Meta-analysis through combining confidence distributions

This dissertation develops a set of new statistical methods for synthesizing joint information of multiple parameters from different sources by combining multivariate normal confidence distributions. These methods support the development of an asymptotic efficient network meta-analysis approach and also several robust multivariate meta-analysis approaches. Both theoretical and numerical results show that the developed methods are superior to the conventional frequentist meta-analysis approach and the commonly used Bayesian methods. They also indicate that the developed approaches can mitigate effectively the undue impact from potential outlying studies. Meta-analysis generally refers to the process of systemically combining the results from independent but similar studies in support of data-driven decision making. It has been widely used in many fields, including clinical researches, social sciences, among others. Many methods have been developed to combine information effectively and efficiently. However, there still remain several challenging problems. This dissertation aims to solve two challenging problems that are often seen in meta-analysis. The first part of this dissertation is on how to efficiently incorporate indirect evidence in the network meta-analysis setting, for which studies in the meta-analysis are from different sources, where target parameters are only partially in common. For example, suppose the primary objective of a meta-analysis is to assess the comparative effectiveness of two experimental treatments. Some studies may directly compare these two treatments and provide direct evidence, while other studies may compare one of the two treatments to placebo and thus provide only indirect evidence. Network meta-analysis aims to strengthen the pairwise direct comparison by borrowing information from indirect comparisons. The developed network meta-analysis approach can efficiently combine all studies from a network of direct and indirect evidence, and, moreover, effectively include studies that compare more than two treatments. The second part of this dissertation is on how to mitigate effectively the effect of inconsistent or outlying studies in the meta-analysis. Those studies may stem from different designs, populations, or objectives, and thus may lead to parameter values which are drastically different from the common parameter values. Such studies, if included in meta-analysis, would provide inconsistent or even outlying information. However, in many applications, it can be difficult or even impossible to identify such inconsistent or outlying studies. Therefore, instead of identifying those studies during the data collecting process, it is more beneficial to down-weight or exclude potential inconsistent studies during the combining process. Hence, we proceed to develop two robust multivariate meta-analysis approaches. One approach assumes that the number of studies goes to infinity, whereas the other assumes that the number of studies is finite but each study size may go to infinity. These approaches are shown to be robust against the effect of outlying studies, as well as model misspecifications for which the outlying studies have not been excluded in the modeling process. We present both theoretical and numerical results to show that these two robust approaches achieve high breakdown points and retain relatively high efficiency in comparison with the most efficient approach. Finally, an R package gmeta has been developed to facilitate the use of the unified univariate meta-analysis framework proposed in Xie et al. (2011). The function gmeta() can combine p-values and fit meta-analytic models using efficient and robust approaches. Furthermore, we demonstrate that the same framework can also unify the two commonly used meta-analysis methods, the Mantel-Haenszel method and the Peto's method, and the two exact combining methods proposed in Tian et al. (2009) and Liu et al. (2013), all for synthesizing inference from 2x2 tables. To visualize the results from the combining process, our gmeta() automatically generates an extended forest plot that displays individual and combined confidence distributions.Ph. D.Includes bibliographical referencesIncludes vitaby Guang Yan