I have a dataset of patient information and I'm looking to find a way to compare two groups of patients and take into account confounding variables. My dataset has an N of ~1500 and I'm looking for a difference between two populations (treated/untreated) and whether they responded to therapy.
I have been using a Fisher's Exact test to asses the significance of the difference between the two populations. However, there are plenty of potentially confounding factors like age, gender, time since diagnosis, etc. Some of these variables are significantly associated with the response variable.
I'm looking for ways to control for these confounding variables. I know how to do it when my response variable is a continuous variable (do a regression analysis and include confounders as terms in the regression).
Can I do that with binary variables? Should I use a logistic regression? Is there something else I should try? Should I make sub-cohorts of the data in-which the confounding variable is constant (ie. only test the Male patients) but then I'll limit my sample size too much.
Any suggestions would be helpful.