MODELING HETEROGENEITY IN BAYESIAN META-ANALYSIS

Abstract

Meta-analysis has been frequently used to combine findings from independent studies in many areas. The first part of this thesis focus on a univariate meta-analysis of odds ratios for binary outcomes. We compare two different methods for conducting a meta-analysis: frequentist methods and Bayesian methods. Under the frequentist framework, we introduce three commonly used estimators of the between-study heterogeneity, namely DerSimonian–Laird (DL) estimator, maximum- likelihood (ML) estimator, and restricted maximum-likelihood (REML) estimator. We present four priors for a Bayesian framework: inverse-gamma, uniform, half-normal, and log-normal, with differ- ent sets of hyper-parameters. Finally, we introduce the general framework of performing Bayesian meta-analyses, choices of prior distributions for the heterogeneity variance, and validation of posterior inference with five real-world examples. Bayesian methods have several significant advantages over the conventional frequentist meta-analysis methods; however, they are used less frequently than frequentist methods in the current literature, primarily because researchers are not very familiar with the implementation process. A critical issue of meta-analysis is that the combined studies could be heterogeneous because of differences in study populations, design conducts, etc. Thus, heterogeneity is an issue that can affect the validity of a meta-analysis. In the existence of heterogeneity, a random-effects meta-analysis is considered an appropriate model to estimate a summary effect and a between-study variance. For many studies, conventional methods could be used to estimate the random-effects meta-analysis model,but the estimate of between-study heterogeneity could be imprecise in the case of few studies as well as this imprecision is not acknowledged. In this situation, a Bayesian random-effects meta-analysis is advantageous in accounting for all sources of uncertainty. The second part of this thesis uses Bayesian methods to examine the impact of meta-analysis characteristics on between-study heterogeneity by analyzing data from a large collection of meta-analyses with binary outcomes. We classify and examine all included meta-analyses by outcome types and intervention comparison types. We derive a set of predictive distributions for the extent of between-study variance expected in a future meta-analysis in various effect measures. These findings may help researchers to use them as informative prior distributions in new meta-analyses of binary outcomes.

The last part of this thesis quantifies the between-study heterogeneity by using prediction intervals. By reporting the prediction interval, we show how often there is a contradiction in the conclusion compared to the conclusion based on the confidence interval. We also show the benefits of reporting the prediction interval in a meta-analysis, which has a straightforward clinical meaning that may guide researchers to expect the true effects in future settings. In addition, we assess whether the previous meta-analysis successfully predicts a future study or a study not included in the meta-analysis based on publication years. This assessment is illustrated using a case study.