Baseline should appear only as a baseline and should be removed from
the set of longitudinal responses. This is often done with a merge( )
operation.
Frank
Frank E Harrell Jr Professor and Chairman School of Medicine
Department of Biostatistics Vanderbilt University
On Tue, 7 Sep 2010, array chip wrote:
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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