Preventive fraction

Preventive fraction (PF), also called preventable fraction, is a calculation that can be derived from relative risk or odds ratio.

It may be used when an exposure seems to reduce the risk (in opposition to attributable risk percent), and gives the percentage of cases that can be prevented if a population is exposed to an intervention, compared to an unexposed population.

It can be calculated as ( 1 − relative risk ) or as ( 1 − odds ratio ).^[1]

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

References

↑ Aschengrau, Ann; Seage, George R. (2003). Essentials of epidemiology in public health. Epidemiology Series. Jones & Bartlett Publishers. pp. 65–66. ISBN 978-0-7637-2537-2.

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