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, term relative risk increase (RRI) is used, and computed as .[1][2] If the direction of risk change is not assumed, a term relative effect is used and computed as .[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
| 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 | 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% | |
| 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 |
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See also
- Population Impact Measures
- Vaccine efficacy
References
- Porta, Miquel, ed. (2014). "Dictionary of Epidemiology - Oxford Reference". doi:10.1093/acref/9780199976720.001.0001. ISBN 9780199976720. Retrieved 2018-05-09.
- Szklo, Moyses; Nieto, F. Javier (2019). Epidemiology : beyond the basics (4th. ed.). Burlington, Massachusetts: Jones & Bartlett Learning. p. 97. ISBN 9781284116595. OCLC 1019839414.
- 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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