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Population Attributable Fraction

The proportion of disease cases in an entire population that would not occur if a specific exposure were eliminated, accounting for its prevalence.

Last reviewedDarrin Baines IP Ltd

Concept Architecture

Concept


Theoretically, Population Attributable Fraction (PAF) is an epidemiological measure that quantifies the proportion of all disease cases in a population that can be attributed to a specific exposure. It represents the fraction of disease that could theoretically be prevented if the exposure were eliminated, assuming the observed association is causal and other factors remain unchanged. The concept is founded on causal inference and comparative risk assessment and exists to estimate the potential population-level impact of preventive interventions.

Mathematically, the Population Attributable Fraction combines the prevalence of exposure with its relative risk to estimate the proportion of disease attributable to the exposure within the entire population. Unlike the Attributable Fraction among the exposed, the Population Attributable Fraction incorporates both the strength of association and the frequency of exposure, producing a dimensionless proportion ranging from 0 to 1 or equivalently 0% to 100%.

In practice, Population Attributable Fraction is estimated using data from cohort studies, surveillance systems and national health surveys. It is widely applied in public health, epidemiology and health economic evaluation to estimate preventable disease burden, prioritise risk factor interventions and inform resource allocation and policy development.

Purpose


Used to estimate the proportion of disease in a population attributable to a specific exposure, quantify preventable disease burden, evaluate public health interventions and support health economic and policy decision-making.


Mathematical Formulae

Primary Formula

PAF = [P?(RR ? 1)] / [1 + P?(RR ? 1)]

where:

  • PAF = population attributable fraction
  • P? = prevalence of exposure in the population
  • RR = relative risk

Supporting Formulae

PAF = (I? ? I?) / I?

where:

  • I? = incidence in the total population
  • I? = incidence in the unexposed population

PAF% = {[P?(RR ? 1)] / [1 + P?(RR ? 1)]} ? 100

Related Mathematical Methods

  • Attributable Fraction
  • Population Attributable Risk
  • Relative Risk
  • Attributable Risk
  • Comparative Risk Assessment
  • Burden of Disease Analysis

Example


A population study reports that 30% of adults smoke and smoking doubles the risk of a disease.

Exposure prevalence:

P? = 0.30

Relative Risk:

RR = 2.0

Population Attributable Fraction:

PAF = [0.30 ? (2.0 ? 1)] / [1 + 0.30 ? (2.0 ? 1)]

PAF = 0.30 / 1.30 = 0.231

PAF = 23.1%

Approximately 23% of disease cases within the population are attributable to smoking, assuming the relationship is causal.


Excel Implementation

FunctionExample FormulaHealth Economics Application
Division=(B2*(C2-1))/(1+B2*(C2-1))Calculates the Population Attributable Fraction using exposure prevalence and relative risk.
Percentage=((B2*(C2-1))/(1+B2*(C2-1)))*100Expresses the Population Attributable Fraction as a percentage.
IF=IF(C2>1,(B2*(C2-1))/(1+B2*(C2-1)),0)Calculates PAF only when the exposure increases disease risk.

VBA (Optional)


A VBA macro can automatically calculate Population Attributable Fractions for multiple risk factors and estimate preventable disease burden across different 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.

Library

Publications

1
  • Book

    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.

Frequently Asked Questions (6)

  • What is the population attributable fraction?

    The proportion of disease cases in an entire population that would not occur if a specific exposure were eliminated, accounting for its prevalence.

    Source: Levin 1953

  • What does the population attributable fraction reveal for public health?

    The population attributable fraction is the share of all disease cases in a whole population that would not occur if a harmful exposure were removed, taking into account how common the exposure is. It reveals, for public health, how much disease could in principle be prevented by eliminating an exposure across the population, not just among the exposed. A common exposure with a modest effect can carry a larger population fraction than a rare one with a strong effect, which guides where broad prevention pays off. Population-wide preventable burden is what it shows. Rothman and colleagues (2008) describe this measure.

    Source: Rothman et al. 2008

  • How is the population attributable fraction calculated?

    The population attributable fraction is calculated by combining the relative effect of the exposure on the disease with the prevalence of the exposure in the population, giving the proportion of total cases attributable to the exposure. A common form uses the exposure prevalence and the relative risk to derive the fraction. So the population attributable fraction is calculated from both how strongly the exposure raises risk and how widespread it is, since a harmful but rare exposure accounts for few cases overall, which is why prevalence enters the calculation alongside the strength of the association to give the exposure's impact across the whole population.

    Source: Levin 1953

  • Why is the population attributable fraction important?

    The population attributable fraction is important because it conveys the public health significance of an exposure by showing how much of the total disease burden in a population it accounts for, which depends on both its harmfulness and its prevalence. A modestly harmful but widespread exposure can cause many cases. So the population attributable fraction is important for prioritising public health action, since it indicates where removing an exposure would prevent the most disease across the population, combining the strength of the association with the exposure's frequency, information that relative measures alone do not provide and that guides where prevention efforts would have the greatest impact.

    Source: Levin 1953

  • How does the population attributable fraction differ from the attributable fraction in the exposed?

    The population attributable fraction is the proportion of cases in the whole population, exposed and unexposed together, attributable to the exposure, while the attributable fraction in the exposed is the proportion of cases among the exposed only that is due to the exposure. The population measure also incorporates the exposure's prevalence, so a rare exposure yields a small population fraction even if it strongly affects the exposed. So the two differ in the group considered and in whether prevalence enters, with the population attributable fraction reflecting the exposure's overall impact across the population and the exposed fraction its impact among those exposed.

    Source: Levin 1953

  • What are the limitations of the population attributable fraction?

    The limitations of the population attributable fraction include that it assumes the association is causal, so it misleads if confounding or bias distorts the estimate; that it depends on accurate estimates of both the effect and the exposure prevalence; and that fractions for multiple exposures need not sum to one hundred per cent, since causes overlap. So the population attributable fraction is interpreted with care, relying on the exposure being a genuine cause and on sound estimates, since treating a non-causal association as attributable overstates the preventable burden, and its value as a guide to prevention depends on these assumptions holding in the population considered.

    Source: Levin 1953

Trust Record

Verified by Dr Darrin Baines

British health economist

Professional identity: darrinbaines.org

Verification date: 9 Dec 2025

Content version: 1.0.0

Canonical Identity

Term code
HE-ES-RM-020

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