Attributable risk

Attributable risk (AR) measures the portion of disease incidence in exposed individuals that can be attributed to the exposure itself. The concept was developed by epidemiologists to quantify how much a risk factor contributes to disease occurrence. In management contexts, attributable risk applies to occupational health analysis, workplace safety programs, and policy evaluation. The measure is sometimes called risk difference, excess risk, or attributable proportion.

Fundamental concepts

Definition and interpretation

Attributable risk represents the difference in incidence rates between exposed and unexposed groups. If smoking causes 50 lung cancer cases per 100,000 smokers annually, and only 10 cases occur per 100,000 non-smokers, the attributable risk equals 40 per 100,000. This means 40 cases can be attributed to smoking exposure.

The calculation assumes a causal relationship exists. Statistical association alone does not establish causation. Bradford Hill's 1965 criteria provide a framework for evaluating causality.^[1]

Risk difference formula

The basic attributable risk calculation is:

AR = Incidence in exposed - Incidence in unexposed

Or equivalently:

AR = Ie - Iu

Where Ie represents incidence among exposed individuals and Iu represents incidence among unexposed individuals.

Related measures

Attributable fraction (AF)

The attributable fraction expresses risk as a proportion rather than absolute difference. It answers: what fraction of cases among exposed individuals is due to the exposure?

AF = (Ie - Iu) / Ie

Or in terms of relative risk:

AF = (RR - 1) / RR

A relative risk of 4.0 yields an attributable fraction of 0.75. This indicates 75% of disease cases among exposed persons are attributable to exposure.

Population attributable risk (PAR)

Population attributable risk extends the concept to entire populations. It estimates the disease burden that would be eliminated if exposure were removed completely.

The formula incorporates exposure prevalence:

PAR = Pe × (RR - 1) / [1 + Pe × (RR - 1)]

Where Pe represents the proportion of the population exposed. Levin proposed this formula in 1953 while studying occupational cancers.

Population attributable fraction (PAF)

The PAF expresses population risk as a proportion. Public health officials use it extensively. A PAF of 0.30 for obesity and type 2 diabetes would indicate that 30% of diabetes cases in the population could be prevented by eliminating obesity.

The World Health Organization applies PAF methodology in Global Burden of Disease studies. Their 2019 report estimated tobacco smoking accounted for 8.7 million deaths globally that year.

Calculation methods

From cohort studies

Prospective cohort designs permit direct calculation. Researchers observe disease incidence in exposed and unexposed groups over time. The Framingham Heart Study has generated numerous attributable risk estimates since 1948.

Example calculation:

• Smokers: 150 heart attacks per 10,000 person-years
• Non-smokers: 50 heart attacks per 10,000 person-years
• AR = 150 - 50 = 100 per 10,000 person-years
• AF = 100/150 = 0.67 or 67%

From case-control studies

Case-control studies cannot directly measure incidence. However, the odds ratio approximates relative risk when disease is rare (under 10% cumulative incidence). Miettinen's 1974 formula allows PAF estimation:

PAF = Pc × (OR - 1) / OR

Where Pc is the proportion of cases who were exposed.

Adjusting for confounders

Confounding variables distort attributable risk estimates. Age, socioeconomic status, and co-exposures require adjustment. Stratification methods address this when few confounders exist. Regression modeling handles multiple confounders simultaneously.

Mantel-Haenszel methods provide adjusted estimates with moderate complexity. Logistic regression and Cox proportional hazards models offer more sophisticated approaches.

Applications in risk management

Occupational health

Workplace exposure assessments employ attributable risk routinely. Asbestos exposure studies established that miners' excess mesothelioma risk was almost entirely attributable to occupational exposure. These findings shaped compensation policies and workplace safety regulations.

The National Institute for Occupational Safety and Health (NIOSH) uses PAF to prioritize hazard reduction efforts. Higher PAF exposures receive greater regulatory attention and research funding.

Cost-benefit analysis

Financial management of health programs requires cost-effectiveness data. Attributable risk calculations inform these analyses. If an intervention prevents exposure, expected disease reduction equals PAF multiplied by total disease burden.

Limitations

Attributable risk is not a causal measure by itself. Statistical associations do not prove causation. Confounding, selection bias, and measurement error all threaten validity.

The measure assumes a baseline rate in unexposed groups is "natural" or irreducible. This assumption may not hold when multiple risk factors interact.

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References

• Hill, A.B. (1965). The environment and disease: Association or causation? Proceedings of the Royal Society of Medicine, 58(5), 295-300.
• Levin, M.L. (1953). The occurrence of lung cancer in man. Acta Unio Internationalis Contra Cancrum, 9, 531-541.
• Miettinen, O.S. (1974). Proportion of disease caused or prevented by a given exposure, trait or intervention. American Journal of Epidemiology, 99(5), 325-332.
• Rothman, K.J. & Greenland, S. (2008). Modern Epidemiology. 3rd ed. Lippincott Williams & Wilkins.

Footnotes

[1] Austin Bradford Hill presented his criteria for evaluating causation at the Royal Society of Medicine in January 1965. These nine considerations, including strength of association, consistency, specificity, temporality, and biological gradient, remain foundational in epidemiological research.