Concept Architecture
Concept
Theoretically, Population Attributable Risk (PAR) is an epidemiological measure that quantifies the absolute excess incidence of disease within an entire population that is attributable to a specific exposure. It represents the difference between the observed disease incidence in the total population and the incidence that would be expected if the exposure were absent, assuming the association is causal. The concept is founded on causal inference and population risk assessment and exists to estimate the absolute burden of disease that could potentially be prevented through exposure elimination.
Mathematically, Population Attributable Risk is represented as the absolute difference between the incidence in the total population and the incidence in the unexposed population. Unlike Population Attributable Fraction, which expresses a proportion, Population Attributable Risk is expressed in the same units as the underlying incidence or risk and quantifies the absolute excess disease burden attributable to the exposure.
In practice, Population Attributable Risk is estimated using population incidence data together with exposure-specific incidence obtained from cohort studies, surveillance systems or registries. It is widely applied in epidemiology, public health and health economic evaluation to estimate preventable disease burden, assess intervention impact and support healthcare resource allocation.
Purpose
Used to quantify the absolute burden of disease attributable to an exposure within a population, estimate preventable disease incidence, evaluate public health interventions and support health economic and policy decision-making.
Mathematical Formulae
Primary Formula
PAR = I? ? I?
where:
- PAR = population attributable risk
- I? = incidence in the total population
- I? = incidence in the unexposed population
Supporting Formulae
PAR = P? ? (I? ? I?)
where:
- P? = prevalence of exposure in the population
- I? = incidence in the exposed population
- I? = incidence in the unexposed population
I? = P? ? I? + (1 ? P?) ? I?
Related Mathematical Methods
- Population Attributable Fraction
- Attributable Risk
- Attributable Fraction
- Relative Risk
- Risk Difference
- Comparative Risk Assessment
- Burden of Disease Analysis
Example
A population has an overall incidence of cardiovascular disease of 15 cases per 1,000 individuals per year. Among individuals who are not exposed to a specific risk factor, the incidence is 9 cases per 1,000 individuals per year.
Population Attributable Risk:
PAR = 15 ? 9 = 6 cases per 1,000 population per year
This indicates that six additional cases of cardiovascular disease per 1,000 individuals each year are attributable to the exposure, assuming a causal relationship.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Subtraction | =B2-C2 | Calculates Population Attributable Risk from overall and unexposed incidence. |
| Multiplication | =D2*(B2-C2) | Calculates Population Attributable Risk using exposure prevalence and attributable risk. |
| IF | =IF(B2>C2,B2-C2,0) | Calculates PAR only when the exposure increases disease incidence. |
| ROUND | =ROUND(B2-C2,3) | Formats Population Attributable Risk for epidemiological reporting. |
VBA (Optional)
A VBA macro can automatically calculate Population Attributable Risks for multiple exposures and generate comparative estimates of preventable disease burden across populations.
Sources
- Rothman KJ, Greenland S, Lash TL. Modern Epidemiology. 4th ed.
- Rockhill B, Newman B, Weinberg C. Use and misuse of population attributable fractions. American Journal of Public Health. 1998;88(1):15?19.
- Gordis L. Epidemiology. 6th ed.
- World Health Organization. Comparative Risk Assessment: Concepts and Methods.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. 4th ed.
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 population attributable risk?
The reduction in disease incidence within a population that would result from eliminating a harmful exposure entirely, expressed as an absolute rate.
Source: Levin 1953
What reduction does population attributable risk describe?
Population attributable risk describes the drop in disease incidence across an entire population that would follow from removing a harmful exposure completely, expressed as an absolute rate. Unlike attributable risk, which concerns only the exposed group, it dilutes that excess by the share of the population actually exposed, giving the real reduction a population could expect. This absolute, population-level figure helps quantify the public health gain from tackling an exposure. The population-wide fall in cases is what it measures. Rothman and colleagues (2008) describe this measure.
Source: Rothman et al. 2008
How is population attributable risk calculated?
Population attributable risk is calculated as the difference between the incidence or risk of the disease in the total population and the incidence or risk in the unexposed group, giving the excess frequency in the population attributable to the exposure. It therefore reflects both the excess risk from the exposure and how common the exposure is. So population attributable risk is calculated from the disease frequency in the whole population minus that in the unexposed, an absolute difference that captures the exposure's overall impact, incorporating its prevalence, since a rare exposure contributes little to the population's disease frequency even if it strongly affects the exposed.
Source: Levin 1953
How does population attributable risk differ from attributable risk?
Population attributable risk is the excess disease frequency in the whole population attributable to an exposure, incorporating the exposure's prevalence, while attributable risk, the risk difference, is the excess risk among the exposed only. The population measure reflects the impact across everyone, so a rare exposure yields a small population attributable risk despite a large effect on the exposed. So the two differ in whether they concern the whole population or the exposed group, with population attributable risk conveying the exposure's absolute public health impact across the population and attributable risk the excess risk borne by those actually exposed.
Source: Levin 1953
Why is population attributable risk useful?
Population attributable risk is useful because it expresses, in absolute terms, how much disease in a population is due to an exposure and how much could be prevented by removing it, which is directly relevant to public health planning and to estimating the burden that interventions could avert. So population attributable risk is useful for judging the absolute public health impact of an exposure and the potential gain from eliminating it, since it accounts for both the strength of the association and the prevalence of the exposure, giving decision makers a measure of the actual disease burden attributable to the exposure across the population.
Source: Levin 1953
What are the limitations of population attributable risk?
The limitations of population attributable risk include that it assumes the association is causal and that eliminating the exposure would remove the attributable disease, so it misleads if the association is confounded; that it depends on accurate estimates of the effect and the exposure prevalence; and that it may not be achievable if exposures cannot be fully eliminated. So population attributable risk is interpreted with attention to causality and to the feasibility of removing the exposure, since it represents a theoretical maximum reduction that assumes a causal relationship and complete elimination, and its usefulness for planning depends on these assumptions and on sound estimates of the inputs.
Source: Levin 1953
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British health economist
Professional identity: darrinbaines.org
Verification date: 9 Dec 2025
Content version: 1.0.0
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