I ran a logistic regression with only 1 independent variable and came with an 18.59 odds ratio with a c statistic of .50.
After adding 4 variables that independent variable odds ratio decreased from 18.59 to 9.9 and the c statistic of the model increased to .68.
Does this mean that if I reported just the odds ratio of single variables that they would be misleading since the c statistic is only .50? Is it better to report the odds ratio of 9.9 instead of 18.59 since the model has a higher c statistic even though the odds ratio is lower?
I've seen papers where they have reported only odds ratio for all independent variables independently and then others where they have run a logistic regression. Just trying to figure out what one is better.