Lin, Zhaotong2023-11-282023-11-282023-06https://hdl.handle.net/11299/258791University of Minnesota Ph.D. dissertation. June 2023. Major: Biostatistics. Advisor: Wei Pan. 1 computer file (PDF); xvi, 227 pages.Mendelian randomization (MR) has been increasingly applied for causal inference among traits, e.g. between potential risk factors and diseases, with observational data by using genetic variants as instrumental variables (IVs). Despite many successful MR applications, there are several gaps in the current literature to be filled. For example, only few (if any) MR methods can handle the violation of all IV assumptions, sample overlap in the GWAS data and/or linkage disequilibrium among IVs. And most MR applications only consider the total causal effect of one trait on the other. In this dissertation, we consider these important aspects to improve the robustness and effectiveness of MR. For the first project, we propose a two-step approach called Graph-MRcML, where we first apply an extended MR method to infer a causal network of total effects among multiple traits, then we modify a graph deconvolution algorithm to infer the corresponding network of direct effects. For the second project, we take a different route to consider multivariable MR, which includes multiple exposures in the model and estimates the direct effect of each exposure on the outcome while adjusting for possible mediating effects of other exposures. We propose an efficient and robust MVMR method based on constrained maximum likelihood, called MVMR-cML. For the third project, we move from polygenic MR to cis-MR, which uses correlated cis-variants from a single genomic region, compared to independent variants across the whole genome. A major difference is the need for taking into account linkage disequilibrium among cis-variants, for which we propose a robust cisMR-cML method. We conduct theoretical investigations, extensive simulations and real data applications to showcase the advantages of the three proposed methods in this work.enThesis or Dissertation