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## Summary

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 $PF_{u}=(I_{u}-I_{e})/I_{u}=1-RR$ , where $I_{e}$ is the incidence in the exposed group, $I_{u}$ is the incidence in the unexposed group, and $RR$ is the relative risk. 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
Quantity 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%
Variable Abbr. Formula Value
Absolute risk reduction ARR CEREER 0.3, or 30%
Number needed to treat NNT 1 / (CEREER) 3.33
Relative risk (risk ratio) RR EER / CER 0.25
Relative risk reduction RRR (CEREER) / CER, or 1 − RR 0.75, or 75%
Preventable fraction among the unexposed PFu (CEREER) / CER 0.75
Odds ratio OR (EE / EN) / (CE / CN) 0.167