Dear All,
I am interested in using random effects/ mixed effects models for
estimation purposes.  Suppose I wish to study 7 treatments in each of 3
clinical
studies with treatments allocated among studies as indicated;
study 1: trt_1, trt_2, trt_3;
study 2: trt_1, trt_4, trt_5;
study 3: trt_1,trt_6, trt_7.

I recognize the fact that this design set up is asymmetric and probably has
little to recommend it.  I am convinced that complete pooling is
inappropriate.  Nevertheless, I want to analyze this data using lmer/lme or
Winbugs.

I believe this study design imposes certain conditional exchangeability
constraints.  For example, given study 1 it would seem to follow that trt2
and trt3 are exchangeable.
For this reason it would seem the model formulation below is reasonable:

trt_i ~ N(s1, sigma^2); i = 2,3
trt_i ~ N(s2, sigma^2); i = 4,5
trt_i ~ N(s3, sigma^2); i = 6,7

Above s1, s2, and s3 denote random effects associated with the three
treatment pairs which I believe may be considered to be exchangeable.

In addition, we have:
trt_1 ~ N(s0, sigma0^2)
where s0 = 1/3*(s1 + s2 + s3)

If I went ahead and imposed vague priors on the appropriate parameters
above, I believe I could set up a WINBUGS program to obtain posterior
estimates for each trt_i; i = 1, 2, ..., 7.  My question: is it possible
to set up and solve this problem using lmer/lme?  If so how would I do it?

Thank you for any assistance on this question.

Regards,
Paul Schmitt

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