Preventable fraction among the unexposed
# 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 $PF_{u}=(I_{u}-I_{e})/I_{u}=1-RR$, 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 | CER − EER | 0.3, or 30% |
| Number needed to treat | NNT | 1 / (CER − EER) | 3.33 |
| Relative risk (risk ratio) | RR | EER / CER | 0.25 |
| Relative risk reduction | RRR | (CER − EER) / CER, or 1 − RR | 0.75, or 75% |
| Preventable fraction among the unexposed | PFu | (CER − EER) / CER | 0.75 |
| Odds ratio | OR | (EE / EN) / (CE / CN) | 0.167 |
