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## What is Attributable Risk?

**Attributable Risk(AR) **(sometimes called* Attributable Proportion* or* Attributable Fraction*) is a measure of the prevalence of a condition or disease. Given a group of people exposed to a risk, it’s the fraction who develop a disease or condition. Put another way, AR is the cases that would be eliminated if the exposure were also eliminated.

Often, attributable risk is given as a percentage (called the **attributable risk percent or AR%**). For example, lung cancer has many causes, including smoking cigarettes and exposure to indoor radon. One study showed that the AR% for cigarette smoking and lung cancer was 85%. That means 85% of lung cancers are caused by cigarette smoking. Another study showed that the AR% for radon gas exposure and lung cancer is between 3% and 20%, depending on factors like sex and smoking status.

## Formulas

The **most common formula** is:

Where:

- RD = Risk Difference (also called Absolute Risk Reduction)
- CI
_{e}= Cumulative Incidence in Exposed group - CI
_{u}= Cumulative Incidence in Unexposed group

## Alternate Formula

If you don’t know the cumulative incidence rates, but do know the risk or rate ratio, you can use this **alternate formula:**

- RR = Relative Risk

## Formula for Contingency Tables

If you have a contingency table like the one above (note the placement of the exposed/unexposed cases and controls), you can calculate the AR with the following formula:

**AR = [a/(a+b)] – [c/(c+d)]**

## Population Attributable Risk

The **population attributable risk (PAR)** (also called the population attributable fraction) is similar, except instead of a group of people (a sample) it applies to the entire population (e.g. “everyone in the United States”). The formula is:

**PAR = P**

_{e}(RR_{e}-1) / [1 + P_{e}(RR_{e-1})]**Where**:

- P
_{e}= Proportion of exposed people, - RR
_{e}= Relative risk because of the exposure.

Like AR, PAR can also be expressed as a percentage, called **population attributable risk percent** (PAR%).

## Population Prevented Fraction

If the fraction is actually preventative (e.g. lives will be saved, or conditions will be prevented), then it’s called a** population prevented fraction (PF)** or **preventive fraction**. The formula is:

**P**

_{e}(1-RR)Although similar to the AR, the PF is more commonly used to measure the impact of public health interventions, where the AR is more often used in epidemiologic studies as a measure of disease prevalence.

## Attributable Number

The attributable number is a count of how many cases are attributable to a specific exposure. The formula is:

**AN = N**

_{e}(I_{e}= I_{u})**Where:**

- N
_{e}= number of people exposed. - I
_{e}= number of cases among exposed persons. - I
_{u}= number of cases among non-exposed persons.

**References:**

Chyou P et al. “A prospective study of the AR of cancer due to cigarette smoking.” Am J Public Health. 1992 January; 82(1): 37–40.

Kim S et al. “AR of lung cancer deaths due to indoor radon exposure”. Ann Occup Environ Med. 2016; 28: 8.

Last JM, ed., et al. A Dictionary of Epidemiology. 4th ed. New York: Oxford University Press; 2000.

Rockhill B et al. “Use and misuse of population attributable fractions”. Am J Public Health 1998;38:15-19.