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Relative Risk for Diseases: Formula & Calculation

Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

The relative risk is important to determine risk factors for particular diseases. In this lesson we will define the relative risk and learn how to calculate it.

Relative Risk Defined

You've probably heard that smoking increases your risk of developing lung cancer. Or that women who drink two or more alcoholic beverages a day have a 50% increased risk of developing breast cancer. Statements such as these are utilizing relative risk.

Relative risk is the comparison of one group developing a particular disease to another group. This is calculated by taking the risk of the group of interest divided by the comparison group.

Relative risk formula

Using the Formula

Types of groups can include certain activities such as smoking or drinking. In this case the primary group are those who smoke or drink. While the 'other' group or 'unexposed' group would be those who do not smoke or drink. It may also be positive attributes such as exercising or eating five or more servings of vegetables a day.

These groups can also be attributes such as race, gender, or weight. If we want to know the relative risk of Hispanics developing a particular disease then we can either compare this group to everyone else (non-Hispanic), or we can compare the risk to another specific group such as African-Americans.

We can compare to typically unrelated groups, for example people who smoke to people who are underweight. These types of comparisons can give us insights into what is really causing a specific relative risk, but we need to be careful; there could be too many other unseen factors that haven't been taken into account.

Example Calculations

Now let's look at some examples. Let's say you were studying complications associated with measles, in particular, developing pneumonia. You wanted to know if there was a higher relative risk of children under the age of 5 developing pneumonia than those older than 5.

From a sample of 100 people who had measles you determined that 9% of children under the age of 5 developed pneumonia and 10% of those over the age of 5 developed pneumonia. The primary, or exposed, group are children under the age of 5, while the unexposed or other group is over the age of 5. So the probability for the primary group is 0.09 and the comparison group probability is 0.1.

0.09/0.1 = 0.9

The relative risk of children under the age of 5 developing pneumonia is 0.9. We can turn this into a percentage by taking 1 - 0.9 = 0.1. So there is a 10% reduced risk for children under the age of 5 developing pneumonia from measles.

As a researcher you find these results surprising, you would expect children under the age of 5 to have a higher rate of pneumonia. This is where the determination of groups becomes important. You realize that there are two different groups that have a higher rate of pneumonia, those under the age of 5 and those over the age of 20. So let's do this again. This time we will do two different calculations.

Measles is a disease that can have deadly complications
Child with measles

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