# odds ratio in logistic regression

I calculated univariate odds ratio as follows:

table(d[,c("copd", "nsurgrespicatelectbpnards")])

nsurgrespicatelectbpnards
copd  N  Y
N 73 19
Y 26 31

m <- glm(nsurgrespicatelectbpnards~copd, data = d, family = 'binomial')
exp(cbind(OR=coef(m)[2], CI95lo=confint(m)[2,1], CI95hi=confint(m)[2,2]))

OR    CI95lo    CI95hi
copdY       4.580972 2.2436010 9.6223563


My intrepretation is that people with COPD (lung disease) have an odds ratio of 4.58 of having a postoperative respiratory complication (nsurgrespicatelectbpnards) compared to people not having COPD. 0.26 being the odds of having a complication while not having COPD (i.e 19/73).

Is that correct, disregarding regression diagnostics?

• There is some helpful information in this Q&Q – mdewey Nov 28 '16 at 15:27
• @mdewey thanks! I have actually read this one, and it is very good, but my supervisor (not a statistician) is so adamant that I am wrong that I am unsure of my comprehension. The problem is that he refuses to explain why I am wrong, and says that such results "defy logic" – Raoul Nov 28 '16 at 15:30
• That is an awkward situation to be in and all we can offer you is sympathy. – mdewey Nov 28 '16 at 15:31

It would usually be preferred to use confidence intervals from the profile likelihood method rather than the Wald method which you are using and they are available in R using confint.