Odds ratio and percentages.... absolute beginner

[RabbitWho]

Imagine that the chances in the USA of adult men having GAD are on average 1 in 100. But what of the subset of adult men who already have MD? What are the chances that such men will have GAD as well as MD? An odds ratio tells us about the increase in the chance that such men will have GAD, already having MD. If having MD increases the chances of having GAD from the usual 1 in 100 to 8.2 in 100, then the odds ratio for having GAD when you have MD is 8.2. If having MD has no effect at all on the chances of having GAD then the odds ratio is 1.00 (it does not affect the odds). An odds ratio of 1.05 means for the population of men with MD the chances of having GAD are increased by 5%. The further away from 1 the odds ratio is, the stronger the effect.


Ok, forgive me because I'm absolutely hopeless at numbers

This is out of 100, so I would have thought to increase the odds ratio which was previously 1, by 5% it would have to now be an odds ratio of 6
So if the 5% is suddenly turning into 0.05 of a whole, it must be 5% not of the current set of 100 but of a different set which this current set is a subset of.

I really don't understand how you are comparing across subsets like that and how Joe Bloggs, as a sufferer of MD, is supposed to figure out how much his chance of GAD has increased relative to what it was before he had MD
^{For the curious: MD = Major Depression, GAD = General Anxiety Disorder}

 

[RabbitWho]

Oh wait wait wait..

So the way odds ratio differs from percentage is that it is ALWAYS in reference to something else? Is that it?

So 1 is ALWAYS the same as the thing its in reference to, and anything above 1 tells you how much it has changed...

So if the GAD odds ratio for people with MD is 3 that means people with MD are 3 times more likely to have GAD than people without it, and the 0.05 is the % of one...

Ok sorry, I get it now, but my little rabbit mind is blown

 

[mathman]

The description is talking about 5% of the 1% that was started from.

 

[RabbitWho]

The description is talking about 5% of the 1% that was started from.

The fact that a number can increase in size in this self-referential way is neat. You number people and the things you do.

 

[PeroK]

The fact that a number can increase in size in this self-referential way is neat. You number people and the things you do.

You have to be careful when reading things about percentages in the newspapers or hearing them on TV about this very point. If you have a small percentage of something often the headline is "doing such and such increases your chance of getting condition X by 20%". And it makes it sound like there's a 20% chance of getting condition X if you do such and such. But, actually, if the chance of getting condition X is only 1% (1 in a hundred), then a 20% increase only increases that to 1.2%. It doesn't increase it to 21%: that would be increasing the risk by a factor of 20.

It's something to look out for in any case.