Attributable risk refers to the difference in incidence rates between people exposed to some risk factor vs. people not exposed to the risk factor.
For example, we might use this metric to understand the difference in cardiovascular disease (the incidence) between smokers (people exposed) and non-smokers (people not exposed).
Typically we calculate attributable risk percentage, which refers to the percentage of an incidence rate that can be attributed to some risk factor.
We can also calculate population attributable risk percentage, which refers to the percentage of an incidence rate in the overall population that can be attributed to some risk factor.
Given the following contingency table:
Attributable risk can be calculated as:
AR = (A/(A+B)) – (C/(C+D))
Attributable risk percentage can be calculated as:
AR % = AR / (A/(A+B)) * 100
Population attributable risk percentage can be calculated as:
PAR % = [ ((A+C) / N) – (C/(C+D)) ] / ((A+C) / N) * 100
where N is the sum of all cells in the contingency table.
The following example shows how to calculate each of these metrics.
Example: Calculating Attributable Risk & Other Metrics
The following table shows the number of people who developed cardiovascular disease based on their smoking history:
The attributable risk of smoking can be calculated as:
- AR = (A/(A+B)) – (C/(C+D))
- AR = (25/(25+140)) – (52/(52+683))
- AR = .08077
The attributable risk percentage of smoking can be calculated as:
- AR % = AR / (A/(A+B)) * 100
- AR % = .08077 / (25/(25+140)) * 100
- AR % = 53.31%
This means 53.31% of incidence of cardiovascular disease among smokers is attributable to their smoking.
The population attributable risk percentage of smoking can be calculated as:
- PAR % = [ ((A+C)/N) – (C/(C+D)) ] / ((A+C) / N) * 100
- PAR % = [ ((25+52)/900) – (52/(52+683)) ] / ((25+52) / 900) * 100
- PAR % = 17.31%
This means 17.31% of incidence of cardiovascular disease in the population is attributable to smoking.
In other words, if smoking were eliminated in the population then we would expect to see a 17.31% reduction in cases of cardiovascular disease.
Bonus: Attributable Risk Calculator
Feel free to use the Attributable Risk Calculator to automatically calculate the attributable risk, attributable risk percentage, and population attributable risk percentage for any 2×2 contingency table.
How can we cite your work? I mean what is your full name?
hi. how can i calculate combined AR for more than one exposure?
Can the population attributable mortality percentage be calculated using this formula? Could you recommend an article or publication that demonstrates the scientific validity and correctness of this formula?
Yes, the population attributable mortality percentage can be calculated using the Population Attributable Fraction (PAF) formula. The PAF estimates the proportion of incidents in the population that are attributable to a specific risk factor. This measure is widely used in epidemiology to assess the public health impact of exposures.
The PAF can be calculated using the following formula:
\[ \text{PAF} = \frac{P_e \times (RR – 1)}{1 + P_e \times (RR – 1)} \]
Where:
– \( P_e \) is the proportion of the population exposed to the risk factor.
– \( RR \) is the relative risk of mortality associated with the exposure.
This formula allows for the estimation of the percentage of mortality in the population that can be attributed to the exposure. For example, if a certain exposure has a high relative risk and is prevalent in the population, the PAF will be higher, indicating a greater impact of that exposure on population mortality.
For a comprehensive understanding and validation of this formula, you may refer to the article “Population attributable fraction” published in *The BMJ*. This publication discusses the application and interpretation of the PAF in assessing the public health impact of exposures.
Additionally, the World Health Organization (WHO) provides detailed explanations and applications of the PAF in estimating the burden of disease due to various risk factors. Their guidelines offer insights into the methodology and scientific validity of using the PAF in public health assessments.
These resources should provide you with a thorough understanding of the PAF formula and its application in calculating the population attributable mortality percentage.
Thank you 🙂
You are very welcome Alpay!
i am confused .. what is the difference of attributable risk and attributable risk percent??
Hi Noelle…Attributable risk and attributable risk percent are closely related, but they answer slightly different questions.
Attributable risk tells you the actual extra amount of disease or outcome that can be linked to the exposure. In other words, it is the difference in risk between the exposed group and the unexposed group.
For example, say:
Risk of disease in smokers = 30%
Risk of disease in non-smokers = 10%
The attributable risk is:
30% – 10% = 20%
So, smoking is associated with an extra 20 cases per 100 people compared with not smoking.
Attributable risk percent takes that same idea and expresses it as a percentage of the risk among the exposed group. It tells you what proportion of the disease in the exposed group is due to the exposure.
Using the same example:
Attributable risk percent = 20% / 30% × 100 = 66.7%
So about 67% of the disease among smokers could be attributed to smoking.
A simple way to remember it is:
Attributable risk = the extra risk caused by the exposure.
Attributable risk percent = the percent of risk among exposed people that is due to the exposure.