why do you wan tto do 2 models? isn't it easier to add sex a variable in your one model? you can there compare the odds of depression in men and women adjusting for all the other factors in a single model- which sounds much simpler than statistically compareing 2 odd ratios from 2 different multivariable models

if your two models are completely different (with different dependent anf outcome variables), there is little value in comparing odds ratio- it's like comparing apples and oranges- you can compare 2 models using a likelihood ratio test (which will tell you whether the models are asignificantly different or not), or look at likelihood ratio to decide whether ot not to include variables in a model. if you give us more details on what exactly you are trying to do 9with details of your models), perhaps we can provide a more detailed answer

Thank you Michael. 

The outcome variable and the independent variables and covariates will be the same in both models. Let me try and give an example: I run a model predicting depression using 5 variables (age, race, education, insurance, BMI) for Women and I run the same model using the same variables for Men. Can I compare the ORs for age in women model to the OR for age in men model? In other words I stratified the analysis by gender. I know you can use the Breslow-Day test to compare ORs from unadjusted models but I am not sure for an adjusted model.

Usually in manuscripts we just look at them and say one is more or less likely but I have been asked several times if there is an actual test. I hope the example helps, thank you!!!

why do you wan tto do 2 models? isn't it easier to add sex a variable in your one model? you can there compare the odds of depression in men and women adjusting for all the other factors in a single model- which sounds much simpler than statistically compareing 2 odd ratios from 2 different multivariable models