# Attributable risk percent

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

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.

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

## 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

1. Cole P, MacMahon B (November 1971). "Attributable risk percent in case-control studies". Br J Prev Soc Med. 25 (4): 242–4. PMC 478665 . PMID 5160433.