Bayesian Network Meta-Analysis with Applications to Cholesterol Lowering Drugs

Network Meta-Analysis (NMA) is an analysis of synthesizing information from multiple independent sources, especially randomized controlled trials (RCTs). The advantages of NMA include: borrowing evidence from indirect treatment comparisons to strengthen confidence in decision making; simultaneously comparing multiple treatments. There are two major research issues in NMA. One is the effect size variability between studies, which is termed as statistical heterogeneity. The other is the incompatibility that arises between direct and indirect comparisons, which is coined as evidence inconsistency. This dissertation is motivated by the real network meta data, which includes 29 RCTs of 11 different treatments. This dataset is composed of three continuous aggregate outcomes and 10 aggregate covariates. In order to compare these treatments while adjusting for aggregate covariates, we develop network meta-regression models with multivariate random effects assumptions for treatment effects and assume a general multivariate \textit{t} distribution for the random effects. To circumvent the issue that some variances of the random effects cannot be estimated due to the fact that some treatments are involved only in a single trials, we propose to formulate possible sets of groups of treatments according to their clinical mechanisms of action, and further use the Bayesian comparison criteria to select the best grouping. We also extend the grouping approach to a modeling approach and assume a log-linear model for the variances of the random effects. The modeling approach is more flexible so that the variances can depend on the arm-by-trial-level aggregate covariates. To address the inconsistency detection issue, we initiate a novel approach and start with a general fixed effects model without any assumptions. We investigate consistency by constructing linear hypotheses and show that the consistency assumption for each loop provides some restrictions on the treatment effect parameters, therefore equivalent to the hypotheses for certain contrasts of parameters. We carry out a detailed analysis of the network meta-data using the proposed methodologies. A simulation study is conducted to compare the proposed Bayesian inconsistency detection approach to a classic frequentist approach. For all the computations, we checked convergence of MCMC samples by examining trace plots and sample correlations