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List: r-sig-mixed-models
Subject: Re: [R-sig-ME] time*treatment vs time + time:treatment in RCTs
From: Karl Ove Hufthammer <karl () huftis ! org>
Date: 2022-08-29 19:25:34
Message-ID: 03270bfc-62de-3ac8-29ba-0e66095264c7 () huftis ! org
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BTW, this is actually a rather annoying feature of the ways model
formulas work in R. For a *randomised* longitudinal study, the
population means for the randomisation groups are *identical* at
baseline (due to the randomisation). So to properly *adjust* for any
(random) group unbalances at baseline in the samples, one should fit a
model *without* a ‘group’ effect at baseline. (I know it sounds strange
to fit a model without group differences at baseline to *adjust* for any
baseline differences, but if you think about it for a while, it makes
sense …)
So instead of fitting
time + group + time:group + ...
(where ‘group’ represents the population differences at baseline)
one would naively *think* that one should fit a
time + time:group + ...
model. But R changes the *meaning* of the ‘time:group’ term in the
second model, so one ends up fitting the exact same model as the first
model (though with a different parametrisation), i.e., a model *not*
adjusting for any sample differences at baseline.
The only way I’ve found to easily fit the proper model, is to create a
factor of all ‘interaction(time, group)’ values and manually collapse
the baseline groups to have the same level. That works fine, but it
makes some tests *much* more complication, as you can no longer use R’s
formula handling for simplifying models.
Karl Ove Hufthammer
Karl Ove Hufthammer skreiv 29.08.2022 20:59:
> Hmm, the automatic HTML-to-plaintext conversion didn’t work too well.
> Here’s a plaintext version:
>
> No, you actually get equivalent results for your two models (which is
> really one model, just parametrised differently). The likelihood for
> the two models should be identical, and the P-value for testing
> whether there is an interaction should be identical. Here’s a simple
> simulation for data very similar to the ones you have:
>
> library(lmerTest)
>
> d_temp = expand.grid(group = c("PLA", "FUT"),
> time = c("Baseline", "3month", "4month"))
> n_varcombo = nrow(d_temp)
> d_temp$exp = c(29, 30, 24.5, 28, 24, 27)
> n_ind = 30
> dat_long = d_temp[rep(1:n_varcombo, each = n_ind), ]
> dat_long$ID = rep(1:n_ind, each = n_varcombo)
> set.seed(6)
> dat_long$ID_effect = rep(rnorm(n_ind, sd = 3), each = n_varcombo)
> dat_long$vo2 = dat_long$exp + rnorm(n_varcombo * n_ind, sd = 3)
>
> # Model without interaction
> res0 <- lmer(vo2 ~ group + time + (1 | ID), data = dat_long)
>
> # Two (equivalent) models with interaction
> res1 <- lmer(vo2 ~ group * time + (1 | ID), data = dat_long)
> summary(res1)
> #> Fixed effects:
> #> Estimate Std. Error df t value Pr(>|t|)
> #> (Intercept) 28.6258 0.5439 24.0000 52.635 < 2e-16 ***
> #> groupFUT 1.2876 0.7691 24.0000 1.674 0.1071
> #> time3month -4.8032 0.7691 24.0000 -6.245 1.87e-06 ***
> #> time4month -4.8628 0.7691 24.0000 -6.322 1.55e-06 ***
> #> groupFUT:time3month 2.7573 1.0877 24.0000 2.535 0.0182 *
> #> groupFUT:time4month 1.5326 1.0877 24.0000 1.409 0.1717
> #>
>
> res2 <- lmer(vo2 ~ time + group:time + (1 | ID), data = dat_long)
> summary(res2)
> #> Fixed effects:
> #> Estimate Std. Error df t value Pr(>|t|)
> #> (Intercept) 28.6258 0.5439 24.0000 52.635 < 2e-16 ***
> #> time3month -4.8032 0.7691 24.0000 -6.245 1.87e-06 ***
> #> time4month -4.8628 0.7691 24.0000 -6.322 1.55e-06 ***
> #> timeBaseline:groupFUT 1.2876 0.7691 24.0000 1.674 0.10710
> #> time3month:groupFUT 4.0449 0.7691 24.0000 5.259 2.16e-05 ***
> #> time4month:groupFUT 2.8202 0.7691 24.0000 3.667 0.00122 **
>
> # The models have the same log likelihood (and degrees of freedom)
> logLik(res1)
> #> 'log Lik.' -442.2284 (df=8)
> logLik(res2)
> #> 'log Lik.' -442.2284 (df=8)
>
> # And the P-values for the interaction are exactly the same
> anova(res0, res1)
> #> refitting model(s) with ML (instead of REML)
> #> Data: dat_long
> #> Models:
> #> res0: vo2 ~ group + time + (1 | ID)
> #> res1: vo2 ~ group * time + (1 | ID)
> #> npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
> #> res0 6 906.62 925.78 -447.31 894.62
> #> res1 8 903.79 929.33 -443.89 887.79 6.8379 2 0.03275 *
> #> ---
> #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> anova(res0, res2)
> #> refitting model(s) with ML (instead of REML)
> #> Data: dat_long
> #> Models:
> #> res0: vo2 ~ group + time + (1 | ID)
> #> res2: vo2 ~ time + group:time + (1 | ID)
> #> npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
> #> res0 6 906.62 925.78 -447.31 894.62
> #> res2 8 903.79 929.33 -443.89 887.79 6.8379 2 0.03275 *
> #> ---
> #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>
> As you can see, the two models are actually equivalent, and any
> inference based on the models should give the same results.
