I’ve been reading an annoying book which uses odds ratio (and hazard ratios). As I don’t use these terms much, I have to keep checking my understanding.

Odds ratios: it’s the ratio of two odds!

The useful and beautiful The Art of Statistics gives a clear example:

• Non-bacon eaters have a 6 out of 100 chance of bowel cancer; bacon eaters have 7 out of 100.
• The odds for non-bacon eaters is 6/94, and it’s 7/93 for bacon eaters.
• The odds ratio is (7/93) ÷ (6/94) or about 1.18.

That’s 18% increase in the odds of cancer in the bacon group compared to non-bacon group.

Key points:

• It’s not the same as relative risk, and tells you nothing about absolute risk
• It has useful properties: “frequent use of ORs likely owes to the fact that the statistic is easy to compute in logistic regression models using commonly available statistical software”.
• It’s confusing.

https://youtu.be/ixKhS0Silb4

There’s a video on that series on hazard ratios too.