Solved – odds ratio in logistic regression

logisticodds-ratiorregression

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?

Best Answer

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.

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