Hi,

Norton et al state in a recent JAMA guide that the magnitude of the odds ratio from a logistic regression is scaled by an arbitrary factor (equal to the square root of the variance of the unexplained part of binary outcome). They say that adding more independent explanatory variables to the model will increase the odds ratio of the variable of interest (eg, treatment) due to dividing by a smaller scaling factor. They thus warn that different odds ratios from the same study cannot be compared when the statistical models that result in odds ratio estimates have different explanatory variables because each model has a different arbitrary scaling factor.

I ran a simple logistic regression on the dataset below using the code below and the crude odds ratio is 2.33 and the adjusted odds ratio is 3.0 for hiv status both of which exactly match the stratified analysis without logistic regression. The arbitrary scaling factor does not surface here.

I would appreciate any thoughts on this issue and if this is actually a valid concern in Stata and if anyone can share a contrary dataset (using categorical variables only)

Thanks
Suhail


Code:
logit risky i.hiv [fw=fw], or
logit risky i.hiv i.nyc [fw=fw], or

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input byte(risky hiv nyc fw)
1 1 0 25
1 0 0 75
0 1 0 10
0 0 0 90
1 1 1 75
1 0 1 25
0 1 1 50
0 0 1 50
end