Relative risk reduction

In epidemiology, the relative risk reduction is a measure calculated by dividing the absolute risk reduction by the control event rate.[1][2][3][4]

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

  Example 1: risk reduction Example 2: risk increase
Experimental group (E) Control group (C) Total (E) (C) Total
Events (E) EE = 15 CE = 100 115 EE = 75 CE = 100 175
Non-events (N) EN = 135 CN = 150 285 EN = 75 CN = 150 225
Total subjects (S) ES = EE + EN = 150 CS = CE + CN = 250 400 ES = 150 CS = 250 400
Event rate (ER) EER = EE / ES = 0.1, or 10% CER = CE / CS = 0.4, or 40% EER = 0.5 (50%) CER = 0.4 (40%)
Equation Variable Abbr. Example 1 Example 2
EER − CER < 0: absolute risk reduction ARR (−)0.3, or (−)30% N/A
> 0: absolute risk increase ARI N/A 0.1, or 10%
(EER − CER) / CER < 0: relative risk reduction RRR (−)0.75, or (−)75% N/A
> 0: relative risk increase RRI N/A 0.25, or 25%
1 / (EER − CER) < 0: number needed to treat NNT (−)3.33 N/A
> 0: number needed to harm NNH N/A 10
EER / CER relative risk RR 0.25 1.25
(EE / EN) / (CE / CN) odds ratio OR 0.167 1.5
EER − CER attributable risk AR (−)0.30, or (−)30% 0.1, or 10%
(RR − 1) / RR attributable risk percent ARP N/A 20%
1 − RR (or 1 − OR) preventive fraction PF 0.75, or 75% N/A

References

  1. ↑ 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. doi:10.1503/cmaj.1021197. PMC 509050. PMID 15313996.
  2. ↑ Relative Risk Reduction
  3. ↑ Relative risk
  4. ↑ Measuring the size of an intervention
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