Attributable Risk and Population Attributable Fraction

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Core Idea

Attributable risk (AR) quantifies the absolute excess risk due to exposure: AR = Risk(Exposed) – Risk(Unexposed). Population attributable fraction (PAF) indicates what proportion of disease in the population results from exposure, accounting for both the RR and the prevalence of exposure. AR and PAF are essential for setting public health priorities.

Explainer

You already know from relative risk (RR) that it answers the question: "How many times more likely is disease in the exposed group compared to the unexposed?" But RR, powerful as it is, tells you nothing about the actual burden of disease attributable to that exposure, nor about the potential impact of eliminating it. Attributable risk (AR) — also called the risk difference — closes this gap by subtracting: AR = Risk(Exposed) − Risk(Unexposed). If exposed workers have a 10% five-year risk of lung disease and unexposed workers have a 2% risk, AR = 8%. That 8% represents the absolute excess disease that would not occur if the exposure were eliminated — the directly preventable fraction among those who were exposed.

Consider two exposures with the same RR of 5 but very different baseline risks. Exposure A raises risk from 1% to 5% (AR = 4%). Exposure B raises risk from 20% to 100% (AR = 80%). The RR is identical, but exposure B is responsible for a vastly greater number of cases per 100 exposed people. This is why AR, not RR, is the correct metric for estimating clinical or policy impact: it tells you the absolute number of cases that an intervention could prevent per unit of exposed population.

The population attributable fraction (PAF) takes this logic to the population level, asking: "What proportion of all disease cases in the entire population — exposed and unexposed combined — are attributable to this exposure?" The formula is PAF = Pe(RR − 1) / [1 + Pe(RR − 1)], where Pe is the prevalence of exposure in the population. Alternatively, PAF = (Risk_population − Risk_unexposed) / Risk_population. The PAF depends on both the strength of the association (RR) and how common the exposure is. A moderately risky exposure that affects 60% of the population (e.g., physical inactivity) can have a larger PAF than a highly risky exposure that affects 1% (e.g., a rare occupational toxin), even though the individual risk ratio for the rare exposure is much higher.

This is the core insight for public health prioritization: high PAF exposures are the ones where population-wide interventions yield the greatest disease reduction. Smoking cessation campaigns, physical activity programs, and dietary interventions target exposures with both substantial RR and high prevalence, resulting in large PAF values. When setting policy, comparing PAFs across exposures — not just RRs — allows health authorities to allocate resources where elimination or reduction of exposure would prevent the most disease at the population level.

Practice Questions 5 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIterated Integrals and Fubini's TheoremDouble Integrals in Cartesian CoordinatesDouble Integrals over Rectangular RegionsDouble Integrals in Polar CoordinatesDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsGreen's TheoremSurface Integrals and Flux of Vector FieldsSurface Integrals and Flux of Vector FieldsDivergence Theorem: Flux and OutflowDivergence TheoremElectric FluxGauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesThe Electromagnetic SpectrumBlackbody Radiation and Planck's LawPhotoelectric EffectThe Photon: Light as QuantaCompton ScatteringWave-Particle Dualityde Broglie WavelengthHeisenberg Uncertainty PrincipleWavefunction and the Born RuleThe Schrödinger EquationState Vectors and WavefunctionsQuantum SuperpositionQuantum EntanglementBell Theorem and Bell InequalitiesPostulates of Quantum MechanicsScattering TheoryIntroduction to Scattering TheoryPartial Wave Analysis in ScatteringSpin Angular MomentumElectron Spin and Intrinsic Magnetic MomentStern-Gerlach Experiment: Spin Quantization and MeasurementElectron Diffraction and Matter Wave PropertiesDavisson-Germer Experiment: Crystal Diffraction of ElectronsElectron Diffraction and Matter Wave InterferenceWavefunctions and Probability Density InterpretationQuantum Superposition and Linear Combinations of StatesQuantum Operators and ObservablesCanonical Commutation Relations and UncertaintyHeisenberg Uncertainty Principle and Measurement LimitsTime-Independent Schrödinger Equation and EigenvaluesHydrogen Atom in Quantum MechanicsSpectral Lines and Energy TransitionsSelection Rules for Atomic TransitionsLS and jj Coupling Schemes in Multi-Electron AtomsPauli Exclusion Principle and Antisymmetric WavefunctionsElectron Configuration and the Aufbau PrincipleThe Periodic Table and Atomic Electronic StructureThe Periodic TableElectron ConfigurationPeriodic TrendsIonization EnergyIonic BondingLewis StructuresResonance Structures and Delocalized ElectronsResonance and Formal ChargeMolecular Polarity and Dipole MomentsIntermolecular ForcesStates of Matter and Phase Changes: Melting, Boiling, and SublimationGas Laws and the Ideal Gas EquationGas Stoichiometry and Volume-Volume CalculationsThermochemistry and EnthalpyHeat Capacity and CalorimetryEntropy and Molecular DisorderSpontaneity and ΔGEntropy and Gibbs Free EnergyChemical EquilibriumChemical KineticsRate Law DeterminationEnzyme KineticsCell Cycle Regulation and CheckpointsMitosisCytokinesisMeiosisChromosomal Theory of InheritanceMendelian GeneticsDominance, Recessiveness, and Allelic InteractionsSex-Linked InheritanceNon-Mendelian Inheritance PatternsPopulation Genetics and Hardy-Weinberg EquilibriumNatural SelectionAdaptation and FitnessLife History Strategies: r- and K-SelectionPredator-Prey Dynamics and the Lotka-Volterra ModelCommunity Ecology: Structure and OrganizationMicrobial Ecology OverviewHuman MicrobiomeEmerging Infectious DiseasesInfectious Disease Surveillance SystemsOutbreak InvestigationEpidemic Curve Interpretation and Outbreak AnalysisTemporal Clustering and Seasonality AnalysisInterrupted Time Series DesignNatural Experiments and Quasi-Experimental DesignDifference-in-Differences AnalysisSynthetic Control and Comparative Case StudiesMatching in Case-Control StudiesOdds Ratio and Case-Control Study AnalysisAttributable Risk and Population Attributable Fraction

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