Statistical methods for meta-analysis

Abstract

Meta-analysis has become a widely-used tool to combine findings from independent studies in various research areas. This thesis deals with several important statistical issues in systematic reviews and meta-analyses, such as assessing heterogeneity in the presence of outliers, quantifying publication bias, and simultaneously synthesizing multiple treatments and factors. The first part of this thesis focuses on univariate meta-analysis. We propose alternative measures to robustly describe between-study heterogeneity, which are shown to be less affected by outliers compared with traditional measures. Publication bias is another issue that can seriously affect the validity and generalizability of meta-analysis conclusions. We present the first work to empirically evaluate the performance of seven commonly-used publication bias tests based on a large collection of actual meta-analyses in the Cochrane Library. Our findings may guide researchers in properly assessing publication bias and interpreting test results for future systematic reviews. Moreover, instead of just testing for publication bias, we further consider quantifying it and propose an intuitive publication bias measure, called the skewness of standardized deviates, which effectively describes the asymmetry of the collected studies’ results. The measure’s theoretical properties are studied, and we show that it can also serve as a powerful test statistic. The second part of this thesis introduces novel ideas in multivariate meta-analysis. In medical sciences, a disease condition is typically associated with multiple risk and protective factors. Although many studies report results of multiple factors, nearly all meta-analyses separately synthesize the association between each factor and the disease condition of interest. We propose a new concept, multivariate meta-analysis of multiple factors, to synthesize all available factors simultaneously using a Bayesian hierarchical model. By borrowing information across factors, the multivariate method can improve statistical efficiency and reduce biases compared with separate analyses. In addition to synthesizing multiple factors, network meta-analysis has recently attracted much attention in evidence-based medicine because it simultaneously combines both direct and indirect evidence to compare multiple treatments and thus facilitates better decision making. First, we empirically compare two network meta-analysis models, contrast- and arm-based, with respect to their sensitivity to treatment exclusions. The arm-based method is shown to be more robust to such exclusions, mostly because it can use single-arm studies while the contrast-based method cannot. Then, focusing on the currently popular contrast-based method, we theoretically explore the key factors that make network meta-analysis outperform traditional pairwise meta-analyses. We prove that evidence cycles in the treatment network play critical roles in network meta-analysis. Specifically, network meta-analysis produces posterior distributions identical to separate pairwise meta-analyses for all treatment comparisons when a treatment network does not contain cycles. This equivalence is illustrated using simulations and a case study.