Relative and absolute risk

Definitions & Key takeaways

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.

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Risk 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.
In others words, what the risk in group A minus the risk in group B. In this case, the risk difference is 0.25 - 0.05 or 0.20.
In other words, going out to fly a kite increased the risk of being struck by lightning by 20% Up until now, the exposure was flying a kite outdoors versus sipping chocolate indoors, and the outcome was being struck by lightning.
But, let’s redefine terms. Now let’s say that all of the 60 lightning strike victims are taken to the hospital and 30 are given a medication while the other 30 are not - so exposure is receiving medication versus not receiving medication, and the outcome is having a heart attack.
Let’s say that out of 30 people that gets medication - only 3 people have a heart attack - so a 10% risk. Whereas out of 30 people that don’t get medication - 18 people have a heart attack - so a 60% risk.
As before, we can calculate a risk ratio of 0.1 / 0.6 = 0.17. Based on the data, the exposure of having the medication protected against the outcome because the risk ratio is less than 1, whereas in the prior example the exposure of flying a kite outside increased the risk of the outcome because the risk ratio was greater than 1.
You can also calculate the risk difference or absolute risk reduction which would be 0.6 - 0.1 = 0.5 or 50%. Finally, you may want to figure out how many lightning strike victims you’d have to treat with the medication to prevent just one person from having a heart attack.
That’s called the number needed to treat, and you would find it by dividing 1 by the absolute risk reduction. In our situation, that’s 1/0.5 which equals 2.
So that means that 2 individuals need to be given the medication to prevent 1 person from having a heart attack. All right, as a quick recap: Absolute risk is the number of event occurrences in a group, divided by the number of individuals in that group.
You can then compare risks between groups by dividing the risk in Group A by the risk in Group B - to give you the relative risk or risk ratio, or you can calculate the risk in group A minus the risk in group B - to give you the risk difference or absolute risk reduction.
Finally, the number needed to treat is 1 divided by the absolute risk reduction.