How To Calculate Population Attributable Risk Example

Calculate the proportion of disease cases in a population that can be attributed to a specific risk factor

Comprehensive Guide: How to Calculate Population Attributable Risk (PAR) with Examples

Population Attributable Risk (PAR) is a crucial epidemiological measure that quantifies the proportion of disease cases in a population that can be attributed to a specific risk factor. This metric helps public health professionals prioritize interventions by identifying which risk factors contribute most significantly to disease burden at the population level.

Key Concept

PAR answers the question: “What proportion of disease cases would be prevented if we could completely eliminate this risk factor from the population?”

Understanding the Core Components

1. Incidence in Exposed Group (I_e): The rate of disease among those exposed to the risk factor
2. Incidence in Unexposed Group (I_u): The rate of disease among those not exposed to the risk factor (baseline risk)
3. Prevalence of Exposure (P): The proportion of the population exposed to the risk factor
4. Relative Risk (RR): The ratio of incidence in exposed vs. unexposed groups (I_e/I_u)

The Population Attributable Risk Formula

The fundamental PAR formula combines these components:

PAR Formula

PAR = P × (RR – 1) / RR

Where RR = I_e/I_u

Alternatively: PAR = P × (I_e – I_u) / I_e

PAR percentage is simply PAR multiplied by 100.

Step-by-Step Calculation Example

Let’s work through a practical example using smoking as a risk factor for lung cancer:

1. Determine incidence rates:
   • Incidence in smokers (I_e): 150 cases per 1,000 people = 0.15
   • Incidence in non-smokers (I_u): 10 cases per 1,000 people = 0.01
2. Determine exposure prevalence:
   • 30% of the population smokes (P = 0.30)
3. Calculate Relative Risk:
   • RR = I_e/I_u = 0.15/0.01 = 15
4. Apply the PAR formula:
   • PAR = 0.30 × (15 – 1)/15 = 0.30 × (14/15) = 0.30 × 0.933 = 0.28
   • PAR% = 0.28 × 100 = 28%

Interpretation: 28% of all lung cancer cases in this population could be prevented if smoking were completely eliminated.

Alternative PAR Formula Using Risk Difference

Some epidemiologists prefer this equivalent formula:

Alternative Formula

PAR = P × (I_e – I_u) / I_total

Where I_total is the overall incidence in the population

Using our smoking example:

• I_total = (P × I_e) + ((1-P) × I_u) = (0.30 × 0.15) + (0.70 × 0.01) = 0.045 + 0.007 = 0.052
• PAR = 0.30 × (0.15 – 0.01) / 0.052 = 0.30 × 0.14 / 0.052 ≈ 0.28 (same result)

Real-World Applications of PAR

Risk Factor	Disease	Reported PAR (%)	Study Population
Smoking	Lung cancer	80-90%	U.S. and Europe
Obesity	Type 2 diabetes	40-60%	North America
Physical inactivity	Coronary heart disease	12-25%	Global
Alcohol consumption	Liver cirrhosis	50-70%	European countries
Unsafe sex	HIV infection	95%+	Sub-Saharan Africa

Common Misinterpretations to Avoid

1. PAR ≠ Individual risk: PAR measures population impact, not individual risk. A high PAR doesn’t mean the risk factor is strong for individuals, just that it’s common in the population.
2. Causality assumption: PAR assumes the association is causal. Always verify the risk factor actually causes the disease.
3. Time sensitivity: PAR values change as exposure prevalence or disease incidence changes over time.
4. Confounding factors: PAR calculations may be confounded by other risk factors if not properly adjusted.

Advanced Considerations

Adjusted PAR

When dealing with multiple risk factors, epidemiologists use adjusted PAR calculations:

Adjusted PAR = P × (RR_adj – 1) / RR_adj

Where RR_adj is the relative risk adjusted for confounding variables through methods like:

• Stratified analysis
• Multivariable regression (most common)
• Propensity score matching

PAR for Multiple Risk Factors

When multiple risk factors contribute to the same disease, the combined PAR can be calculated using:

Combined PAR = 1 – ∏(1 – PAR_i)

Where PAR_i represents the PAR for each individual risk factor.

