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 ${\displaystyle (I_{u}-I_{e})/I_{u))$, where ${\displaystyle I_{e))$ is the incidence in the exposed group, and ${\displaystyle I_{u))$ 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 ${\displaystyle (I_{e}-I_{u})/I_{u))$.[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
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 CEREER 0.3, or 30%
Number needed to treat NNT 1 / (CEREER) 3.33
Relative risk (risk ratio) RR EER / CER 0.25
Relative risk reduction RRR (CEREER) / CER, or 1 − RR 0.75, or 75%
Preventable fraction among the unexposed PFu (CEREER) / 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 EERCER 0.1, or 10%
Number needed to harm NNH 1 / (EERCER) 10
Relative risk (risk ratio) RR EER / CER 1.25
Relative risk increase RRI (EERCER) / CER, or RR − 1 0.25, or 25%
Attributable fraction among the exposed AFe (EERCER) / EER 0.2
Odds ratio OR (EE / EN) / (CE / CN) 1.5

3. ^ J., Rothman, Kenneth (2012). Epidemiology : an introduction (2nd ed.). New York, NY: Oxford University Press. p. 59. ISBN 9780199754557. OCLC 750986180.`((cite book))`: CS1 maint: multiple names: authors list (link)