Attributable risk is the difference in disease rates between people exposed to a risk factor and people not exposed. The formula is straightforward: subtract the incidence rate in the unexposed group from the incidence rate in the exposed group. The result tells you how many additional cases per unit of population can be attributed to that specific exposure, assuming the relationship is causal.
The Basic Formula
Attributable risk (AR) is calculated as:
AR = Incidence in exposed group − Incidence in unexposed group
Some textbooks call this the “risk difference” instead of attributable risk. They mean the same thing. The BMJ defines it as “the disease rate in exposed persons minus that in people who are unexposed.”
If you know the relative risk instead of raw incidence rates, you can rearrange the formula: AR = incidence in unexposed × (relative risk − 1). This is useful when studies report relative risk but not the raw rates for each group.
Step-by-Step Calculation With a 2×2 Table
Most attributable risk calculations start with a standard 2×2 contingency table. Here’s a worked example from a study on neonatal abstinence syndrome (NAS) in newborns, examining whether maternal drug use during pregnancy increased the risk.
The data looked like this: out of 30 mothers who used drugs, 10 newborns developed NAS. Out of 70 mothers who abstained, 2 newborns developed NAS. Total sample size was 100.
Step 1: Calculate the incidence (risk) in the exposed group. Divide the number of cases among exposed individuals by the total number of exposed individuals: 10 ÷ 30 = 0.33, or 33%.
Step 2: Calculate the incidence in the unexposed group. Divide cases among unexposed individuals by total unexposed: 2 ÷ 70 = 0.029, or about 2.9%.
Step 3: Subtract: 0.33 − 0.029 = 0.304.
The attributable risk is 0.304, or about 30.4%. This means that for every 100 mothers exposed to drug use during pregnancy, roughly 30 additional cases of NAS can be attributed to the drug exposure beyond what you’d expect from the baseline rate.
Population Attributable Risk
Standard attributable risk tells you the excess risk for exposed individuals. Population attributable risk (PAR) answers a different question: how much of the disease burden in the entire population, including both exposed and unexposed people, is due to the exposure?
PAR is the difference between the overall disease rate in the total population and the rate in the unexposed group. If a disease occurs at a rate of 15% across an entire population but only 5% among unexposed people, the PAR is 10 percentage points.
Population Attributable Fraction
The population attributable fraction (PAF) expresses the same concept as a proportion rather than an absolute number. It answers: what percentage of all cases in the population would disappear if the exposure were eliminated?
The most widely used formula is known as Levin’s formula:
PAF = Pe × (RR − 1) ÷ [Pe × (RR − 1) + 1]
Here, Pe is the prevalence of the risk factor in the population and RR is the relative risk. If 40% of a population smokes (Pe = 0.40) and smoking triples the risk of a certain disease (RR = 3), the PAF = 0.40 × 2 ÷ (0.40 × 2 + 1) = 0.80 ÷ 1.80 = 0.44, or 44%. That means 44% of cases in the population could theoretically be prevented by eliminating smoking.
There’s an important caveat with Levin’s formula. It works well when there’s no confounding, but when relative risks have been adjusted for confounders, a different formula should be used: PAF = Pd × (RR − 1) ÷ RR, where Pd is the proportion of cases (not the general population) exposed to the risk factor. When confounding exists, these two formulas give different results, and the second one is considered more accurate.
How Public Health Officials Use These Numbers
The World Health Organization uses PAF estimates to prioritize which risk factors deserve the most resources. The logic is simple: if physical inactivity accounts for a larger fraction of heart disease than any other modifiable risk factor, interventions targeting physical activity will prevent more cases per dollar spent. PAF helps rank competing priorities.
One important limitation: these calculations apply to populations, not individuals. A PAF of 30% for a given risk factor means that 30% of cases across a population are attributable to that exposure. It does not mean any specific person’s illness was 30% caused by the exposure. You cannot point to an individual and say their disease was or wasn’t caused by the risk factor in question.
When Attributable Risk Is More Useful Than Relative Risk
Relative risk tells you how many times more likely exposed people are to develop a disease compared to unexposed people. Attributable risk tells you the actual number of excess cases. These answer fundamentally different questions.
Consider a rare disease with a baseline rate of 1 in 100,000. Even if exposure doubles the risk (relative risk of 2), the attributable risk is only 1 additional case per 100,000 people. Now consider a common disease with a baseline rate of 20%. If exposure increases risk by just 50% (relative risk of 1.5), the attributable risk is 10 additional cases per 100 people. The second scenario has a smaller relative risk but a vastly larger public health impact.
As the BMJ notes, relative risk is less relevant to risk management decisions than attributable risk. When you need to decide where to allocate prevention resources, the absolute number of preventable cases matters more than the ratio.
Assumptions Behind the Calculation
Attributable risk assumes a causal relationship between the exposure and the disease. If the association is driven by confounding, meaning some third factor is responsible for both the exposure and the outcome, then the “excess” cases aren’t truly caused by the exposure and the calculation is misleading.
Establishing causality in epidemiology is rarely straightforward. A dose-response relationship strengthens the case: if more exposure leads to proportionally more disease, that supports a causal link. But the absence of a clean dose-response pattern doesn’t automatically rule causality out. Before interpreting any attributable risk estimate as the true impact of removing an exposure, the underlying evidence for causation needs to be solid. Otherwise, you’re quantifying an association, not a preventable burden.