Concept Architecture
Concept
Theoretically, Attributable Fraction (AF) is an epidemiological measure that quantifies the proportion of disease among an exposed population that is attributable to a specific exposure. It represents the fraction of disease occurrence that would not have occurred if the exposure had been absent, assuming the observed association is causal. The concept is founded on causal inference and comparative risk assessment and exists to estimate the public health impact of eliminating harmful exposures.
Mathematically, the Attributable Fraction is represented as the proportion of risk among exposed individuals that exceeds the baseline risk in an unexposed population. It is commonly expressed as a function of the relative risk or directly from incidence measures, producing a dimensionless proportion ranging from 0 to 1, or equivalently 0% to 100%.
In practice, the Attributable Fraction is estimated using incidence data from cohort studies, outbreak investigations or clinical studies in which exposure status is known. It is widely applied in epidemiology, health economics and public health to estimate the preventable burden of disease associated with modifiable risk factors and to inform resource allocation and prevention strategies.
Purpose
Used to estimate the proportion of disease among exposed individuals attributable to a specific exposure, quantify the potential benefit of eliminating harmful exposures and support public health and health economic decision-making.
Mathematical Formulae
Primary Formula
AF = (RR ? 1) / RR
where:
- AF = attributable fraction among the exposed
- RR = relative risk
Supporting Formulae
AF = (I? ? I?) / I?
where:
- I? = incidence in the exposed population
- I? = incidence in the unexposed population
AF% = [(RR ? 1) / RR] ? 100
Related Mathematical Methods
- Relative Risk
- Attributable Risk
- Population Attributable Fraction
- Population Attributable Risk
- Risk Difference
- Comparative Risk Assessment
Example
A cohort study reports an incidence of cardiovascular disease of 18% among smokers and 9% among non-smokers.
Relative risk:
RR = 0.18 / 0.09 = 2.0
Attributable Fraction:
AF = (2.0 ? 1) / 2.0 = 0.50
AF = 50%
This indicates that 50% of cardiovascular disease occurring among smokers is attributable to smoking, assuming a causal relationship.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Division | =(B2-1)/B2 | Calculates the attributable fraction from the relative risk. |
| Division | =(C2-D2)/C2 | Calculates the attributable fraction directly from exposed and unexposed incidence. |
| Percentage | =((B2-1)/B2)*100 | Converts the attributable fraction to a percentage for reporting. |
VBA (Optional)
A VBA macro can automatically calculate attributable fractions for multiple exposures, generate confidence intervals and produce epidemiological summary reports.
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 an attributable fraction?
The proportion of disease cases within a population that would not have occurred without a specific exposure, showing its public health impact.
Source: Levin 1953
What share of disease does the attributable fraction assign to an exposure?
The attributable fraction is the proportion of disease cases that would not have happened without a particular exposure, assigning that share of the burden to the exposure. It answers how much of the illness in a group is down to the exposure rather than other causes, which shows the potential gain from removing it. A fraction of, say, a third means eliminating the exposure could in principle prevent a third of cases. The preventable share of disease is what it estimates. Rothman and colleagues (2008) describe this measure.
Source: Rothman et al. 2008
How is an attributable fraction calculated?
An attributable fraction is calculated from the strength of the association between the exposure and the disease and, for a population measure, the prevalence of the exposure. For the exposed group, it relates to how much higher the risk is among the exposed; for the whole population, it also reflects how common the exposure is. So an attributable fraction is calculated by combining the relative effect of the exposure with, for population measures, its prevalence, to give the share of disease cases attributable to the exposure, requiring an estimate of the association and, often, the exposure frequency.
Source: Levin 1953
Why is the attributable fraction useful?
The attributable fraction is useful because it conveys the public health importance of an exposure by showing how much of the disease burden it causes, which depends not only on how strongly the exposure raises risk but on how common it is. A modestly harmful but widespread exposure can account for many cases. So the attributable fraction is useful for prioritising public health action, since it indicates where reducing an exposure would prevent the most disease, combining the strength of the association with the exposure's prevalence, which relative measures alone do not capture, and thereby guiding where prevention efforts would have the greatest impact.
Source: Levin 1953
What is the difference between the attributable fraction in the exposed and the population attributable fraction?
The attributable fraction in the exposed is the proportion of cases among exposed individuals that is due to the exposure, while the population attributable fraction is the proportion of cases in the whole population, exposed and unexposed together, that is due to the exposure. The population measure also depends on how common the exposure is, since a rare exposure, however harmful to those exposed, accounts for few cases overall. So the two differ in the group considered: the exposed fraction concerns the exposed only, and the population fraction the entire population, incorporating exposure prevalence to convey the exposure's overall public health impact.
Source: Levin 1953
What are the limitations of the attributable fraction?
The limitations of the attributable fraction include that it assumes the association reflects a causal effect, so it misleads if confounding or bias distorts the association; that it depends on accurate estimates of both the effect and, for population measures, the exposure prevalence; and that attributable fractions for multiple exposures need not sum to one hundred per cent, since causes overlap. So the attributable fraction is interpreted with care, relying on the association being causal and the estimates being sound, since treating a non-causal or confounded association as attributable overstates preventable disease, and its value as a guide to prevention depends on these assumptions holding.
Source: Rothman, Greenland & Lash 2008
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 8 Dec 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-ES-RM-006
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