# Adjusting time*treatment mixed model for other covariate

I'm conducting an analysis of a non-randomised trial in which I have measures of Y at 3 timepoints: baseline, week 2 and week 48. Subjects are divided into 3 groups and lets assume that all were measured at each timepoint.

I am interested in whether there are significant differences in the change from baseline between the 3 groups. I.e. I want to identify differences between the slopes of the 3 groups for Y.

I am using this model:

Y = Group + Time + Group*Time


Where the Group*Time parameter is of primary interest.

Since this is a non-randomised study there are baseline differences which I need to account or adjust for. I have spent some time searching for advice / help on how to do this but have only found examples where people have adjusted ANCOVA type models in a manner similar to the following:

Post-test = Pretest + Group + Confounder


Since my primary variable of interest is an interaction variable, I am concerned that simply adding in the confounding variable to the model will not suffice:

Y = Group + Time + Group*Time + Confounder


Because of this I was thinking that I need to add the confounder to the interaction term in something like:

Y = Group + Time + Group*Time + Group*Time*Confounder


But this produces a prohibitively complicated model.