group}}}}\right)}$
${\displaystyle {\mbox{Control event rate (CER)}}=\left({\frac {\mbox{Cell C}}{{\mbox{Total in the }}control{\mbox{ group}}}}\right)}$
${\displaystyle {\mbox{Relative risk}}=\left({\frac {\mbox{EER}}{\mbox{CER}}}\right)}$

Note that the relative risk ratio is that same as 1 - the relative risk reduction.

The relative risk ratio may be used to derive the number needed to treat:[2][3]

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

## 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. 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]
3. 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]