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

[Viechtbauer, Wolfgang (NP)]

If 'time' is categorical, then neither m2 nor m3 violate the 'principle of marginality'.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces using r-project.org] On
>Behalf Of Jorge Teixeira
>Sent: Tuesday, 30 August, 2022 12:13
>To: Phillip Alday
>Cc: R-mixed models mailing list
>Subject: Re: [R-sig-ME] time*treatment vs time + time:treatment in RCTs
>
>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