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In the post-genome wide association study era, an important objective is developing a more comprehensive understanding of the biological mechanisms through which genetic variants affect complex traits such as disease susceptibility. Integrative multi-omics association analyses have the potential to elucidate these underlying molecular mechanisms, and the increasing availability of summary-level data makes integrative methods that use only summary statistics as input particularly valuable. But, there are several challenges in performing integrative association analyses using summary statistics. In this dissertation, we develop novel statistical methods and computational tools to address existing challenges and limitations in the joint analyses of multi-omics data from multiple perspectives. In addition to the development of general integrative analysis methods, we make tailored developments to address specific questions in identifying molecular associations of complex trait-associated genetic variants, to integrate statistics from mediation analyses, and to identify genes that are consistent with a causal model in which their expression levels affect variation of a complex trait (such as disease susceptibility). The proposed methods and tools have been applied to study multiple diseases and traits, and they can also be broadly used in many other areas to infer multi-study joint associations, conditional associations, mediations and potential causal associations with only summary statistics as input.




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