Concept Architecture
Concept
Theoretically, Attributable Risk (AR) is an epidemiological measure that quantifies the absolute excess risk of disease among an exposed population that is attributable to a specific exposure. It represents the difference in disease occurrence between exposed and unexposed populations and estimates the amount of disease that could theoretically be prevented if the exposure were eliminated, assuming a causal relationship. The concept is founded on causal inference and absolute risk assessment.
Mathematically, Attributable Risk is represented as the arithmetic difference between the incidence of disease in the exposed population and the incidence in the unexposed population. Unlike relative measures such as the Relative Risk, it provides an absolute measure of additional disease burden attributable to the exposure and is expressed in the same units as the underlying risk or incidence.
In practice, Attributable Risk is calculated using incidence data obtained from cohort studies, clinical studies and outbreak investigations where exposure status is known. It is widely applied in epidemiology, health economics and public health to quantify the absolute health benefit that could be achieved through exposure reduction or preventive interventions.
Purpose
Used to quantify the absolute excess disease risk attributable to an exposure, estimate the preventable disease burden, evaluate intervention impact and support health economic and public health decision-making.
Mathematical Formulae
Primary Formula
AR = I? ? I?
where:
- AR = attributable risk
- I? = incidence in the exposed population
- I? = incidence in the unexposed population
Supporting Formulae
AR = Risk? ? Risk?
AR = Incidence? ? Incidence?
Related Mathematical Methods
- Relative Risk
- Attributable Fraction
- Population Attributable Risk
- Population Attributable Fraction
- Risk Difference
- Comparative Risk Assessment
Example
A cohort study reports an incidence of venous thromboembolism of 12% among individuals receiving a treatment and 5% among those not receiving the treatment.
Attributable Risk:
AR = 0.12 ? 0.05 = 0.07
AR = 7%
This indicates that seven additional cases of venous thromboembolism occur per 100 treated individuals that are attributable to the treatment, assuming the association is causal.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Subtraction | =B2-C2 | Calculates the attributable risk from exposed and unexposed incidence. |
| Percentage | =(B2-C2)*100 | Expresses attributable risk as a percentage point difference. |
| IF | =IF(B2>C2,B2-C2,0) | Prevents negative attributable risk values where only excess risk is being reported. |
VBA (Optional)
A VBA macro can automatically calculate attributable risks across multiple exposures, generate comparative risk tables and summarise preventable disease burden for health economic analyses.
Sources
- Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 4th ed.
- Gordis L. Epidemiology. 6th ed.
- Friis RH, Sellers TA. Epidemiology for Public Health Practice. 6th ed.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. 4th ed.
- World Health Organization. Comparative Risk Assessment: Concepts and Methods.
Related Concepts (2)
Library
Publications
1
Statistical Analysis of Cost-Effectiveness Data — Willan & Briggs, 1st Edition ed., 2006 (John Wiley & Sons)
A synthesis of statistical methods for analysing cost-effectiveness data, including net-benefit regression, confidence intervals for the ICER, cost-effectiveness acceptability curves, and covariate adjustment. Part of the Wiley Statistics in Practice series.
BookView source →
Frequently Asked Questions (6)
What is attributable risk?
The difference in risk of an outcome between an exposed group and an unexposed group, the portion attributable to the exposure itself.
Source: Levin 1953
What does attributable risk isolate about an exposure's effect?
Attributable risk is the difference in the risk of an outcome between an exposed group and an unexposed group, isolating the portion of risk that the exposure itself adds. It strips away the background risk everyone faces and shows the excess borne by those exposed, for instance the extra cases of lung cancer per thousand smokers beyond what non-smokers experience. This absolute excess conveys the real burden an exposure imposes, which a ratio cannot. The added risk from exposure is what it captures. Rothman and colleagues (2008) describe this measure.
Source: Rothman et al. 2008
How is attributable risk calculated?
Attributable risk is calculated by subtracting the risk of the outcome in the unexposed group from the risk in the exposed group, giving the excess risk attributable to the exposure. Each risk is the proportion experiencing the outcome in that group. So attributable risk is calculated as the exposed-group risk minus the unexposed-group risk, an absolute difference that quantifies how much extra risk the exposure adds among those exposed, which, unlike the risk ratio, conveys the effect on the scale of the outcome itself and forms the basis for estimating the amount of disease the exposure causes.
Source: Levin 1953
How does attributable risk differ from relative risk?
Attributable risk is the absolute difference in risk between exposed and unexposed groups, showing the excess risk due to the exposure, while relative risk is the ratio of those risks, showing how many times more likely the outcome is with exposure. Attributable risk conveys the actual added risk, whereas relative risk conveys the proportional increase. A large relative risk can correspond to a small attributable risk if the baseline risk is low. So the two differ in scale: attributable risk gives the absolute excess and relative risk the proportional comparison, and both are needed to convey an effect fully.
Source: Rothman, Greenland & Lash 2008
Why is attributable risk important?
Attributable risk is important because it conveys the absolute excess risk caused by an exposure, which indicates the actual impact on those exposed and, when combined with exposure frequency, the disease burden in a population. This matters for public health, where the number of cases an exposure causes guides prevention. So attributable risk matters for judging the real-world impact of an exposure and the potential benefit of removing it, since knowing the absolute excess risk, not only the ratio, is what shows how much disease the exposure produces and how much could be prevented, informing where prevention efforts are most worthwhile.
Source: Levin 1953
How does attributable risk relate to the attributable fraction?
Attributable risk relates to the attributable fraction in that the attributable fraction is the proportion of cases due to the exposure, which can be derived from the attributable risk relative to the total risk. Attributable risk gives the absolute excess risk in the exposed, while the attributable fraction expresses the share of cases attributable to the exposure, and for the exposed group the fraction is the attributable risk divided by the risk in the exposed. So the two are linked measures of an exposure's impact, with attributable risk giving the absolute excess and the attributable fraction the proportion of disease attributable to the exposure.
Source: Levin 1953
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 8 Dec 2025
Content version: 1.0.0
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