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]}
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 |
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 | AF_{e} | (EER − CER) / EER | 0.2 |
Odds ratio | OR | (EE / EN) / (CE / CN) | 1.5 |