[R-sig-ME] time*treatment vs time + time:treatment in RCTs

[Jorge Teixeira]

Hi. In medicine's RCTs, with 3 or more time-points, whenever LMMs are used
and the code is available, a variation of  y ~ time*treatment + (1 | ID)
*(M1)* is always used (from what I have seen).

Recently I came across the model  time + time:treatment + (1 | ID)* (M2)*
in Solomun Kurz's blog and in the book of Galecki (LMMs using R).

Questions:
*1)* Are there any modelling reasons for M2 to be less used in medicine's
RCTs?

*2)* Can anyone explain, in layman terms, what is the estimand in M2? I
still struggle to understand what model is really measuring.

*3)* On a general basis, in a RCT with 3 time points (baseline, 3-month and
4-month), would you tend to gravitate more towards model 1 or 2?

Thank you
Jorge

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