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
EER − CER	> 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
(EER − CER) / CER	> 0: relative risk increase	RRI	N/A	0.25, or 25%
1 / (EER − CER)	< 0: number needed to treat	NNT	(−)3.33	N/A
1 / (EER − CER)	> 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 2 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.
↑ For example: Corry, Richard (2016). "Did Climate Change Cause That ?". In Lippert-Rasmussen, Kasper; Brownlee, Kimberley; Coady, David. A Companion to Applied Philosophy. Blackwell Companions to Philosophy. Chichester: Wiley. p. 475. ISBN 9781118869116. Retrieved 2016-10-14. Epidemiologists have long estimated such probabilities using the concept of Fraction of Attributable Risk (FAR), and in 2004, Stott, Stone, and Allen applied this concept to the question of whether climate change was responsible for the heat wave that struck Europe in 2003 [...]. The Fraction of Attributable risk is a way of measuring the contribution a particular factor makes to an outcome.

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