# Relative risk reduction

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 ${\displaystyle (I_{u}-I_{e})/I_{u}}$, 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%
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 = 100 115
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%
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