[R-sig-ME] Model for irregular design

paul pwschmitt at gmail.com
Mon Aug 6 22:08:16 CEST 2012

Dear All,
I am interested in using random effects/ mixed effects models for 
estimation purposes.  Suppose I 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 will assume 
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 treatment 
pairs which may be considered 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.


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