What Is Attributable Risk? Definition, Formula, and Example
Attributable Risk, is an important epidemiological measure used to quantify the excess incidence of a disease or health outcome associated with a particular exposure or risk factor.
It helps answer an important question:
How much additional disease occurrence among exposed individuals can be attributed to the exposure?
Attributable risk is widely used in epidemiology, public health, clinical research, occupational health, and environmental studies. It can help researchers evaluate the potential impact of modifiable risk factors and prioritize preventive interventions.
In this article, we will explain attributable risk, attributable risk percentage, population attributable risk, how to calculate these measures, and how to interpret them using a smoking and cardiovascular disease example.
Attributable Risk?
Attributable risk is the difference between the incidence of disease among exposed individuals and the incidence among unexposed individuals.
The formula is: AR=Ie−Iu
Where:
- Ie = incidence among the exposed group
- Iu = incidence among the unexposed group
In other words, attributable risk represents the excess risk associated with the exposure.
For example, suppose researchers investigate whether smoking is associated with cardiovascular disease.
If the incidence of cardiovascular disease is higher among smokers than nonsmokers, the difference between the two incidence rates represents the attributable risk associated with smoking.
Why Is Risk Important?
Relative measures such as relative risk (RR) indicate how strongly an exposure is associated with an outcome.
However, public health decisions also need to consider the absolute excess risk associated with the exposure.
For example:
- Exposure increases risk by 2 times.
- But the absolute increase in risk may be only 1 percentage point.
Attributable risk provides this absolute difference.
This makes AR particularly useful when assessing the potential benefit of eliminating or reducing an exposure.
Risk Formula
For a cohort study, attributable risk is: AR=Ie−Iu
Suppose: Ie=0.152
and: Iu=0.071
Then: AR=0.152−0.071 AR=0.081
Therefore, the attributable risk is 0.081, or 8.1 cases per 100 individuals over the specified follow-up period.
The interpretation should always include the study population and time period.
Risk Percentage
Attributable risk can also be expressed as a percentage.
The attributable risk percentage (AR%) represents the proportion of disease incidence among exposed individuals that is attributable to the exposure.
The formula is: AR%=IeIe−Iu×100
It can also be expressed using relative risk: AR%=RRRR−1×100
where: RR=IuIe
Interpretation
An AR% of 40% means that, under the assumptions required for a causal interpretation, approximately 40% of the disease incidence among the exposed group could be attributed to the exposure.
It does not mean that 40% of the entire population’s disease burden is attributable to the exposure.
Population Risk
Attributable risk focuses on the exposed population.
When researchers want to understand the impact of an exposure on the entire population, they can use population attributable risk (PAR).
The formula is: PAR=Ip−Iu
Where:
- Ip = incidence in the total population
- Iu = incidence among the unexposed population
Population risk percentage is: PAR%=IpIp−Iu×100
PAR% is particularly useful for public health planning because it considers both the strength of the exposure-disease association and how common the exposure is in the population.
Attributable Risk vs Population Risk
| Measure | What It Measures |
|---|---|
| Attributable Risk (AR) | Excess risk among exposed individuals |
| Attributable Risk % | Percentage of risk among exposed individuals attributable to exposure |
| Population Attributable Risk (PAR) | Excess risk in the overall population associated with exposure |
| Population Attributable Risk % | Percentage of population disease burden attributable to exposure |
This distinction is important because an exposure can have a strong association with disease but contribute relatively little to overall population disease burden if very few people are exposed.
Example: Smoking and Cardiovascular Disease
Consider a hypothetical cohort study investigating the relationship between smoking and cardiovascular disease.
The study follows smokers and nonsmokers and records whether they develop cardiovascular disease.
| Group | Developed Disease | Did Not Develop Disease | Total |
|---|---|---|---|
| Smokers | 25 | 140 | 165 |
| Non-Smokers | 52 | 683 | 735 |
Step 1: Calculate Incidence Among Smokers
Ie=16525 Ie=0.1515
Therefore, the incidence among smokers is approximately: 15.15%
Step 2: Calculate Incidence Among Non-Smokers
Iu=73552 Iu=0.07075
Therefore, the incidence among nonsmokers is approximately: 7.08%
Step 3: Calculate Attributable Risk
AR=Ie−Iu AR=0.1515−0.07075 AR=0.08077
Therefore: AR≈8.08%
This means there were approximately 8.08 additional cardiovascular disease cases per 100 individuals associated with smoking, over the study period.
Step 4: Calculate Risk Percentage
AR%=IeIe−Iu×100 AR%=0.15150.1515−0.07075×100 AR%≈53.3%
Thus, approximately 53.3% of the cardiovascular disease incidence among smokers is attributable to smoking, assuming the association is causal and the study design and assumptions support that interpretation.
