UKH

Quick consultation for the UKC hive mind. I'm using a source which quotes univariate odds of 2.74 for something happening. Could I also express that as 63.5%? I've always thought in terms of probability not odds ratio so struggling to get my head round it. 

Thanks! 

Surely if the odds are 2.74 to 1, then 2.74 in 3.74 outcomes will be positive, giving a probability of around 0.733?

I thought it means it is 2.74 times more likely than something else rather than a probability as such?  

I think you'd need more information.  

Full disclosure this is not my area and I'm really not sure.  

Odds are what you get from the bookies, after they've taken a bit for the house. Probability is what the bookies start with.

What's the context? At a bookies, odds represent total return; i.e. your £1 returns £2.74. So, you are wagering £1 to win £1.74. 

As a fraction, 174/100 or 87/50. This represents a (breakeven) probability of 50/(50+87) ≈ 36.5%

For a simple example, imagine someone laying you 9/1. The bet is breakeven if you win 1 out of 10 times, (as 9 times you lose £1, 1 time you win £9) so the implied probability is 10%. 

I should also say, if it's in a statistical context, then I'm interpreting it as odds of 2.74 to 1, which would represent a probability of 2.74/(2.74+1) ≈ 73.3% as stated above.

Or

100/2.74=36.49....

The values come from a study were the authors wanted to test the accuracy of a screening tool/check list.

The screening tool/check list is used to determine if a patient is a "major trauma" patient. The screening tool is basically a list of possible scenarios. If you meet any of the criteria you are deemed to be a major trauma patient which means you'll have life threatening injuries - i.e bits missing, bits that should be on the inside are on the outside etc

But the criteria are not all equal for example some are - death of another passenger in vehicle, ejected from vehicle, fall from greater than 6 meters. But one is fell off bicycle going faster than 5 miles per hour. 

So the authors looked at cases where a patient had met the criteria such as fell off bike, and then looked at their medical records to determine if they actually had serious injuries and merited been called major trauma patients. They expressed this as univariate odds ratio.

So death in the vehicle was 5.10, ejection was 4.22, fall from 6 meters or greater was 2.74 and falling of bicycle was 0.21

To me 2.74 isnt very accessible. So i want to say, people who fall from greater than 6 meters are likely to be major trauma patients. Can i say 73% of people who fall from height are major trauma? Is that tje same as 2.74 OR 

Thanks so much for the help. Hope it makes sense

my limited understanding .....

in a word No.

the odds ratio is more like marsbar says, its a ratio of things happening (being classed as a major trauma) versus not (being classed) IF they have a particular event (crash, bike, trip etc).

so if you fall 6m off a wall you are  2.74  times more likely to be classed as having major trauma than not.

if you fall off a bike you are  1/.21  (4.7) times more likely to not be classed as having a major trauma than having one

let's say you have got major trauma injuries, and you fell 6m off a wall, it DOESNT MEAN the fall caused it, these are associations like correlations,  not causations.  We could do that (causation) by getting lots of people and chucking them off the wall and measuring the outcome (as long as we control for everything else - brittle bones, previous injuries etc etc etc) Might struggle with ethics, but depends where you do it!

the difference from saying straight percentage is you included where the cases where they did'nt fall 6m but had major trauma. It's an association between the 2 variables (A - fall and B -trauma)

In other words it tries to allow for those people who  fall 6m and have trauma but the fall wasnt what did it!

https://www.statisticshowto.datasciencecentral.com/odds-ratio/  is quite good may help, Wikipedia entry https://en.wikipedia.org/wiki/Odds_ratio is a quite detailed but the example might clarify the difference, i'll copy it here ....

---

Suppose that in a sample of 100 men, 90 drank wine in the previous week, while in a sample of 100 women only 20 drank wine in the same period. The odds of a man drinking wine are 90 to 10, or 9:1, while the odds of a woman drinking wine are only 20 to 80, or 1:4 = 0.25:1. The odds ratio is thus 9/0.25, or 36, showing that men are much more likely to drink wine than women.

This example also shows how odds ratios are sometimes sensitive in stating relative positions: in this sample men are (90/100)/(20/100) = 4.5 times as likely to have drunk wine than women, but have 36 times the odds. 

