# Absolute risk reduction

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In epidemiology, the **absolute risk reduction** is the decrease in risk of a given activity or treatment in relation to a control activity or treatment. It is the inverse of the number needed to treat.^{[1]}

For example, consider a hypothetical drug which reduces the relative risk of colon cancer by 50%. Even without the drug, colon cancer is fairly rare, maybe 1 in 3,000 in every 5 year period. The rate of colon cancer for a 5-year treatment with the drug is therefore 1/6,000, as by treating 6,000 people with the drug, one can expect to reduce the number of colon cancer cases from 2 to 1.

In general, absolute risk reduction is usually computed with respect to two treatments *A* and *B*, with *A* typically a drug and *B* a placebo (in our example above, *A* is a 5-year treatment with the hypothetical drug, and *B* is treatment with placebo, i.e. no treatment). A defined endpoint has to be specified (in our example: the appearance of colon cancer in the 5 year period). If the probabilities *p _{A}* and

*p*of this endpoint under treatments

_{B}*A*and

*B*, respectively, are known, then the absolute risk reduction is computed as (

*p*-

_{B}*p*).

_{A}The inverse of the absolute risk reduction, NNT, is an important measure in pharmacoeconomics. If a clinical endpoint is devastating enough (*e.g.* death, heart attack), drugs with a low absolute risk reduction may still be indicated in particular situations. If the endpoint is minor, health insurers may decline to reimburse drugs with a low absolute risk reduction.

## Worked exampleEdit

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 |
---|---|---|---|---|

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

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

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

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

1 / (CER − EER) | < 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 |

## ReferencesEdit

- ↑ Laupacis A, Sackett DL, Roberts RS. An assessment of clinically useful measures of the consequences of treatment.
*N Engl J Med*1988;318:1728-33. PMID 3374545.

## See alsoEdit

## External linksEdit

- Measures of effect size of an intervention - unmc.edu.

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