In the following logistic regression model, I am trying to model the logit of Y, where Y is a binary variable (Yes or No).
Let my model be: logit($Y$) = $\beta_0$ + $\beta_1$*$x_1$+ $\beta_2$*$x_2$+ $\beta_3$$x_1*x_2$
Both $x_1$ and $x_2$ are binary variables which are used as covariates to the logistic model. $x_1$ is the treatment term (Treatment A and Treatment B), while $x_2$ is the gender (Male vs Female)
If I need to calculate the odds ratio of Treatment A vs Treatment B, what I learned from school is that I would actually compute both Treatment A vs Treatment B at $x_2$ = Male" and Treatment A vs Treatment B at $x_2$ = Female. So my first question: is this approach correct?
Second question: If I must produce 1 single odds ratio of "Treatment A vs Treatment B" with this model, would it make sense for me to take the mean of the 2 odds ratios? Let's assume I cannot produce another model taking away the interaction term. If not, is there anyway to produce that single Odds Ratio in SAS with this model?
Thank you very much!