Statistical Methods for Assessing Publication Bias and Heterogeneity in Meta-Analysis

Meta-analysis has been a popular statistical tool to combine scientific findings from multiple studies addressing the same topic. Publication bias and heterogeneity are two critical issues that may influence the validity of the synthesized results. This dissertation focuses on statistical methods and applications for assessing these two issues in meta-analyses of medical research, including empirically evaluating the trim-and-fill method, summarizing various Egger-type regressions, proposing a Bayesian model to assess publication bias, and extending the Bayesian framework to quantify between-study heterogeneity. Firstly, we implement the widely-used trim-and-fill method, which can both detect and adjust publication bias, to a large database of meta-analyses in the Cochrane Library and investigate its overall empirical performance. The findings offer practical guidelines and recommendations for the proper application of the method. Secondly, we examine the most popular method, Egger's regression test, to assess publication bias. As the error term in the original regression test was not specified, several variants of this regression are summarized and compared; their performance is investigated based on 51 high-quality meta-analyses collected from the BMJ. Thirdly, although Egger's regression is simple and easy to implement, it shows inflated false positive rates for meta-analyses with binary outcomes. Therefore, we further propose a new approach to assessing publication bias via Bayesian hierarchical models to reduce the inflation of false positive rates for meta-analyses of odds ratios. The proposed method is evaluated by conducting simulations, real-world analysis, and sensitivity analysis. Lastly, the assessment of heterogeneity in the meta-analysis may be underestimated due to sampling errors. We extend the Bayesian framework to quantify heterogeneity in meta-analyses of odds ratios, which aims to account for the non-ignorable sampling errors. The Bayesian approach produces more acceptable results compared to the frequentist method in specific settings, especially for those meta-analyses of small studies with relatively rare event rates.