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

[Jorge Teixeira]

Thank you, Philip.

1) would the model y (y1, y2 - but not y0) ~ y0 + time + time:treatment +
(1|ID) (*m3*) also violate the  principle of
marginality, in your opinion?

1.1) Would you still prefer m1 compared to m3?


*Final notes*:
Here is an interesting stata (sorry) about this:
https://stats.oarc.ucla.edu/stata/faq/what-happens-if-you-omit-the-main-effect-in-a-regression-model-with-an-interaction/


Solomon's post.
https://solomonkurz.netlify.app/post/2022-06-13-just-use-multilevel-models-for-your-pre-post-rct-data/

Thanks!




Phillip Alday <me using phillipalday.com> escreveu no dia segunda, 29/08/2022
à(s) 14:26:

>
> On 8/29/22 05:53, Jorge Teixeira wrote:
> > 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?
>
> It depends a bit on what `y` is: change from baseline or the 'raw'
> measure. If it's the raw measure, then (M2) doesn't include a
> description of differences at baseline between the groups.
>
> Perhaps most importantly though: (M2) violates the principle of
> marginality discussed e.g. in Venables' Exegeses on Linear Models
> (https://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf)
>
> > *2)* Can anyone explain, in layman terms, what is the estimand in M2? I
> > still struggle to understand what model is really measuring.
>
> Approximately the same thing as M1, except that the "overall" effect of
> treatment is assumed to be zero. "Overall" is a bit vague because it
> depends on the contrast coding used for time and treatment.
>
> You can see this for yourself. M1 can also be written as:
>
> y ~ time + time:treatment + treatment + (1|ID).
>
> If you force the coefficient on treatment to be zero, then you have M2.
>
> >
> > *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?
>
> Definitely (1).
>
> > Thank you
> > Jorge
> >
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> >
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