[R-sig-ME] time*treatment vs time + time:treatment in RCTs
Phillip Alday
me @end|ng |rom ph||||p@|d@y@com
Mon Aug 29 15:28:20 CEST 2022
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).
PS: When referencing a blog entry, please provide a link to it. :)
>
> Thank you
> Jorge
>
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>
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