Combining information for heterogeneous studies and rare events studies: A confidence distribution approach

OF THE DISSERTATION Combining Information for Heterogeneous Studies and Rare Events Studies: a Confidence Distribution Approach by Dungang Liu Dissertation Director: Regina Liu and Minge Xie This dissertation develops efficient statistical methodologies for combining information from independent sources. The developments focus on two settings where the studies are heterogeneous or the studies involve rare events. In these settings, the conventional combining approaches often lead to inefficient or even invalid statistical inference. In this dissertation, we propose effective and efficient combining approaches using confidence distributions. The proposed approaches are justified both theoretically and numerically. They are also shown to be superior to the conventional approaches. Combining information from multiple studies, often referred to as meta-analysis in the literature, has been used extensively in many fields, including health sciences, social sciences, and others. However, there remain many unresolved problems on how to effectively and efficiently combine information. For example, • Heterogeneous studies – When the effect of interest is not estimable in heterogeneous studies (e.g., indirect evidence), how can we utilize these studies to