Attributable risk

In epidemiology, attributable risk is the difference in rate of a condition between an exposed population and an unexposed population. Attributable risk is mostly calculated in cohort studies, where individuals are assembled on exposure status and followed over a period of time. Investigators count the occurrence of the diseases. The cohort is then subdivided by the level of exposure and diseases frequency is compared subgroups. One is considered exposed and another unexposed. The formula commonly used in Epidemiology books for Attributable risk is Ie - Iu = AR, where Ie = Incidence in exposed and Iu = incidence in unexposed. We can calculate AR percent once we calculate AR. The formula for that is Ie - Iu/Ie *100. Note: that (Ie) is simply dividing the number of people who get the diseases by the total number who are exposed (N-diseased/N-exposed = Ie) similarly, the Iu is dividing the number of people who get the disease by the total number who are not exposed (N-disease/N-unexposed).

The concept was first proposed by Levin in 1953.

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. 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.

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

It is defined as:

$EF = \frac{N_e - N_n}{N_e}$

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 etiologic cases are excess 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. (Larger than etiologic fraction)

Uses

Population attributable fraction guides policymakers in planning public health interventions. 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 were left unchanged, the number of lung cancer cases would decrease. This decrease is the population attributable risk for lung cancer from radon.

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:

$\text{Combined PAR} = 1 - (1-\text{PAR}_1)(1-\text{PAR}_2)(1-\text{PAR}_3)\cdots. \,$

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

EE is the number of events in the experimental group. CE is the number of events in the control group. EN is the number of non-events in the experimental group. CN is the number of non-events in the control group. ES is the total number of Events and Non-events in the Experimental group. CS is the toal number of events and non-events in the control group. EER is the proportion or fraction of events over the total in the experimental group. CER is the proportion or fraction of events over the total in the control group.