Confidence Distributions and a Unifying Framework for Meta-Analysis
This article develops a unifying framework, as well as robust meta-analysis approaches, for combining studies from independent sources. The device used in this combination is a confidence distribution (CD), which uses a distribution function, instead of a point (point estimator) or an interval (confidence interval), to estimate a parameter of interest. A CD function contains a wealth of information for inferences, and it is a useful device for combining studies from different sources. The proposed combining framework not only unifies most existing meta-analysis approaches, but also leads to development of new approaches. We illustrate in this article that this combining framework can include both the classical methods of combining p-values and modern model-based meta-analysis approaches. We also develop, under the unifying framework, two new robust meta-analysis approaches, with supporting asymptotic theory. In one approach each study size goes to infinity, and in the other approach the number of studies goes to infinity. Our theoretical development suggests that both these robust meta-analysis approaches have high breakdown points and are highly efficient for normal models. The new methodologies are applied to study-level data from publications on prophylactic use of lidocaine in heart attacks and a treatment of stomach ulcers. The robust methods performed well when data are contaminated and have realistic sample sizes and number of studies.