[R] some questions about longitudinal study with baseline

[array chip]

Hi all,

I asked this before the holiday, didn't get any response. So would like to 
resend the message, hope to get any fresh attention. Since this is not purely 
lme technical question, so I also cc-ed R general mailing list, hope to get some 
suggestions from there as well. 


I asked some questions on how to analyze longitudinal study with only 2 time 
points (baseline and a follow-up) previously. I appreciate many useful comments 
from some members, especially Dennis Murphy and Marc Schwartz who refered the 
following paper addressing specifically this type of study with only 2 time 
points: 

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1121605/

Basically, with only 2 time points (baseline and one follow-up), ANCOVA with 
follow-up as dependent variable and baseline as covariate should be used:

follow-up = a + b*baseline + treatment

Now I have a regular longitudinal study with 6 time points, 7 treatments 
(vehicle, A, B, C, D, F, G), measuring a response variable "y". The dataset is 
attached. I have some questions, and appreciate any suggestions on how to 
analyze the dataset.

dat<-read.table("dat.txt",sep='\t',header=T,row.names=NULL)
library(MASS)
dat$trt<-relevel(dat$trt,'vehicle')

xyplot(y~time, groups=trt, data=dat, 
ylim=c(3,10),col=c(1:6,8),lwd=2,type=c('g','a'),xlab='Days',ylab="response",
 key = list(lines=list(col=c(1:6,8),lty=1,lwd=2),
                  text = list(lab = levels(dat$trt)),
                  columns = 3, title = "Treatment"))

So as you can see that there is some curvature between glucose level and time, 
so a quadratic fit might be needed. 



dat$time2<-dat$time*dat$time

A straight fit like below seems reasonable:

fit<-lmer(y~trt*time+trt*time2+(time|id),dat)

Checking on random effects, it appears that variance component for random slope 
is very small, so a simpler model with random intercept only may be sufficient:

fit<-lmer(y~trt*time+trt*time2+(1|id),dat)

Now, I want to incorporate baseline response into the model in order to account 
for any baseline imbalance. I need to generate a new variable "baseline" based 
on glucose levels at time=0:

dat<-merge(dat, dat[dat$time==0,c('id','y')], by.x='id',by.y='id',all.x=T)
colnames(dat)[c(4,6)]<-c('y','baseline')

so the new fit adding baseline into the mixed model is:

fit<-lmer(y~baseline+trt*time+trt*time2+(1|id),dat)

Now my question is 1). Is the above model a reasonable thing to do? 2) when 
baseline is included as a covariate, should I remove the data points at baseline 
from the dataset? I am kind of unsure if it's reasonable to use the baseline 
both as a covariate and as part of the dependent variable values.

Next thing I want to do with this dataset is to do multiple comparisons between 
each treatment (A, B, C, D, F, G) vs. vehicle at a given time point, say time=56 
(the last time points) after adjusting the baseline imbalance. This seems to be 
done using Dunnet test. When I say "after adjusting baseline imbalance", I mean 
the comparisons should be done based on the difference between time=56 and 
time=0 (baseline), i.e. is there any difference in the change from baseline for 
treatment A (or B, C, D, F, G) vs. vehicle?. How can we test this? Will glht() 
in multcomp work for a lmer fit? If yes, how can I specify the syntax?

Finally, with the above model, how to estimate the difference (and the standard 
error) between time=56 and time=0 (baseline) for each treatment groups?

Thank you all for your attention.

John


      
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