Odds ratio — interpret and derive.

medium

Answer

$Odds = p / (1 - p).$
$(\mathrm{OR})\; = \;\mathrm{odds}_{A}\; / \;\mathrm{odds}_{B}$
$\operatorname{log}(\mathrm{odds})\; = \;x$
$OR > 1: positive association; OR = 1: no association; OR < 1: negative.$
$Not a ratio of probabilities.$
$For rare outcomes, OR \approx relative risk; for common outcomes, OR overstates RR.$

Check yourself — multiple choice

Ratio of p
Odds = p/(1-p); OR = ratio of odds; $\operatorname{exp}({\beta}_{j})$ in logistic = OR per unit ${\Delta}x_{j}$ ; ≈ RR for rare events, overstates RR otherwise
Same as probability
Random

$\mathrm{OR}\; = \;\operatorname{exp}({\beta}_{j})$ in logistic; ratio of odds; ≈ RR for rare events.

#regression#glm

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