# Preventable fraction among the unexposed

In epidemiology, **preventable fraction among the unexposed** (PFu), is the proportion of incidents in the unexposed group that could be prevented by exposure. It is calculated as , where is the incidence in the exposed group, is the incidence in the unexposed group, and is the relative risk.[1][2] It is a synonym of the relative risk reduction.

It is used when an exposure reduces the risk, as opposed to increasing it, in which case its symmetrical notion is attributable fraction among the exposed.

## Numerical example

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 |

## References

- Aschengrau, Ann; Seage, George R. (2014).
*Essentials of epidemiology in public health*(3rd ed.). Burlington, MA: Jones & Bartlett Learning. p. 67. ISBN 9781449657338. OCLC 826123155. - Rothman, Kenneth J.; Greenland, Sander; Lash, Timothy L. (2012).
*Modern epidemiology*(3rd ed.). Philadelphia: Lippincott Williams & Wilkins. ISBN 9780781755641. OCLC 169455558.

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