# 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 [math]\displaystyle{ (I_u - I_e) / I_u }[/math], where [math]\displaystyle{ I_e }[/math] is the incidence in the exposed group, and [math]\displaystyle{ I_u }[/math] 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 [math]\displaystyle{ (I_e - I_u)/I_u }[/math].^{[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 | |||
---|---|---|---|

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 | AF_{e} |
0.2 |

## See also

- Population Impact Measures
- Vaccine efficacy

## References

- ↑ Porta, Miquel, ed (2014). "Dictionary of Epidemiology - Oxford Reference" (in en). doi:10.1093/acref/9780199976720.001.0001. http://www.oxfordreference.com/view/10.1093/acref/9780199976720.001.0001/acref-9780199976720.
- ↑ Szklo, Moyses; Nieto, F. Javier (2019).
*Epidemiology : beyond the basics*(4th. ed.). Burlington, Massachusetts: Jones & Bartlett Learning. pp. 97. ISBN 9781284116595. OCLC 1019839414. - ↑ J., Rothman, Kenneth (2012).
*Epidemiology : an introduction*(2nd ed.). New York, NY: Oxford University Press. pp. 59. ISBN 9780199754557. OCLC 750986180.

Original source: https://en.wikipedia.org/wiki/Relative risk reduction.
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