Practical Limitations of PAR

Limitation	Impact	Potential Solution
Requires accurate exposure data	Under/overestimation of PAR	Use high-quality surveillance systems
Assumes causality	May attribute cases incorrectly	Verify with experimental studies
Static measurement	Doesn’t account for changing exposures	Regularly update calculations
Difficult for rare exposures	Unstable estimates	Use larger study populations
Ignores effect modification	May not apply to all subgroups	Calculate stratum-specific PARs

Case Study: PAR for Obesity and Diabetes

A 2018 study published in the New England Journal of Medicine calculated the PAR for obesity as a risk factor for type 2 diabetes in the U.S. population:

• Incidence in obese (BMI ≥30): 12.5 cases per 1,000 person-years (I_e = 0.0125)
• Incidence in normal weight (BMI 18.5-24.9): 3.2 cases per 1,000 person-years (I_u = 0.0032)
• Prevalence of obesity: 39.8% (P = 0.398)
• Calculated PAR:
  • RR = 0.0125/0.0032 ≈ 3.91
  • PAR = 0.398 × (3.91 – 1)/3.91 ≈ 0.398 × 0.744 ≈ 0.296 or 29.6%

Public health implication: Nearly 30% of type 2 diabetes cases in the U.S. could be prevented by eliminating obesity as a risk factor.

Comparing PAR with Other Epidemiological Measures

Measure	Formula	Interpretation	Key Difference from PAR
Relative Risk (RR)	Ie/Iu	How many times more likely exposed are to get disease	Measures strength of association, not population impact
Attributable Risk (AR)	Ie – Iu	Excess risk due to exposure in exposed individuals	Individual-level measure; PAR is population-level
Odds Ratio (OR)	(a/c)/(b/d)	Odds of exposure among cases vs. controls	Case-control study measure; approximates RR for rare diseases
Population Attributable Fraction (PAF)	Same as PAR	Same as PAR	Different terminology, same concept
Number Needed to Treat (NNT)	1/AR	How many need treatment to prevent one case	Clinical measure; PAR is for population planning

When to Use PAR in Public Health Decision Making

PAR is particularly valuable in these scenarios:

1. Resource allocation: Helps decide where to focus prevention efforts for maximum population impact
2. Policy development: Supports arguments for regulations targeting high-PAR risk factors
3. Program evaluation: Measures potential impact of existing prevention programs
4. Health communication: Quantifies the burden of modifiable risk factors for public messaging
5. Cost-effectiveness analysis: Input for economic models of prevention strategies

Calculating PAR from Odds Ratios in Case-Control Studies

When working with case-control study data, you can estimate PAR using the odds ratio (OR) as an approximation of RR (valid when disease is rare):

PAR ≈ P × (OR – 1) / OR

Example from a case-control study of Helicobacter pylori and gastric cancer:

• OR = 6.0
• Prevalence of H. pylori infection (P) = 0.50
• PAR ≈ 0.50 × (6.0 – 1)/6.0 ≈ 0.50 × 0.833 ≈ 0.417 or 41.7%

Important Note

This approximation becomes less accurate as disease prevalence increases above 10%. For common diseases, use RR from cohort studies when possible.

Software Tools for PAR Calculation

While our calculator provides manual calculations, these professional tools also compute PAR:

• R packages:
  • epiR – Comprehensive epidemiological functions
  • popEpi – Specialized for population attributable fractions
• Stata commands:
  • punaf – Population attributable fractions
  • punafcc – For case-control studies
• SAS macros:
  • %PAR – Available from SAS user communities
• Online calculators:
  • CDC Epi Info™ (includes PAR functions)
  • OpenEpi.com (free web-based calculator)

Ethical Considerations in PAR Application

When using PAR to guide public health actions, consider these ethical dimensions:

1. Stigma potential: High PAR for sensitive behaviors (e.g., drug use) may increase stigma if not communicated carefully
2. Individual blame: Population measures shouldn’t be used to blame individuals for their health status
3. Structural factors: PAR calculations may overlook social determinants that influence exposure prevalence
4. Cultural sensitivity: Some risk factors may have different cultural meanings across populations
5. Equity impact: Interventions based on PAR should be evaluated for differential effects on vulnerable groups

Future Directions in PAR Methodology

Emerging approaches are enhancing traditional PAR calculations:

• Dynamic PAR models: Incorporate time-varying exposures and lag effects
• Counterfactual approaches: Use causal inference methods to estimate “what if” scenarios
• Genetic PAR: Quantify attributable risk from genetic factors alongside environmental exposures
• Machine learning: Identify complex exposure patterns that contribute to disease
• Geospatial PAR: Calculate localized PAR values for targeted interventions

Authoritative Resources on Population Attributable Risk

For additional technical guidance, consult these expert sources:

Centers for Disease Control and Prevention (CDC) – Principles of Epidemiology: Measures of Association University of Florida – Attributable Risk Module National Library of Medicine – Population Attributable Fraction