Relative risk reduction

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 , where is the incidence in the exposed group, and 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 .[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]

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).

Numerical examples

Risk reduction
Example of risk reduction
Quantity 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% —
Variable Abbr. Formula Value
Absolute risk reduction ARR CER − EER 0.3, or 30%
Number needed to treat NNT 1 / (CER − EER) 3.33
Relative risk (risk ratio) RR EER / CER 0.25
Relative risk reduction RRR (CER − EER) / CER, or 1 − RR 0.75, or 75%
Preventable fraction among the unexposed PFu (CER − EER) / CER 0.75
Odds ratio OR (EE / EN) / (CE / CN) 0.167

Risk increase
Example of risk increase
Quantity 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% —
Variable Abbr. Formula Value
Absolute risk increase ARI EER − CER 0.1, or 10%
Number needed to harm NNH 1 / (EER − CER) 10
Relative risk (risk ratio) RR EER / CER 1.25
Relative risk increase RRI (EER − CER) / CER, or RR − 1 0.25, or 25%
Attributable fraction among the exposed AFe (EER − CER) / EER 0.2
Odds ratio OR (EE / EN) / (CE / CN) 1.5

See also

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