# Number needed to treat

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The **number needed to treat** (NNT) is an epidemiological measure used in assessing the effectiveness of a health-care intervention, typically a treatment with medication. The NNT is the number of patients who need to be treated in order to prevent one additional bad outcome (i.e. to reduce the expected number of cases of a defined endpoint by one). It is defined as the inverse of the absolute risk reduction. It was described in 1988.^{[1]}

## DerivationEdit

In general, NNT is computed with respect to two treatments *A* and *B*, with *A* typically a drug and *B* a placebo (e.g., *A* might be a 5-year treatment with a drug, while *B* is no treatment). A defined endpoint has to be specified (e.g., the appearance of colon cancer in a five-year period). If the probabilities *p _{A}* and

*p*of this endpoint under treatments

_{B}*A*and

*B*, respectively, are known, then the NNT is computed as 1/(

*p*–

_{B}*p*).

_{A}## RelevanceEdit

The NNT is an important measure in pharmacoeconomics. If a clinical endpoint is devastating enough (*e.g.* death, heart attack), drugs with a high NNT may still be indicated in particular situations. If the endpoint is minor, health insurers may decline to reimburse drugs with a high NNT.

## Example: statins for primary preventionEdit

For example, the ASCOT-LLA manufacturer-sponsored study addressed the benefit of atorvastatin 10 mg (a cholesterol-lowering drug) in patients with hypertension (high blood pressure) but no previous cardiovascular disease (primary prevention). The trial ran for 3.3 years, and during this period the relative risk of a "primary event" (heart attack) was reduced by 36% (relative risk reduction, RRR). The *absolute* risk reduction (ARR), however, was much smaller, because the study group did not have a very high rate of cardiovascular events over the study period: 2.67% in the control group, compared to 1.65% in the treatment group.^{[2]} Taking atorvastatin for 3.3 years, therefore, would lead to an ARR of only 1.02% (2.67% minus 1.65%). The number needed to treat to prevent one cardiovascular event would then be 99.7 for 3.3 years.^{[3]} ^{[4]}

## 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 |

The relative risk (odds ratio) is .25 in the example above. It is always 1-relative risk reduction, or vice versa.

## See alsoEdit

- Number needed to harm - the converse for side-effects

## ReferencesEdit

- ↑ Laupacis A, Sackett DL, Roberts RS (1988). An assessment of clinically useful measures of the consequences of treatment.
*N. Engl. J. Med.***318**(26): 1728–33. - ↑ Sever PS, Dahlöf B, Poulter NR,
*et al*(2003). Prevention of coronary and stroke events with atorvastatin in hypertensive patients who have average or lower-than-average cholesterol concentrations, in the Anglo-Scandinavian Cardiac Outcomes Trial--Lipid Lowering Arm (ASCOT-LLA): a multicentre randomised controlled trial.*Lancet***361**(9364): 1149–58. - ↑ Bandolier - Statin effectiveness: ASCOT update. URL accessed on 2008-03-31.
- ↑ includeonly>"Do Cholesterol Drugs Do Any Good?",
*Business Week*. Retrieved on 2008-03-31. “'That means in a large clinical study, 3% of patients taking a sugar pill or placebo had a heart attack compared to 2% of patients taking Lipitor.' ... The numbers in that sentence mean that for every 100 people in the trial, which lasted 3 1/3 years, three people on placebos and two people on Lipitor had heart attacks.... One fewer heart attack per 100 people. So to spare one person a heart attack, 100 people had to take Lipitor for more than three years. The other 99 got no measurable benefit. Or to put it in terms of a little-known but useful statistic, the number needed to treat (or NNT) for one person to benefit is 100.”

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