# 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 ${\displaystyle (I_{u}-I_{e})/I_{u}}$, 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, term relative risk increase (RRI) is used, and computed as ${\displaystyle (I_{e}-I_{u})/I_{u}}$.[1][2] If the direction of risk change is not assumed, a term relative effect is used and computed as ${\displaystyle (I_{e}-I_{u})/I_{u}}$.[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%
EquationVariableAbbr.Value
CER - EERabsolute risk reduction ARR0.3, or 30%
(CER - EER) / CER relative risk reduction RRR 0.75, or 75%
1 / (CER EER)number needed to treatNNT3.33
EER / CERrisk ratioRR0.25
(EE / EN) / (CE / CN)odds ratioOR0.167
(CER - EER) / CERpreventable fraction among the unexposedPFu0.75

### Risk increase

Example of risk increase
Experimental group (E) Control group (C) Total
Events (E) EE = 75 CE = 100 115
Non-events (N) EN = 75 CN = 150 285
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%
EquationVariableAbbr.Value
EER CER absolute risk increaseARI0.1, or 10%
(EER CER) / CER relative risk increaseRRI0.25, or 25%
1 / (EER CER) number needed to harmNNH10
EER / CERrisk ratioRR1.25
(EE / EN) / (CE / CN)odds ratioOR1.5
(EER CER) / EERattributable fraction among the exposedAFe0.2