I'm coming from a background with regards to randomizing treatment and just conducting measurement at one point in time. In my current setup, there are just four groups of interest: A control group (C), an education treatment (T1), a medicine treatment (T2), and the combination of the education and medicine treatment (T3). In a multiple regression framework, I would be interested in the effect of T1, the effect of T2, and the interaction effect coming from T3 (the reference group is the Control group).
However, my setting in reality allows for repeated measures across time of my outcome of interest (say, at the daily level). Moreover, while the education treatment cannot vary across time, the medicine treatment can. I am thinking the right set-up to study what I list above is to do some sort of ANOVA, where I have a control group and an education group, and within both the control and education group, have the medicine be randomized for individuals every day. I think the latter should help for statistical power. What is the formal name for this kind of set up (is it ANOVA repeated measures within-between interaction)? Does the ANOVA depend on which comparison is being made?
Relatedly, if anyone could recommend an appropriate program with which to calculate power in the above scenario, I would appreciate it. Thank you.