I have encountered problems with the Bayesian analysis of a crossover trial with three treatments in three periods using six treatment sequences (3-by-6 Williams design). SAS PROC MCMC does not yield the correct estimates for between and within subject variability, and the standard deviations of the parameters are too large. The data are analyzed using a linear mixed effects model with fixed effects for the factors treatment, period and sequence, and subject as random effect. The Bayesian analysis uses non-informative priors for all fixed effect parameters. Treatment effects (trt1, trt2) shall be estimated as well as the between and within subject variability standard deviations (sd_s, sd). SAS PROC MCMC does not provide acceptable estimates for sd=9.1 and sd_s=13.6. Since I use non-informative priors, this can be compared with the corresponding PROC MIXED in the framework of a frequentist analysis, which gives values SD=6.2 and SD_s=6.0 for this example dataset. Furthermore, the analysis of the same dataset with the same model implemented in R/WinBUGS or using the R function lme also yields the latter results. Therefore I think that the results of proc MCMC are incorrect. An example dataset and a code for the analysis is attached.
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