Examples Of Calculating Attributable Risk

Calculate the proportion of disease cases in exposed individuals that can be attributed to the exposure

Comprehensive Guide to Calculating Attributable Risk with Real-World Examples

Attributable risk (AR), also known as risk difference, is a fundamental concept in epidemiology that quantifies the proportion of disease cases in exposed individuals that can be directly attributed to the exposure. This metric helps public health professionals understand the potential impact of eliminating a specific risk factor on disease burden.

Understanding the Core Concepts

The attributable risk formula compares the incidence of disease between exposed and unexposed groups:

• Incidence in Exposed (I_e): The proportion of exposed individuals who develop the disease
• Incidence in Unexposed (I_u): The proportion of unexposed individuals who develop the disease
• Attributable Risk (AR) = I_e – I_u: The absolute difference in disease risk
• Attributable Risk Percent (AR%) = (AR / I_e) × 100: The proportion of cases in exposed individuals attributable to the exposure

Step-by-Step Calculation Process

1. Identify your groups: Clearly define your exposed and unexposed populations based on the risk factor being studied
2. Measure incidence rates: Calculate the proportion of individuals who develop the disease in each group
3. Compute the difference: Subtract the unexposed incidence from the exposed incidence
4. Calculate the percentage: Determine what proportion of the exposed group’s risk is due to the exposure
5. Determine confidence intervals: Calculate the range within which the true AR likely falls (typically 95% CI)

Real-World Examples of Attributable Risk Calculations

Example 1: Smoking and Lung Cancer

In a landmark study of British doctors:

• Incidence in smokers (exposed): 140 cases per 100,000 person-years
• Incidence in non-smokers (unexposed): 10 cases per 100,000 person-years
• AR = 140 – 10 = 130 cases per 100,000 person-years
• AR% = (130/140) × 100 = 92.9%

Interpretation: 92.9% of lung cancer cases in smokers are attributable to smoking. If smoking were eliminated, we would expect 130 fewer cases per 100,000 person-years.

Example 2: Occupational Asbestos Exposure and Mesothelioma

From a cohort study of construction workers:

• Incidence in asbestos-exposed workers: 45 cases per 100,000
• Incidence in unexposed workers: 2 cases per 100,000
• AR = 45 – 2 = 43 cases per 100,000
• AR% = (43/45) × 100 = 95.6%

Example 3: Alcohol Consumption and Liver Cirrhosis

Based on a population-based case-control study:

• Incidence in heavy drinkers: 300 cases per 100,000
• Incidence in non-drinkers: 50 cases per 100,000
• AR = 300 – 50 = 250 cases per 100,000
• AR% = (250/300) × 100 = 83.3%

Comparing Attributable Risk to Other Epidemiological Measures

Measure	Formula	Interpretation	Example (Smoking & Lung Cancer)
Attributable Risk (AR)	Ie – Iu	Absolute difference in risk	130 per 100,000
Attributable Risk Percent (AR%)	(AR / Ie) × 100	Proportion of exposed cases due to exposure	92.9%
Relative Risk (RR)	Ie / Iu	How many times more likely exposed are to develop disease	14
Odds Ratio (OR)	(a/c) / (b/d)	Odds of exposure among cases vs controls	~14 (when disease is rare)
Population Attributable Risk (PAR)	(It – Iu) / It	Proportion of all cases in population due to exposure	Varies by smoking prevalence

Common Applications in Public Health

• Tobacco control policies: Demonstrating the burden of smoking-related diseases to justify regulation
• Occupational health: Identifying workplace hazards that contribute significantly to disease
• Vaccine development: Quantifying the preventable disease burden from infectious agents
• Environmental health: Assessing the impact of pollutants on population health
• Health economics: Calculating cost savings from risk factor reduction

Limitations and Considerations

While attributable risk is a powerful metric, it has important limitations:

1. Causality assumptions: AR assumes the exposure-disease relationship is causal, which requires careful study design
2. Confounding factors: Other risk factors may influence the observed association
3. Population specificity: AR values may vary between different populations
4. Exposure measurement: Accurate classification of exposure status is critical
5. Rare diseases: May produce unstable estimates with wide confidence intervals

Advanced Concepts: Confidence Intervals and Statistical Significance

The confidence interval for attributable risk helps assess the precision of the estimate. The formula for the 95% CI is:

CI = AR ± (1.96 × SE)

Where SE (standard error) is calculated as:

SE = √[I_e(1-I_e)/n_e + I_u(1-I_u)/n_u]

A confidence interval that doesn’t include zero suggests the attributable risk is statistically significant.

Study	Exposure	Disease	AR (per 100,000)	AR%	95% CI
Framingham Heart Study	Hypertension	Stroke	250	62.5%	210-290
Nurses’ Health Study	Oral Contraceptives	Venous Thromboembolism	30	50%	20-40
Physicians’ Health Study	Aspirin Use	Myocardial Infarction	-180	-47.4% (preventive)	-220 to -140
WHI Study	HRT	Breast Cancer	8	26.7%	2-14

Practical Tips for Accurate Calculations

1. Use high-quality data: Ensure your incidence rates come from well-designed studies with minimal bias
2. Standardize time periods: Compare rates over the same follow-up duration
3. Adjust for confounders: Use statistical methods to control for other risk factors
4. Consider the exposure definition: Clearly define what constitutes “exposed” vs “unexposed”
5. Calculate confidence intervals: Always report the precision of your estimates
6. Validate with multiple studies: Look for consistency across different populations

Authoritative Resources on Attributable Risk

For more in-depth information about calculating and interpreting attributable risk, consult these authoritative sources:

• Centers for Disease Control and Prevention (CDC) – Principles of Epidemiology: Comprehensive introduction to epidemiological measures including attributable risk
• Boston University School of Public Health – Measures of Association: Detailed explanation of attributable risk and related measures
• National Center for Biotechnology Information (NCBI) – Epidemiologic Measures: Technical reference for epidemiological calculations

Frequently Asked Questions

How is attributable risk different from relative risk?

Attributable risk measures the absolute difference in disease rates between exposed and unexposed groups, while relative risk compares the ratio of these rates. AR answers “how many more cases occur due to exposure?” while RR answers “how many times more likely are exposed individuals to develop the disease?”

Can attributable risk be negative?

Yes, a negative AR indicates that the exposure is protective against the disease (the exposed group has lower incidence than the unexposed group). This would be reported as a preventive fraction rather than a risk.

How is population attributable risk different from attributable risk?

Population attributable risk (PAR) considers the entire population (both exposed and unexposed) and estimates what proportion of all cases in the population could be prevented if the exposure were eliminated. AR focuses only on the exposed group.

What confidence level should I use for my calculations?

95% confidence intervals are the most commonly used in epidemiological studies, but you might use 90% for exploratory analyses or 99% when you need to be more conservative about type I errors.

How do I interpret a wide confidence interval?

A wide confidence interval indicates less precision in your estimate, typically due to small sample sizes or rare outcomes. This suggests the true attributable risk could reasonably fall anywhere within that range.