# Attributable risk percent

Attributable risk percent (ARP) is a calculation that can be derived from attributable risk.[1]

It gives the portion of cases attributable (and avoidable) to this exposure in relation to all cases.

It can be calculated as (relative risk - 1) / relative risk.[1]

Compare the concept of "fraction of attributable risk" (FAR).[2]

## Worked example

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
EER CER < 0: absolute risk reduction ARR ()0.3, or ()30% N/A
> 0: absolute risk increase ARI N/A 0.1, or 10%
(EER CER) / CER < 0: relative risk reduction RRR ()0.75, or ()75% N/A
> 0: relative risk increase RRI N/A 0.25, or 25%
1 / (EER CER) < 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