First post here, I have a question regarding optimal choice of statistical analysis for a future study.

Overview(simplified): Patients can recieve treatment A or B. Each hospital has a prefered treatment depending on local tradition and the choice of A or B is not affected by patient factors. Treatment A or B can be given in different dosages. We have a dichotomous outcome, Remission: Yes or No.

For choice of dose there are a few important confounders between dosage and remission, for example age.

Our hypothesis is that treatment A is superior to treatment B in terms of increasing remission. We also hypothesize that lower dosages of A and B is favourable in terms of remission.

How do I best handle the statistical analysis?

Comparing A vs B

Considering that patient factors do not influence the choice of A and B, can I do a simple chi-Square test to see if there is a significant difference? Should I do a logistic regression and adjust for potential differences in the populations even though from my viewpoint there are no clear confounders? If I would do a logistic regression with both choice of treatment and hospital there would be a very strong relationship between these two variables seeing as they are linked.

Dosage

The dosage is measured in mg and is a continous variable. I can make it in to a categorical variable. My assumption is I should make a logistic regression and adjust for confounders? Would the hospital be considered a confounder or an instrumental variable?(the hospital does not directly influence outcome but it can effect it trhough mediators, the hospital does also effect dosage through mediators such as experience in staff).

Thanks for any help!