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
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.
I haven't seen this done elsewhere, can anyone advise as to whether I'm going about this the right way?