Step 5: Calculate Relative Risk
Relative risk provides another useful measure: RR=IuIe RR=0.070750.1515 RR≈2.14
This means the observed risk of cardiovascular disease among smokers was approximately 2.14 times the risk among nonsmokers.
The relative and attributable measures provide different information:
- RR ≈ 2.14: compares the risk between the two groups.
- AR ≈ 8.08 percentage points: measures the absolute excess risk.
- AR% ≈ 53.3%: estimates the proportion of disease incidence among exposed individuals attributable to the exposure.
Population Risk
The total population contains: 165+735=900
individuals.
The total number of cardiovascular disease cases is: 25+52=77
Therefore, population incidence is: Ip=90077 Ip=0.08556
or approximately 8.56%.
Population risk is: PAR=Ip−Iu PAR=0.08556−0.07075 PAR=0.01481
Therefore: PAR≈1.48%
The population risk percentage is: PAR%=0.085560.08556−0.07075×100 PAR%≈17.3%
Thus, approximately 17.3% of cardiovascular disease incidence in this hypothetical population could be attributed to smoking, assuming a causal relationship and the other required assumptions hold.
Why AR% and PAR% Are Different
This is one of the most important concepts to understand.
In our example: AR%≈53.3%
but: PAR%≈17.3%
Why?
Because AR% considers only smokers, whereas PAR% considers the entire population.
Smoking is associated with a substantial excess risk among smokers, but smokers represent only part of the population. Therefore, the population-level impact is smaller.
This distinction is particularly important when prioritizing public health interventions.
Risk and Causality
An important caution is that risk should not automatically be interpreted as proof that an exposure causes a disease.
AR can be calculated from an observed association, but a causal interpretation requires appropriate study design and assumptions.
Researchers should consider:
- Confounding
- Selection bias
- Information bias
- Measurement error
- Temporality
- Appropriate study design
- Consistency with existing evidence
For example, if smokers differ from nonsmokers in other important ways, the observed difference in disease incidence may not be entirely due to smoking.
Therefore, statements such as “X% of disease is caused by the exposure” require stronger justification than simply calculating an attributable-risk measure.
Attributable Risk vs Relative Risk
| Feature | Attributable Risk | Relative Risk |
|---|---|---|
| Measures | Absolute excess risk | Relative comparison |
| Formula | Ie−Iu | Ie/Iu |
| Units | Risk/incidence difference | Ratio |
| Useful for | Public health impact | Strength of association |
| Affected by baseline risk | Yes | Yes, but expressed differently |
| Directly communicates excess cases | Yes | No |
Both measures should often be reported together.
For example:
RR = 2.14, while AR = 8.08 percentage points.
This gives a much clearer picture than reporting either measure alone.
Common Mistakes When Interpreting Attributable Risk
Mistake 1: Confusing AR With Relative Risk
AR is an absolute difference, whereas RR is a ratio.
Mistake 2: Confusing AR% With PAR%
AR% describes the attributable proportion among exposed individuals.
PAR% describes the attributable proportion in the total population.
Mistake 3: Assuming Association Means Causation
An attributable risk calculation alone does not establish causality.
Mistake 4: Ignoring the Time Period
Incidence should always be interpreted within the relevant follow-up period.
For example, “8 additional cases per 100 people” is incomplete without knowing whether the measurement represents one year, five years, or another period.
Mistake 5: Ignoring Confounding
A third variable may influence both exposure and disease, creating or exaggerating an observed association.
When Is Attributable Risk Useful?
Attributable risk is particularly useful in:
- Epidemiological studies
- Public health research
- Occupational health
- Environmental health
- Clinical research
- Disease prevention
- Risk-factor analysis
- Health policy planning
It can help answer questions such as:
How much disease could potentially be prevented if a particular exposure were eliminated?
That makes attributable risk particularly valuable for evaluating preventable disease burden.
Conclusion
Attributable risk is an important epidemiological measure that quantifies the excess incidence of disease associated with an exposure.
The basic formula is: AR=Ie−Iu
Attributable risk percentage provides the attributable proportion among exposed individuals: AR%=IeIe−Iu×100
For population-level assessment, researchers can use population attributable risk and population attributable risk percentage: PAR=Ip−Iu PAR%=IpIp−Iu×100
Using the smoking example, the observed attributable risk was approximately 8.08 percentage points, while the attributable risk percentage was approximately 53.3%. At the population level, the population attributable risk percentage was approximately 17.3%.
These measures provide complementary information about the impact of risk factors and can support evidence-based public health decisions. However, their interpretation should always consider study design, confounding, bias, and whether a causal relationship is justified.
