I am trying to measure the effect of a treatment on a binary outcome using observational data. However, the group that was treated and the group that was not treated are not equivalent: assignment to the treatment or control group is not randomized and probably depends on many different variables.
I want to perform regression adjustment to estimate the effect of treatment while taking into account confounding variables, in order to have an idea of the "true" effect of my treatment. Essentially, I want to fit a logistic regression model where the dichotomous outcome is explained by treatment and other confounding variables. Then I want to look at the coefficient of treatment to estimate treatment effect.
My main question is: how can I know whether my model is satisfactory? I don't know what the "true" confounding variables are and I have access to a large volume of data and predictors. However, I don't know when I can safely say that my model has efficiently corrected for the structural bias of the data. I'm thinking about reading the pseudo R squared in the logistic regression results, but I'm not sure what a "good" value would be. I'm also wondering if there are other methods to assess that my model correctly estimates treatment effect.