Repeated measurements of some continuous variable of interested is very common in clinical trials.
Usually patients are randomized between treatment arms. Hence it is reasonable to assume that all patients and especially all groups in the trial have equal value of this variable of interest.
Lets assume I run a clinical trial with three groups or arms and I make repeated measurements on variable of interest.
Against this reasoning I would say that only reasonable and justified linear mixed model would assume fixed intercept and random slopes. I would include group id as covariate and allow varying slopes for it. To me, it would be odd to include a random intercept since I assume that groups are balance regarding the baseline value of my measured variable.
So, is this model the only correct one or why should I use other models, like random intercept and fixed slope?