This was my query:
Dear allstaters,
I have a query which may be trivial, but I'd be grateful for
suggestions.
I have a dichotomous outcome variable y and two correlated dichotomous
predictors, x1 and x2, plus some covariates.
I do logistic regression of y on x1 + covariates and logistic
regression of y on x2 plus covariates.
How can I compare the log odds ratios for x1 and x2? A confidence
interval for the difference would be nice.
Just to make it more complicated this is a cluster sample, but I don't
think that matters. I am using logistic regression in Stata using the
cluster option.
Sorry to be so slow, but I don't have easy access to any books right
now.
Martin
Many thanks to Patrick Musonda, Merce Serrano, and David Boniface for
the following replies:
Presumably the reason you can not have x1 and x2 in the same model is
because they are highly correlated, which means if my statistical
knowldge is right, putting x1 and x2 in the same model will not give
you any more information. But seems these two explanatory variables
for some reason you need them in the model with the same dependent
variable y. I would make a binary variable denoting 1 if in x1 and say
0 if in x2, then use this new variable say x3, representing x2 as the
reference category, and then use it in the model with y as response
variable. Include the other covariates in the same model.
Patrick Musonda
Dear Martin,
Why not do regression of y on both x1 and x2 and their interaction?
It's a matter of sampling?
Being for both regressions the same response and covariates, a
confidence interval for the difference between log-odds could include
the term +2rS1S2 for the variance of the difference?
Hope this helps,
Merce Comas Serrano
Martin,
I have thought about this without coming to a clear conclusion. The
estimates of the two odds ratios will be correlated You could explore
this by re-sampling, but perhaps, in the end, you prefer to do the
calculation as if they were independent and issue a health warning
with the result. Please let me know if you receive better advice.
David Boniface
I am not sure that I have the answer here. However, it occurs to me
that a test of significance is easy. All I need to to do is consider
only subjects who are discordant for x1 and x2. I then create a
variable z=1 if x1=1 and z=0 if x2=1 and regress on y on z for
discordant subjects only. As I’m in a hurry, I’ll settle for that.
Thanks to all,
Martin
***************************************************
Martin Bland
Prof. of Medical Statistics
St. George's Hospital Medical School
London SW17 0RE
[log in to unmask]
http://www.mbland.sghms.ac.uk/
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