Bayesian inference for multivariate meta-analysis Box-Cox transformation models for individual patient data with applications to evaluation of cholesterol-lowering drugs.

In this paper, we propose a class of Box-Cox transformation regression models with multidimensional random effects for analyzing multivariate responses for individual patient data in meta-analysis. Our modeling formulation uses a multivariate normal response meta-analysis model with multivariate random effects, in which each response is allowed to have its own Box-Cox transformation. Prior distributions are specified for the Box-Cox transformation parameters as well as the regression coefficients in this complex model, and the deviance information criterion is used to select the best transformation model. Because the model is quite complex, we develop a novel Monte Carlo Markov chain sampling scheme to sample from the joint posterior of the parameters. This model is motivated by a very rich dataset comprising 26 clinical trials involving cholesterol-lowering drugs where the goal is to jointly model the three-dimensional response consisting of low density lipoprotein cholesterol (LDL-C), high density lipoprotein cholesterol (HDL-C), and triglycerides (TG) (LDL-C, HDL-C, TG). Because the joint distribution of (LDL-C, HDL-C, TG) is not multivariate normal and in fact quite skewed, a Box-Cox transformation is needed to achieve normality. In the clinical literature, these three variables are usually analyzed univariately; however, a multivariate approach would be more appropriate because these variables are correlated with each other. We carry out a detailed analysis of these data by using the proposed methodology.