In epidemiology, attributable risk is the difference in rate of a condition between an exposed population and an unexposed population.^[1]

The concept was first proposed by Levin in 1953.^[2][3]

Contents 1 Diversity of interpretation 2 Uses 3 Combined PAR 4 Worked example 5 References 6 External links

[edit] Diversity of interpretation

There is some variation in how the term is used.

The term population attributable risk (PAR) has been described as the reduction in incidence that would be observed if the population were entirely unexposed, compared with its current (actual) exposure pattern.^[4] In this context, the comparison is to the existing pattern of exposure, not the absence of exposure.

There is some ambiguity in terminology. Population attributable risk is often simply called "attributable risk" (AR), and the latter term is most often associated with the above PAR definition. However, some epidemiologists use "attributable risk" when referring to the excess risk, also called the risk difference or rate difference.

Greenland and Robins distinguished between excess fraction and etiologic fraction in 1988.^[5]

• Etiologic fraction is the proportion of the cases that the exposure had played a causal role in its development.

It is defined as:^[6]

Where:

EF = Etiologic fraction

N_e = Number of exposed individuals in a population that develop the disease

N_n = Number of unexposed individuals in the same population that develop the disease.

• Excess fraction, however, is the proportion of the cases that occurs among exposed population that is in excess in comparison with the unexposed.

All excess cases are etiologic cases, but not vice versa. From the standpoint of both law and biology it is important to measure the etiology fraction. In most epidemiological studies, PAR measures only the excess fraction. (Smaller than etiologic fraction)

[edit] Uses

Population attributable fraction estimates can help guide policymakers in planning public health interventions.^[7] Population attributable fraction (PAF), population attributable risk proportion, and population attributable risk percent are all the same as PAR.

As a hypothetical example, if all the radon in a community were removed, and everything else was left unchanged, the number of lung cancer cases would fall. This fall is the population attributable risk for lung cancer from radon.

[edit] Combined PAR

The PAR for a combination of risk factors is the proportion of the disease that can be attributed to any of the risk factors studied. The combined PAR is usually lower than the sum of individual PARs since a diseased case can simultaneously be attributed to more than one risk factor and so be counted twice.

When there is no multiplicative interaction (no departure from multiplicative scale), combined PAR can be manually calculated by this formula:

[edit] Worked example

	Example 1: risk reduction			Example 2: risk increase
	Experimental group (E)	Control group (C)	Total	(E)	(C)
Events (E)	EE = 15	CE = 100	115	EE = 75	CE = 100
Non-events (N)	EN = 135	CN = 150	285	EN = 75	CN = 150
Total subjects (S)	ES = EE + EN = 150	CS = CE + CN = 250	400	ES = 150	CS = 250
Event rate (ER)	EER = EE / ES = 0.1, or 10%	CER = CE / CS = 0.4, or 40%	N/A	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
EE / (EE + CE) − EN / (EN + CN)	attributable risk	AR	(−)0.34, or (−)34%	0.095, or 9.5%
(RR − 1) / RR	attributable risk percent	ARP	N/A	20%
1 − RR (or 1 − OR)	preventive fraction	PF	0.75, or 75%	N/A

[edit] References

[edit] External links

• Population Attributable Risk Calculator (http://www.urmc.rochester.edu/smd/cpm/mach/pubs.html)

v • d • e Biomedical research: Study designs / Design of experiments Overview Clinical trial · Clinical trial protocol · Clinical trial management · Academic clinical trials · Study design Controlled study (EBM I to II-1; A to B) Randomized controlled trial (Blind experiment, Open-label trial) Observational study (EBM II-2 to II-3; B to C) Cross-sectional study vs. Longitudinal study Cohort study (Retrospective cohort study, Prospective cohort study) Case-control study (Nested case-control study) Case series · Case study/Case report Epidemiology/ methods occurrence: Incidence (Cumulative incidence) · Prevalence (Point prevalence, Period prevalence) association: absolute (Absolute risk reduction, Attributable risk, Attributable risk percent) · relative (Relative risk, Odds ratio, Hazard ratio) other: Virulence · Infectivity · Mortality rate · Morbidity · Case fatality · Specificity and sensitivity · Likelihood-ratio test Trial/test types In vitro/In vivo · Animal testing · Animal testing on non-human primates · First-in-man study · Multicenter trial · Seeding trial · Vaccine trial Analysis of clinical trials Risk-benefit analysis Interpretation of results Selection bias · Correlation does not imply causation · Null result Category • Glossary • List of topics