From this paper:

The one man in seven who harbors risk alleles at both 20p11.22 and AR (encoding the androgen receptor) has a sevenfold-increased odds of androgenic alopecia (OR = 7.12, P = 3.7 x 10(-15)).

If the prior probability of a man going bald is say 50%, what is the posterior probability given that he harbors these risk alleles? $7 * 0.5 = 3.5$ is obviously wrong.

Put another way, if I have these risk alleles how do I calculate my overall probability of going bald?

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    $\begingroup$ Odds are not probability $\endgroup$ – Glen_b Mar 25 '16 at 10:58
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    $\begingroup$ Possible duplicate of Odds Made Simple $\endgroup$ – Tim Mar 25 '16 at 11:32

Odds are a way of expressing probabilities that are bounded by 0 and infinity. It's common to hear them used in gambling, where you might get 5-to-1 odds on a horse winning a race.

Odds are related to probability by:

$odds = probability/(1-probability)$

$probability = odds/(1+odds)$

So for your example, a 50% likelihood of baldness would correspond to odds of 1, meaning a $1/2$ chance of baldness. A sevenfold increase would be odds of 7, meaning a $7/8$ chance of baldness.



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