### A: It turns out, how we describe risks REALLY matters and helps us better understand our healthcare choices.

Read below for a review of how risk is calculated and communicated (and can be used for trickery!). The TLDR version: Absolute risk reduction is the number you actually want to know most of the time. Buckle up fellow math nerds and live the statistics dream!

Risk is the likelihood of something bad happening, like getting a disease. The goal of medical treatment is to reduce that risk. Risk reduction is often presented in 2 different ways: absolute risk reduction and relative risk reduction.

Let’s start with absolute risk reduction. Absolute risk (AR) is the risk of something happening. For example, a person has a 7 in 10 chance of tripping on the stairs walking if they wear high heels.

The absolute risk would be 70% (don’t judge me, I’m clumsy!). Now, let’s make a change and put on comfortable, practical shoes. Now that person has a 6 in 10 chance of tripping on the stairs, or a 60% absolute risk (Turns out, I’m still clumsy). The absolute risk reduction is the difference between those two risks, or 70%-60% = 10%. That means if I walked up the stairs 100 times, 10 falls would be prevented if I wear comfortable shoes. Another way to think about it, I would need to wear comfortable shoes 10 times to prevent 1 fall. This is called the number needed to treat (NNT).

This is calculated by dividing 100 with the absolute risk reduction (as a percent, not a decimal). In this case, that would be 100/10, which equals 10.

Next, let’s look at relative risk reduction and why it’s a bit sneaky. The relative risk (RR) tells us the probability of something happening in one group compared to another. For example, we have 200 people with Saturday Night Fever. 100 of those people get treatment with a new drug, Disco, and 1 person dies. The risk of death in this group is 1%. The other 100 don’t get the new drug, and 2 people die. The risk of death in this group is 2%. The RR is calculated by dividing the risk of death in the first group by the risk of death in the other group. In this example, that is 1%/2% and the relative risk of 0.5. A RR of less than 1 means that risk is reduced, a RR equal to 1 means there is no change in the risk between the groups, and a RR greater than 1 means the risk is increased. This is sometimes called the risk ratio.

The relative risk reduction (RRR) tells you by how much the risk changes proportionally between the two groups. In our Saturday Night Fever scenario, the group that received Disco died half as often than the other group (put it another way, they died 50% less often)! Sounds great, right? But the absolute risk reduction is only 1% (ARR = 2%-1% = 1%). A lot less impressive, don’t you think? This is why drug companies often advertise their relative risk reductions. You are way more likely to want to buy Disco if we tell you that you are half as likely to die if you take the drug. You are way less likely to buy it if I tell you Disco reduces your risk of death by only 1% or that you need to give 100 people Disco to prevent 1 death. All are mathematically true, but one sounds way better (this is called framing).

Both ARR and RRR have their place. Absolute risks help put into perspective how much benefit an individual is likely to have from a treatment or prevention. The relative risk can help us find disparities, like if one group is having better outcomes than another. But be wary, relative risk reductions are often used to exaggerate the effects of a treatment.

Ok. Let me sum it up:

– Relative risk reductions give a percentage reduction in one group compared to another. These can be misleading and over-exaggerate how helpful something is.

– Absolute risk reductions give the actual difference in risk between one group and another. These are usually a lot less sexy but give a more realistic picture of how likely someone is to benefit from a given treatment.

Not yet done looking at stats? Maybe want some more examples? Check out these links for more information.

### Post Update:

We got lots of questions about why vaccine efficacy (VE) is given as relative risk reduction instead of absolute risk reduction. This is a special case, and relative risk reduction is a more useful metric in vaccine science. Vaccine efficacy is looking at improvement in population risks using clinical trials that compare a group of people who got the vaccine compared to the group who did not. Absolute risks here are widely variable and would change ALL THE TIME based on lots of individual things, like exposure, health status, and other risk factors. The absolute risk of infection also depends on the transmission in your area at that moment, something that is not fixed in time. (Sadly, it doesn’t look like COVID-19 is going anywhere anytime soon and the cumulative risk of catching it over time is sky high). Vaccine clinical trials are NOT designed to accurately determine absolute risk reduction or account for these variables. Randomized control clinical trials of specific treatments and interventions for diseases take lots of steps to control these variables and give much more accurate estimates of absolute risk. Check out our post here on what vaccine efficacy means: https://dearpandemic.org/what-does-95-efficacy-mean/.

Other random thought I wanted to add: Just because an absolute risk reduction is small, doesn’t make it meaningless! A 1% reduction is something awful like death or needing to be hospitalized might be really darn important. We just want to know what these numbers mean and how numbers can be manipulated so we can think critically about the info we are presented. Enjoy “mathing!” 😊