# Relative and absolute risk

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## Biostatistics and epidemiology

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### Relative and absolute risk

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A researcher is studying a new vaccine for respiratory syncytial virus (RSV) in premature infants and is comparing it with the current standard of care treatment. 8% of infants who received the standard of care treatment developed symptomatic RSV, and 2% of infants who received the new vaccine developed symptomatic RSV. Which of the following is the relative risk reduction attributable to this new vaccine?

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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.

Risk is the probability of an event occurring, for example, the risk of being struck by lightning. Absolute risk refers to the actual probability of an outcome occurring in a specific group regardless of any other factors. In this case, it would be the chance of being struck by lightning. Relative risk on the other hand, compares the risk of an outcome between exposed and unexposed groups. In this case, it would be the risk of being struck by lightning when flying a kite in a storm, versus when sitting still in a house.