[R] treatment effect at specific time point within mixedeffects model

[Afshartous, David]

-----Original Message-----
From: Chuck Cleland [mailto:ccleland at optonline.net] 
Sent: Friday, October 06, 2006 5:32 AM
To: Afshartous, David
Subject: Re: [R] treatment effect at specific time point within
mixedeffects model

Afshartous, David wrote:
> The data structure is a repeated measures crossover design, i.e., N 
> patients measured at 6 time points, each on drug and placebo; thus no 
> clustering of individuals within groups
> if I understand you correctly.   

	David:
 	 That is not the same as the structure of data.grp, where there
is no crossover.  I believe this makes drug a 	within-subjects effect
in the mixed model.  In the simple t-test, drug is essentially a
between-subjects effect 	since only one time is considered.  If I
understand correctly, the simple t-test is an independent sample t-test
since at a particular time each subject serves in only one drug
condition.

<DA>
sorry, the pseudo data of data.grp should have had crosover.
RE the t-test, a paired t-test would account for the dependence.

> I just ran the mixed model w/ the new contrast coding so that the 
> coefficient for Drug now tests the signifiance of Drug at Hour 3.  The

> p-value is comparable to that obtained from the paired t-test at hour 
> 3.
> 
> However, for a different dataset the relevant mixed model p-value is
> .003 while that
> for the paired t-test is .04.   
> 
> Given this data structure, does anyone have any suggestions as to what

> to look for that could explain why in one case p-values are consistent

> and in
> the other case they are not?   
> This would be especially helpful since the medical people want to 
> solely focus on hour 3 and perform the paired t-test.  Sorry to 
> belabor the question but I've been getting various
> answers to this question and would like to resolve it.   

  	Are the coefficients for this comparison the same with each
approach?
      Here is one way of doing the simple t-test which gives the
coefficient for that approach:
	lm(z ~ drug, data = data.grp, subset = (time == "Time-3"))

<DA>
but this wouldn't be a paired t-test, correct?

  	If the coefficients for this simple t-test approach and the
contrast in the mixed-model are the same, then the 	difference in
significance results from differences in the standard errors.  The
mixed-model approach takes into 	account many more observations
of z, so I would consider its estimate of the standard error to be
better than the 	estimate that only considers one time point.

<DA>
RE the coefficients: they are the same for both approaches for both my
datasets above, 
as expected.  For the latter case where the mixed model obtained much
greater significance 
than the paired t-test, I guess your explantion how it uses more data to
estimate the standards 
error is on target.  Finally, would it be okay to say that the paired
t-test is a "valid conservative 
method" for this question at a single time point if that time point is
the main endpoint of the study?  
There is an article in the British Journal of Medicne ("Analysis of
Serisal Measurments in Medical 
Research", v300, p.230, Mathews et al) that critiques testing several
separate 
time points, but I don't think their arguments invalidate doing a single
paired t-test.





hope this helps,

Chuck

--
Chuck Cleland, Ph.D.
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