# Attributable risk percent

**Attributable risk percent** (ARP) is a calculation that can be derived from attributable risk.^{[1]}

It gives the portion of cases attributable (and avoidable) to this exposure in relation to all cases.

It can be calculated as (relative risk - 1) / relative risk.^{[1]}

Compare the concept of "fraction of attributable risk" (FAR).^{[2]}

## Worked example

Example 1: risk reduction | Example 2: risk increase | |||||
---|---|---|---|---|---|---|

Experimental group (E) | Control group (C) | Total | (E) | (C) | Total | |

Events (E) | EE = 15 | CE = 100 | 115 | EE = 75 | CE = 100 | 175 |

Non-events (N) | EN = 135 | CN = 150 | 285 | EN = 75 | CN = 150 | 225 |

Total subjects (S) | ES = EE + EN = 150 | CS = CE + CN = 250 | 400 | ES = 150 | CS = 250 | 400 |

Event rate (ER) | EER = EE / ES = 0.1, or 10% | CER = CE / CS = 0.4, or 40% | EER = 0.5 (50%) | CER = 0.4 (40%) |

Equation | Variable | Abbr. | Example 1 | Example 2 |
---|---|---|---|---|

EER − CER | < 0: absolute risk reduction | ARR | (−)0.3, or (−)30% | N/A |

> 0: absolute risk increase | ARI | N/A | 0.1, or 10% | |

(EER − CER) / CER | < 0: relative risk reduction | RRR | (−)0.75, or (−)75% | N/A |

> 0: relative risk increase | RRI | N/A | 0.25, or 25% | |

1 / (EER − CER) | < 0: number needed to treat | NNT | (−)3.33 | N/A |

> 0: number needed to harm | NNH | N/A | 10 | |

EER / CER | relative risk | RR | 0.25 | 1.25 |

(EE / EN) / (CE / CN) | odds ratio | OR | 0.167 | 1.5 |

EER − CER | attributable risk | AR | (−)0.30, or (−)30% | 0.1, or 10% |

(RR − 1) / RR | attributable risk percent | ARP | N/A | 20% |

1 − RR (or 1 − OR) | preventive fraction | PF | 0.75, or 75% | N/A |

## See also

## References

- 1 2 Cole P, MacMahon B (November 1971). "Attributable risk percent in case-control studies".
*Br J Prev Soc Med*.**25**(4): 242–4. PMC 478665. PMID 5160433. - ↑ For example: Corry, Richard (2016). "Did Climate Change Cause That ?". In Lippert-Rasmussen, Kasper; Brownlee, Kimberley; Coady, David.
*A Companion to Applied Philosophy*. Blackwell Companions to Philosophy. Chichester: Wiley. p. 475. ISBN 9781118869116. Retrieved 2016-10-14.Epidemiologists have long estimated such probabilities using the concept of Fraction of Attributable Risk (FAR), and in 2004, Stott, Stone, and Allen applied this concept to the question of whether climate change was responsible for the heat wave that struck Europe in 2003 [...]. The Fraction of Attributable risk is a way of measuring the contribution a particular factor makes to an outcome.

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