Hi Robert:

It appears to me that you have a split-plot structure, so let me see if I
have it right.

The 'whole-plot' experiment looks like a replicated randomized block design
- the studies are the blocks, the treatments A and B are the whole-plot
treatments, each of which is assigned randomly to three subjects...basically
the 'between-subjects' part of the design.

The within-subject treatment factor is site (let's call them 1 and 2 to
avoid confusion with the treatment labels), and it makes sense to me that
the two measurements are correlated within animal, but I don't quite see why
it makes sense that they should be correlated between animals not treated
alike in the same study. I'm not in pharma, so I might learn something by
asking.  I tend to look at the means model part of a design with ANOVA just
because I'm old:

Study                      9
Treatment               1
Study * treatment    9
Subjects                40          (whole-plot error)

Site                         1
Site * Study            9
Site * Treatment      1
Site * Study * Trt     9
Residual                40          (split plot error)

Study and subjects can reasonably be thought of as random effects. If the
same sites are chosen for each subject, they would have to be fixed. The
interactions with study and subject are random. I agree with the fixed
effects specification so far, but some of the random interactions aren't
obvious to me, although I can understand how they arise from the structure
of the data.

A couple of questions:
(1) Are the studies expected to be correlated, and if so, was that the
motivation for the replicate subjects per treatment level? I'm rather
accustomed to blocks representing independent replications of the
experiment, which I would have expected by the use of different subjects in
each study. Or is all of this a necessary precaution in the clinical trial?

(2) Since sites were the same for each subject, I can see the within-subject
correlation and between-subject correlation for subjects in the same study
with the same treatment, but I'm curious as to why the Site * Study
interaction is relevant.

The whole-plot part of this is pretty easy, but I think I (and perhaps
others) would need some data to play with to work on getting the random
effects and correlation structure specified properly. It also appears you
will need to use lme4 rather than nlme for this problem due to the crossed
random effects, which lme() can't handle. That may be the source of your
trouble :)

This is certainly an interesting problem; thanks for sharing it. I might
also suggest that this be taken to the r-sig-mixed-models list, where you
are likely to have more people who are interested in this type of problem.

Cheers,
Dennis

On Thu, Nov 25, 2010 at 5:00 AM, Robert Kinley <KINLEY_ROBERT@lilly.com>wrote:

> My small brain is having trouble getting to grips with lme()
>
> I wonder if anyone can help me correctly set the   random = argument
> to lme() for this kind of setup with  (I think) 9  variance/covariance
> components ...
>
>                               Study.1          Study.2         ...
> Study.10
>  Treatment.A:   subject:  1  2  3               4  5  6      etc. 28 29 30
>
>  Treatment.B:   subject: 31 32 33            34 35 36           58 59 60
>   A variable is measured at 2 fixed sites (A and B) on each subject
>
> so we have fixed effects :-
>
>  between-Treatments
>  between-sites (A and B)
>  Treatment*site interaction
>
>
> and we have random effects :-
>
>  study effects at site A
>  study effects at site B
>  correlation between site A and site B study effects
>
>  study*treatment interaction effects at site A
>  study*treatment interaction effects at site B
>  correlation between site A and B study*treatment interaction effects
>
>  residual (between-subject) effects at site A
>  residual (between-subject) effects at site B
>  correlation between site A and B residuals (between-subject) effects
>
> My problem is formulating the  random = argument to give estimates
> of all 9 random components ...
>
> Hope someone can help ...
>
>      Robert Kinley
>
>
>
>
> Study:                  Pos tissue VC, Neg tissue VC, Pos/Neg tissue
> correlation
> Study*Group:            Pos tissue VC, Neg tissue VC, Pos/Neg tissue
> correlation
> Residual (animal):      Pos tissue VC, Neg tissue VC, Pos/Neg tissue
> correlation
>
>
>
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>
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