2
$\begingroup$

I am running two logistic regression analyses, and I am very confused about the interpretation of the odds ratio, specifically in the case of an OR below 1. I have looked into all kind of different related posts on this forum, but nowhere I can seem to find a similar situation with an explanation. So I hope you will be able to help me out! This is the situation:

Model 1: I have a dichotomous outcome: yes/no diagnosis I have a continuous predictor: score A

Model 2: I have a dichotomous outcome: yes/no diagnosis I have a continuous predictor: score B

For model 1 I have an OR above 1 (Exp(B), thus the OR, =1.17), I interpreted this as: "the odds of having a diagnosis was 1.17 times greater with one point increase in score A" I think this is correct isn't it?

For model 2 I have an OR below 1 (Exp(B), thus OR, =0.91). Based on some other posts on stats forums I figured I have to take the reciprocal of 0.91 (being 1.10), so I interpreted this as: "the odds of having a diagnosis was 1.10 times smaller with one point increase score B" Is this correct? I started doubting because somewhere else I read that I should not take the reciprocal but instead do 1-0.91=0.09 and use this number for my interpretation. Although I am not sure how exactly I would use this number in my interpretation...

I hope someone can shed some light on the different numbers and ways of interpreting my OR's!

Thanks a lot! Sabine

$\endgroup$
2
$\begingroup$

The odds of having a diagnosis in model 2 decreases by a factor 0.91 for a unit increase in score B. Some people don't like these numbers less than 1, so they take the invers. This is now interpreted that the odds of a diagnosis increases by a factor 1,10 for a unit decrease in factor B.

If you multiply something by 1.10, you increase it by 10%. In general the relationship between a factor increase and the percentage change is (f - 1) * 100%. So an odds ratio of 0.91 corresponds to a (0.91 - 1)*100% = -9% change in odds for a unit increase in factor B, or a 9% decrease in the odds for a unit change in factor B.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.