Bayesian network meta-regression models for multivariate aggregate responses with partially observed or completely...

In this paper, we propose a Bayesian multivariate network meta-regression model to compare multiple treatments used to treat cardiovascular and diabetes diseases, where the multivariate aggregate outcomes include low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, and triglycerides. We assume a log-linear regression model for the standard deviation of the treatment random effects to overcome the difficulty that some treatments may present only in a single study. As the within-study sample covariance matrix $\boldsymbol {S}$ is partially observed or completely missing and the within-study sample correlations are not observed at all, we postulate a hierarchical structure on the unknown within-study covariance matrices. We further develop a Markov chain Monte Carlo sampling algorithm to sample from the posterior distribution and a Monte Carlo procedure to rank the treatment effects for the multivariate outcomes. DIC is used for model comparison. Two variations of DIC are further developed to quantify (i) the overall improvement in the fit and (ii) the gain in the fit of each outcome due to the multivariate model versus the univariate model alone. A detailed analysis of the aggregate data from real randomized controlled trials is carried out to further demonstrate the proposed methodology.