---

in your case gender(m) = fall 6m,  wine = trauma  you may want to recover the 90%  but if you do 36/(36+1) you get 97%

does that help - i'd give it an OR or 1  (ie independent !)

I should have realised it was in a statistical context as you said it was univariate, so disregard the gambling stuff! The context is important, an odds ratio is not the same as the odds of something happening (the figure of 73.3% was assuming odds of 2.74:1). The odds ratio gives you an idea of the conditional relationship between two events, if the ratio is 1 then event A has the same chance of happening whether event B occurs or not (i.e. they are independent). To answer your question, it's not possible to give a probability for A without further information, because we only have a proportional relationship.

For example, let's say the odds of getting some disease for a smoker are 1:3, so a probability of 25%, and the odds for non-smokers are 1:6(≈14%), then the odds ratio is 1:3/1:6 = 2.

Now consider a different disease with odds of 1:4 (20%) for the smoker and 1:8 (≈11%) for the non-smoker, this would again give an odds ratio of 2, even though the probabilities are different.

I don't think you can sorry.

marsbar is right, I just think it's needs a bit more explanation:

sorry if this is condescending a wee bit: odds can be represented as probability, odds-ratio is not odds. you can turn odds ratios into a difference in probability, not probability itself.

OR of 2.72 means X is 73% more likely than Y. BUT you'll need to get into the detail of the paper to get what X and Y are (and never mind all the rest about correlation/causation, stat significance, confidence intervals etc.)

No not condescending at all...i'm really struggling to understand it. To me it seems like if you had 100 patients who fell from 6 meters. 73 were injured and 27 were uninjured, you could say you have a 73% chance of injury if you fall from 6 meters?

However, as there is a lack of parity between falls - some people might have landed on their head vs feet or landed on grass vs concrete etc. So because there are other variables involved rather than purely height of fall, Odds ratio is a better way of expressing the probability than percentage? 

Thank you for the explanation. I now understand what you're saying about odds ratio with disease comparing two groups like healthy vs smoker and those examples are really helpful . The thing I dont quite get is that with the example in this paper, there is only a single group? Everyone has fallen but not everyone is injured, would this not be the same as saying  "odds of getting some disease for a smoker are 1:3, so a probability of 25%" Like there is no comparison group such as smoker vs non-smoker? There is no group of healthy people whose limbs have exploded, they have all fallen from height? 

but what if the injury wasn't from the fall (wasn't caused by it).  Because you are looking for a 'relationship' between the two variables you need to take account of those people not falling but still being injured or not.  Two variables with two levels mean 4 possibilities, you are only looking at 2 of them.  The links in my reply may help, Wikipedia also talks about why certain papers/journals  use and abuse ORs

and BTW its not obvious and lots of people struggle

it's not possible to derive this from the info given. It may not be wrong, but it would only be coinsidence that the probability of X (major trauma from fall>6m) is the same as ratio of X to Y (Y being undefined in the info above)

looking at OR=(a/b)/(c/d) as a table: (I can only hope this looks like a table once it's posted)

xxxxxxxxxx   Major T   Not Major

criteria 1          a            b

Not crit 1        c             d

what's not clear from your info what Criteria 1; is this fall>6m / fall<6m

or,

all the data is fall>6m, and criteria 1 is a.n.other - possibly something to do with the screenign tool (tool or not-tool)

either way, it's not posible (without ging back to the data) to determine the prop of major trauma from fall>6m

ah okay. I think i've got it. I can't find any mention of what the second criteria is (the c/d bit)... but it must be there somewhere. I think that's why I was finding it so confusion was that there seemed to be only 1 criteria. 

From the wiki:

"The odds ratio is defined as the ratio of the odds of A in the presence of B and the odds of A in the absence of B."

So in the disease example I gave, event A is getting the disease, event B is smoking. 

I can't be certain without seeing your data, but I think in your case, we are looking at the odds of having major trauma (event A) in the presence of some other event B (in this case there are multiple possibilities and therefore multiple odds ratios, i.e. falling>6m, ejected from vehicle). As you would expect, the odds ratio is higher for the vehicle related events). The point is, not every case where someone fell>6m caused major trauma, and not every major trauma was caused by falling>6m, so we can draw up a 2x2 table as there are 4 possibilities. Hope that makes sense.