odds ratio in logistic regression

Question

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](http://stats.stackexchange.com/questions/8661/logistic-regression-in-r-odds-ratio?rq=1) — 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

score 6 · Accepted Answer · answered Nov 28 '16 at 17:30

Your interpretation is correct but you have left out the intercept from your output display which is presumably the source for your text statement that the odds in the reference category were 0.26. If 0.26 is exp(the intercept coefficient) then you should be OK.

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.

odds ratio in logistic regression

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