Relative risk reduction
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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]}
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 exampleEdit
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 
Nonevents (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 

CER − EER  < 0: absolute risk reduction  ARR  (−)0.3, or (−)30%  N/A 
> 0: absolute risk increase  ARI  N/A  0.1, or 10%  
(CER − EER) / CER  < 0: relative risk reduction  RRR  (−)0.75, or (−)75%  N/A 
> 0: relative risk increase  RRI  N/A  0.25, or 25%  
1 / (CER − EER)  < 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 
ReferencesEdit
 ↑ Barratt A, Wyer P, Hatala R, McGinn T, Dans A, Keitz S, Moyer V, For G (2004). Tips for learners of evidencebased medicine: 1. Relative risk reduction, absolute risk reduction and number needed to treat. CMAJ 171 (4): 353–8.
 ↑ Relative Risk Reduction
 ↑ Relative risk
 ↑ Measuring the size of an intervention
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