# 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]

## 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 | AF_{e} | 0.2 |

## References

- "Dictionary of Epidemiology - Oxford Reference". doi:10.1093/acref/9780199976720.001.0001. 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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