# Medicine: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 $\displaystyle{ PF_u = (I_u - I_e)/I_u = 1 - RR }$, where $\displaystyle{ I_e }$ is the incidence in the exposed group, $\displaystyle{ I_u }$ is the incidence in the unexposed group, and $\displaystyle{ RR }$ 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
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