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FMB
Risk vs Odds in formulas
06/10/2017
odds = a/b
= a/(a+b-a)
= a/(a+b) / (a+b-a)/(a+b)
= a/(a+b) / [ (a+b)/(a+b) – a/(a+b) ]
= p / (1-p )
If p (risk) is small: odds ~ p
log (odds) = log (p / (1-p))
log (p/(1-p)) = a + b
x + …
NOTE: if I apply logistic regression to a cohort study I’m estimating the odds
(or odd ratio) not the risk (or relative risk), unless p is small