Mixed models for bivariate response repeated measures data using Gibbs sampling.

Repeated measures data are frequently incomplete, unbalanced and correlated. There has been a great deal of recent interest in mixed effects models for analysing such data. In this paper, we develop bivariate response mixed effects models that are a generalization of linear mixed effects models for a single response variable. We describe their estimation procedures using a Markov chain Monte Carlo method, the Gibbs sampler. We illustrate the methods with analyses of intravenous vitamin D3 administration for secondary hyperparathyroidism in hemodialysis patients. In these data there were two response variables on each individual (PTH and calcium level). This study also suffered from attrition, like many longitudinal studies. While, considering the study design, it was reasonable to assume the drop-out mechanism for the calcium (Ca) level to be 'missing at random', the drop-out mechanism for the PTH level was likely to be non-ignorable. We found that the posterior treatment effects for the PTH level by the single response model were underestimated compared with those obtained by the bivariate response model, while there were little differences in the posterior features for the Ca level under both models.