MIXED MODELS FOR BIVARIATE RESPONSE REPEATED-MEASURES DATA USING GIBBS SAMPLING

Repeated measures data are frequently incomplete, unbalanced and corre lated. There has been a great deal of recent interest in mixed effects models for analysing such data. In this paper, we develop bivariate r esponse mixed effects models that are a generalization of linear mixed effects models for a single response variable. We describe their esti mation procedures using a Markov chain Monte Carlo method, the Gibbs s ampler. We illustrate the methods with analyses of intravenous vitamin D-3 administration for secondary hyperparathyroidism in hemodialysis patients. In these data there were two response variables on each indi vidual (PTH and calcium level). This study also suffered from attritio n, 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 PT H level was likely to be non-ignorable. We found that the posterior tr eatment effects for the PTH level by the single response model were un derestimated compared with those obtained by the bivariate response mo del, while there were little differences in the posterior features for the Ca level under both models. (C) 1997 by John Wiley & Sons Ltd.