[R-sig-ME] time*treatment vs time + time:treatment in RCTs
Karl Ove Hufthammer
k@r| @end|ng |rom hu|t|@@org
Mon Aug 29 20:59:41 CEST 2022
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 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
>> [[alternative HTML version deleted]]
>>
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Karl Ove Hufthammer
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