# Relative and absolute risk

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### Relative and absolute risk

To find the "number needed to treat," the equation is

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#### Content Reviewers:

Rishi Desai, MD, MPH#### Contributors:

Tanner Marshall, MS, Evan Debevec-McKenneyRisk is the probability of an event occurring - for example let’s say that we’re talking about the risk of being struck by lightning.

You might want to know - your chance of being struck by lightning - that would be the absolute risk. You might also want to know your chance of getting struck by lightning if you’re sipping hot chocolate under a blanket in your bed, versus your chance if you’re out flying a kite in a storm.

Now, let’s say that the kite-fliers are at higher risk then the chocolate-sippers of getting struck by lightning.

Well - you may want to know how many times higher is the risk - the risk ratio, or how much higher is the risk - the risk difference.

So let’s use some numbers to make this concrete. Say we have 400 people in the lightening study - imagine the incentives you’d need to get folks to sign up for that study.

So, let’s say that 200 of the people are sent out to fly a kite in a terrible storm, while the other 200 are sent indoors with a cup of hot chocolate and a blanket.

Now let’s say that 50 of the kite-fliers are struck by lighting.

Based on that data, the absolute risk of being struck by lightning if you’re out flying a kite is the number of lightning strikes, which is 50, divided by the number of people in the group, which is 200.

So, 50/200 or 0.25 is answer - a 25% risk.

Absolute risk = Number of events in a group / individuals in that group

While all that is happening, let’s say that 10 unfortunate chocolate-sipper also gets struck by lightning while sitting under a blanket.

Based on that data, the absolute risk of being struck by lightning if you’re sipping chocolate inside is the number of lightning strikes, which is 10, divided by the number of people in the group, which is 200.

So, 10/200 or 0.05 is answer - a 5% risk.

If you want to compare these two risks, you could say that the relative risk or risk ratio, is the risk in one group, let’s call that group A, divided by the risk in another group, let’s call that group B.

In this case that means 0.25 / 0.05 or a relative risk of 5.

Put differently, When you go outside to fly a kite, your risk of getting hit by lightning is 5 times the risk of getting hit by lightning if you just stayed in and drank that hot chocolate!

Risk ratio or relative risk = Risk in group A / Risk in group B

Now, you may want to know what the risk difference is in absolute terms, this is also called the absolute risk reduction.