Relative risk reduction

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Illustration of two groups: one exposed to a treatment, and one unexposed. Exposed group has smaller risk of adverse outcome (RRR = 0.5).
The group exposed to treatment (left) has the risk of an adverse outcome (black) reduced by 50% (RRR = 0.5) compared to the unexposed group (right).

In epidemiology, the relative risk reduction (RRR) or efficacy is the relative decrease in the risk of an adverse event in the exposed group compared to an unexposed group. It is computed as [math]\displaystyle{ (I_u - I_e) / I_u }[/math], where [math]\displaystyle{ I_e }[/math] is the incidence in the exposed group, and [math]\displaystyle{ I_u }[/math] is the incidence in the unexposed group. If the risk of an adverse event is increased by the exposure rather than decreased, the term relative risk increase (RRI) is used, and it is computed as [math]\displaystyle{ (I_e - I_u)/I_u }[/math].[1][2] If the direction of risk change is not assumed, the term relative effect is used, and it is computed in the same way as relative risk increase.[3]

Numerical examples

Risk reduction

  Example of risk reduction
Experimental group (E) Control group (C) Total
Events (E) EE = 15 CE = 100 115
Non-events (N) EN = 135 CN = 150 285
Total subjects (S) ES = EE + EN = 150 CS = CE + CN = 250 400
Event rate (ER) EER = EE / ES = 0.1, or 10% CER = CE / CS = 0.4, or 40%
Equation Variable Abbr. Value
CER - EER absolute risk reduction ARR 0.3, or 30%
(CER - EER) / CER relative risk reduction RRR 0.75, or 75%
1 / (CER − EER) number needed to treat NNT 3.33
EER / CER risk ratio RR 0.25
(EE / EN) / (CE / CN) odds ratio OR 0.167
(CER - EER) / CER preventable fraction among the unexposed PFu 0.75

Risk increase

  Example of risk increase
Experimental group (E) Control group (C) Total
Events (E) EE = 75 CE = 100 175
Non-events (N) EN = 75 CN = 150 225
Total subjects (S) ES = EE + EN = 150 CS = CE + CN = 250 400
Event rate (ER) EER = EE / ES = 0.5, or 50% CER = CE / CS = 0.4, or 40%
Equation Variable Abbr. Value
EER − CER absolute risk increase ARI 0.1, or 10%
(EER − CER) / CER relative risk increase RRI 0.25, or 25%
1 / (EER − CER) number needed to harm NNH 10
EER / CER risk ratio RR 1.25
(EE / EN) / (CE / CN) odds ratio OR 1.5
(EER − CER) / EER attributable fraction among the exposed AFe 0.2

See also

References

  1. ↑ Porta, Miquel, ed (2014). "A Dictionary of Epidemiology" (in en). Dictionary of Epidemiology - Oxford Reference. Oxford University Press. doi:10.1093/acref/9780199976720.001.0001. ISBN 9780199976720. http://www.oxfordreference.com/view/10.1093/acref/9780199976720.001.0001/acref-9780199976720. Retrieved 2018-05-09. 
  2. ↑ Szklo, Moyses; Nieto, F. Javier (2019). Epidemiology : beyond the basics (4th. ed.). Burlington, Massachusetts: Jones & Bartlett Learning. pp. 97. ISBN 9781284116595. OCLC 1019839414. 
  3. ↑ J., Rothman, Kenneth (2012). Epidemiology : an introduction (2nd ed.). New York, NY: Oxford University Press. pp. 59. ISBN 9780199754557. OCLC 750986180. 



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