time*treatment vs time + time:treatment in RCTs
M2 is an appropriate model if time corresponds to "time on treatment" or in general if the covariate over which the measurements are repeated has a scale where 0 is meaningful. I think of it as the "zero dose" model because zero dose of treatment 1 is the same as zero dose of treatment 2 is the same as zero dose of the placebo. Similarly zero time on treatment is the same for any of the treatments or the placebo. In those cases we would not expect a main effect for treatment because that corresponds to systematic differences before the study begins (or at zero dose), but we would expect an interaction of time (or dose) with treatment.
On Mon, Aug 29, 2022 at 8:28 AM Phillip Alday <me at phillipalday.com> wrote:
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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