In a randomized trial, should we exclude random intercepts and use only slopes? Let's say I have a longitudinal study, with patients assessed at several time points, which goal is to compare the treatment vs. placebo.
If, theoretically, I used a mixed model to analyse the difference over time, should I include only the random slopes for time without random intercepts?
My reasoning is as follows. Random slopes allows each patient to have own regression line over time, which accounts for different within-patient correlation over time (does it, indeed, or should I consider also some residual covariance?)
But random intercepts allow each patient to vary in the outcome of interest at baseline, which is out of interest in randomized trials. And since my patients are randomized and all start from comparably same levels of this outcome, allowing them for random intercepts is like comparing the baseline outcomes between the arms seems to make no sense at all.
Thus, if I want to use the lme4::lmer4 package to model it, should I use specification formula: Response ~ Time + (Time + 0 | ID) rather than Response ~ Time + (Time|ID)?
Am I right about this reasoning?
 A: The standard model for this that is commonly used in randomized controlled trials (RCTs) is response ~ 1 + treatment as factor + visit as factor + baseline (pre-treatment) value + visit as factor  : baseline (pre-treatment) value  + visit as factor : treatment as factor with an unstructured covariance matrix between visits. You will find many examples of this when searching for "MMRM" or "Mixed effects model for repeated measures". Anything else like just using random effects on intercepts or slopes, which implies an extremely strong assumption on correlation structure over time, would seem to need careful justification.
As pointed out by others, patients do differ and artificially restricting the model to not reflect this seems questionable. The unstructured covariance matrix for the residuals within a patient can also be expressed as having a random effect on each of the $V$ visit for a patient, within a $V \times V$ covariance matrix between these visits (while a "standard" random patient effect on the intercept would imply that all visits equally correlated). You also want to put the baseline measurement of the outcome of interest into your model and allow its influence to be different for each visit (=interaction term with visit).
Note also that these types of models will implicitly perform missing data imputation under a particular estimand that may not match your estimand of interest for the RCT.
