Novel Bayesian multivariate hierarchical models of random coefficients of casemix adjustment variables in a survey assessing healthcare experiences
Keywords: Bayesian, Case-mix adjustment, Covariance structure, Health care quality, Kronecker product, Multilevel-multivariate model
Surveys of healthcare experiences, an important tool for assessment and improvement of healthcare quality, may be adjusted by linear models for differences in characteristics among patients of various healthcare units. Regression coefficients vary across units, inducing a multilevel model structure for individual outcomes. Two models are considered for the level-2 correlation structure of the random coefficients: completely unstructured and separable. The latter assumes that the covariance structure of regression coefficients of six outcome variables on four casemix components can be expressed as the Kronecker product of matrices for the associations across outcome measures and across predictors, potentially making the results more interpretable (31 distinct parameters instead of 300). We also extend this model with a third level to assess the stability of the coefficients across regions or across time. Again, the most general model allows unstructured correlation matrices at levels 2 and 3 while more restrictive and interpretable results are obtained by imposing separable structures at one or both levels or by assuming equal correlation matrices at both levels. This yields eight distinct 3-level models with the number of correlation parameters ranging from 600 to 32. We present Bayesian methods for fitting these models, comparing models, and selecting a parsimonious model. The results of the model comparisons and a discussion of the interpretive meaning of the substantive results will conclude the talk.