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

Mon Aug 29 20:20:58 CEST 2022

Thank you all for the replies. Still processing them...

Indeed, Wolfgang, I was mainly thinking of time as a factor. Although, I
welcome comments as if it was numeric as well.

Your reply is surprising to me, because in my data I get different results.
The ES and p-values are very different regarding the interactions at 3 and
4-months, which are the relevant data to me. My df has 3 time points.

 res1 <- lmer(vo2 ~  group*time + ( 1  | ID  ), data =  dat_long )

   res2 <- lmer(vo2 ~  time + group:time + ( 1 | ID  ), data =  dat_long )

*res1:*
Fixed effects:
                       Estimate Std. Error      df t value Pr(>|t|)
(Intercept)             29.0705     0.9998 61.4510  29.076  < 2e-16 ***
groupFUT              1.0395     1.4140 61.4510   0.735 0.465036
time3month              -4.4917     1.0918 64.1740  -4.114 0.000113 ***
time4month              -5.0305     1.0622 63.8295  -4.736 1.26e-05 ***
*groupFUT:time3month *  2.5467     1.4396 61.8093   1.769 0.081822 .
*groupFUT:time4month*   1.7643     1.4424 61.8409   1.223 0.225909

*res2:*
Fixed effects:
                       Estimate Std. Error      df t value Pr(>|t|)
(Intercept)             29.0705     0.9998 61.4510  29.076  < 2e-16 ***
time3month              -4.4917     1.0918 64.1740  -4.114 0.000113 ***
time4month              -5.0305     1.0622 63.8295  -4.736 1.26e-05 ***
time0month:groupFUT   1.0395     1.4140 61.4510   0.735 0.465036
*time3month:groupFUT*   3.5862     1.5402 73.4895   2.328 0.022643 *
*time4month:groupFUT*  2.8038     1.5428 73.7427   1.817 0.073226 .

Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
escreveu no dia segunda, 29/08/2022 à(s) 16:11:

> I strongly suspect that 'time' is treated as a factor in the examples
> Jorge is referring to. In this case, the two formulations are just
> different parameterizations of the same model. We can use the 'Orthodont'
> data to illustrate this. Think of 'age' as the time variable (as a
> four-level factor) and 'Sex' as the treatment variable (as a two-level
> factor). In fact, I will throw in a third parameterization, which I think
> is even more intuitive.
>
> library(lme4)
>
> data("Orthodont", package="nlme")
>
> Orthodont$age <- factor(Orthodont$age)
>
> res1 <- lmer(distance ~ age*Sex + (1 | Subject), data=Orthodont)
> summary(res1)
>
> res2 <- lmer(distance ~ age + age:Sex + (1 | Subject), data=Orthodont)
> summary(res2)
>
> res3 <- lmer(distance ~ 0 + age + age:Sex + (1 | Subject), data=Orthodont)
> summary(res3)
>
> logLik(res1)
> logLik(res2)
> logLik(res3)
>
> The fit is identical.
>
> In 'res3', we get the estimated intercepts (means) of the reference group
> (in this case for 'Male') at all 4 timepoints and the age:Sex coefficients
> are the difference between the Female and Male groups at those 4 timepoints.
>
> Since these are just all different parameterizations of the same model,
> there is no reasons for preferring one over the other.
>
> One has to be careful though when using anova() on those models, esp. with
> respect to the age:Sex test. In anova(res1), the test examines if the
> difference between males and females is the same at all 4 timepoints, while
> in anova(res2) and anova(res3) the test examines if the difference is 0 at
> all 4 timepoints. However, one could get either test out of all three
> parameterizations, by forming appropriate contrasts. So again, no reason to
> prefer one over the other (except maybe convenience depending on what one
> would like to test).
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces using r-project.org]
> On
> >Behalf Of Douglas Bates
> >Sent: Monday, 29 August, 2022 16:14
> >To: Phillip Alday
> >Cc: R-mixed models mailing list; Jorge Teixeira
> >Subject: Re: [R-sig-ME] 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 using 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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