Something that I find amazing is how many headlines talking about risk are simply wrong
Why?
Let's take a quick look at odds ratios #tweetorialpic.twitter.com/XyCldkJiRm
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There are a number of ways of doing this The most intuitive is the relative risk ratiopic.twitter.com/2VJ3cuO4Cx
Risk is simple and easy to understand - it's essentially the percentage chance of something happening For example, say 10 in 100 people have an event. The risk is just 10/100 = 10%
Relative risk ratios are also pretty easy. It's just the risk of one thing divided by another Let's say we've got 2 groups A and B. A has a 10% risk of the event, B has a 20% risk What's the risk ratio of B:A?
As I said, it's easy and intuitive The risk in group B is double that of A This is how VIRTUALLY ALL DIFFERENCES are represented in the media
The problem is, sometimes relative risk doesn't make sense to use. In those cases, what's often used instead as an estimate of the risk ratio is what's called an odds ratio
Odds are fairly simple to calculate, but a bit less intuitive than risks The odds of something happening are the events divided by the non-events So if 10 in 100 people have an event, the ODDS are 10/90 = 0.11
The ODDS RATIO is the ratio of one odds to another Take the same example - 10/100 events in group A, 20/100 events in group B What's the odds ratio?
Well, the first odds we've worked out already - 0.11 For group B, it's 20/80 = 0.25 So the ratio of the odds B:A is 0.25/0.11 = 2.25
So our relative risk ratio is 2 Our odds ratio is 2.25 They are different, but used interchangeably by the press!pic.twitter.com/aq9Aw0jduN
The thing is, by definition odds ratios are higher than relative risk ratios - it's mathematically certain When the risks are low, this effect is small, but if the risks are big it's very noticeable
For example, if your two risks are 0.01% and 0.02%, the risk ratio is 2 and the odds ratio is: (0.02/99.98)/(0.01/99.99) = 2.0002 Barely different
But if the two risks are 20% and 40%, the risk ratio is still 2 (40/20) but the odds ratio becomes VERY different: (40/60)/(20/80) = 2.67 That's a lot higher!pic.twitter.com/73Fc7CxeUU
Going back to this headline that I picked up - it looks at a study that used logistic regression, which spits out odds ratiospic.twitter.com/8vHaEBaLIS
The results were reported as odds, with vapers having a 1.83 times higher odds of stroke than non-vapers Given that the prevalence of stroke was 2-4% in the groups, that means that the risk ratio would be a bit lower than 1.83
In other words, the headline rounds UP from 83% to a 100% increase (double), but in actual fact it's more likely that the risk is somewhere around 75% instead!
And this is done almost ubiquitously across the board It's not really the media's fault - scientists do it all the time as well!pic.twitter.com/BjxCDlughU
It's also really hard to tell if the study used risks or odds unless you actually read it, which adds a layer of complexity to the matter
Honestly, I want to end on a nice easy note, but the fact is that odds are confusing, a lot of researchers get them wrong, and it's unlikely we'll have a solution to this any time soon Hurray!
Anyway, a reasonable proportions of the headlines you've seen probably overestimate the actual risk because the studies used odds ratios 
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