>
>
> Karl Ove Hufthammer
>
>
> Karl Ove Hufthammer skreiv 29.08.2022 20:56:
> > No, you actually get equivalent results for your two models (which is
> > really one model, just parametrised differently). The likelihood for the
> > two models should be identical, and the P-value for testing whether
> > there is an interaction should be identical. Here’s a simple simulation
> > for data very similar to the ones you have:
> >
> > > library(lmerTest)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-13>d_temp \
> >
> > = expand.grid(group = c("PLA", "FUT"),
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-14> \
> >
> > time = c("Baseline", "3month", "4month"))
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-15>n_varcombo \
> >
> > = nrow(d_temp)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-16>d_temp$exp \
> >
> > = c(29, 30, 24.5, 28, 24, 27)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-17>n_ind \
> >
> > = 30
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-18>dat_long \
> >
> > = d_temp[rep(1:n_varcombo, each = n_ind), ]
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-19>dat_long$ID \
> >
> > = rep(1:n_ind, each = n_varcombo)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-20>set.seed(6) \
> >
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-21>dat_long$ID_effect \
> >
> > = rep(rnorm(n_ind, sd = 3), each = n_varcombo)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-22>dat_long$vo2 \
> >
> > = dat_long$exp + rnorm(n_varcombo * n_ind, sd = 3)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-23> \
> >
> > # Model without interaction
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-25>res0 \
> >
> > <- lmer(vo2 ~ group + time + (1 | ID), data = dat_long)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-26> \
> >
> > # Two (equivalent) models with interaction
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-28>res1 \
> >
> > <- lmer(vo2 ~ group * time + (1 | ID), data = dat_long)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-29>summary(res1) \
> >
> > #> Fixed effects:
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-48>#> \
> >
> > Estimate Std. Error df t value Pr(>|t|)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-49>#> \
> >
> > (Intercept) 28.6258 0.5439 24.0000 52.635 < 2e-16 ***
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-50>#> \
> >
> > groupFUT 1.2876 0.7691 24.0000 1.674 0.1071
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-51>#> \
> >
> > time3month -4.8032 0.7691 24.0000 -6.245 1.87e-06 ***
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-52>#> \
> >
> > time4month -4.8628 0.7691 24.0000 -6.322 1.55e-06 ***
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-53>#> \
> >
> > groupFUT:time3month 2.7573 1.0877 24.0000 2.535 0.0182 *
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-54>#> \
> >
> > groupFUT:time4month 1.5326 1.0877 24.0000 1.409 0.1717 #>
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-65>res2 \
> >
> > <- lmer(vo2 ~ time + group:time + (1 | ID), data = dat_long)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-66>summary(res2) \
> >
> > #> Fixed effects:
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-85>#> \
> >
> > Estimate Std. Error df t value Pr(>|t|)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-86>#> \
> >
> > (Intercept) 28.6258 0.5439 24.0000 52.635 < 2e-16 ***
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-87>#> \
> >
> > time3month -4.8032 0.7691 24.0000 -6.245 1.87e-06 ***
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-88>#> \
> >
> > time4month -4.8628 0.7691 24.0000 -6.322 1.55e-06 ***
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-89>#> \
> >
> > timeBaseline:groupFUT 1.2876 0.7691 24.0000 1.674 0.10710
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-90>#> \
> >
> > time3month:groupFUT 4.0449 0.7691 24.0000 5.259 2.16e-05 ***
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-91>#> \
> >
> > time4month:groupFUT 2.8202 0.7691 24.0000 3.667 0.00122 ** # The models
> > have the same log likelihood (and degrees of freedom)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-104>logLik(res1) \
> >
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-105>#> \
> >
> > 'log Lik.' -442.2284 (df=8)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-106>logLik(res2) \
> >
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-107>#> \
> >
> > 'log Lik.' -442.2284 (df=8)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-108> \
> >
> > # And the P-values for the interaction are exactly the same
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-110>anova(res0, \
> >
> > res1)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-111>#> \
> >
> > refitting model(s) with ML (instead of REML)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-112>#> \
> >
> > Data: dat_long
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-113>#> \
> >
> > Models:
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-114>#> \
> >
> > res0: vo2 ~ group + time + (1 | ID)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-115>#> \
> >
> > res1: vo2 ~ group * time + (1 | ID)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-116>#> \
> >
> > npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-117>#> \
> >
> > res0 6 906.62 925.78 -447.31 894.62 #> res1 8 903.79 929.33 -443.89
> > 887.79 6.8379 2 0.03275 *
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-119>#> \
> >
> > ---
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-120>#> \
> >
> > Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-121>anova(res0, \
> >
> > res2)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-122>#> \
> >
> > refitting model(s) with ML (instead of REML)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-123>#> \
> >
> > Data: dat_long
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-124>#> \
> >
> > Models:
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-125>#> \
> >
> > res0: vo2 ~ group + time + (1 | ID)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-126>#> \
> >
> > res2: vo2 ~ time + group:time + (1 | ID)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-127>#> \
> >
> > npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-128>#> \
> >
> > res0 6 906.62 925.78 -447.31 894.62 #> res2 8 903.79 929.33 -443.89
> > 887.79 6.8379 2 0.03275 *
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-130>#> \
> >
> > ---
> > <http://localhost:28019/session/grave-cobra_reprex_preview.html?viewer_pane=1&capabilities=1&host=http%3A%2F%2F127.0.0.1%3A55034#cb1-131>#> \
> >
> > Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1|
> >
> >
> > As you can see, the two models are actually equivalent, and any
> > inference based on the models should give the same results.
> >
> >
> > Karl Ove Hufthammer
> >
> > Jorge Teixeira skreiv 29.08.2022 20:20:
> > > 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@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@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@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
> > > [[alternative HTML version deleted]]
> > >
> > > _______________________________________________
> > > R-sig-mixed-models@r-project.org mailing list
> > > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> > >
>
--
Karl Ove Hufthammer
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