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Hi!
Many thanks to everyone who responded in my query. The overall opinion was 
that my “strange odds ratio” was due to the range of values the assay I was 
trying to analyse had and that I had   to change the scale of it. Many 
suggest using log-transformation, as the log scale is very often used for 
concentrations. Some also suggest dividing the concentrations by 100 or 1000 
or in ranges that would be biologically more meaningful.
Ioanna




Original query:

Dear Allstaters,
I am a little bit puzzled about something and I was wondering if someone had 
any suggestion related to this…
I have the concentration results of an assay which clinicians would like to 
use in order to discriminate between subjects of CAD (Coronary Arterial 
Disease) and subjects of no CAD.
The CAD group has 109 subjects and the no-CAD 53.
I try to perform logistic regression modelling for the probability of a 
subject having CAD. However, the results are a little bit confusing. 
Although, the model fits the data well and the p-value of the estimate of 
the assay was highly significant (<0.001), the odds ratio of it came out to 
be 1.004(1.002, 1.006)!!!
Therefore, I got confused.
Then, I implemented a ROC plot which gave me really nice plot of AUC of 
0.895 (the two groups were found to have significantly different means with 
the CAD group having bigger mean   concentration than the no-CAD).
Then I thought that maybe it was the different group sizes (53 non-CAD 
versus 109 CAD). I generated some data so that the group’s size would be 
quite similar (106 non-Cad versus 109 CAD this time.) Again, the estimate of 
the assay was found to be significant (P<0.001) but the odds ratio 
1.004(1.003, 1.005).
I am thinking that these strange results could be due to the very high range 
of concentrations I have to deal with, (47µg/ml-10307.40µg/ml).
Anybody has any suggestion..?
Ioanna

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