Mendelian randomization (MR) is a method that uses genetic variants as instrument variables to investigate causality in epidemiology. The application of MR has increased over the years due to genotype-exposure and genotype-disease estimates being published in large genome-wide association studies (GWAS). This research investigates statistical models using GWAS estimates.
To increase the application of Bayesian models in MR, an R package mrbayes, which implements univariate and multivariate Bayesian estimation for commonly used two-sample MR estimators, specifically; the inverse variance weighted (IVW), MR-Egger, and radial MR-Egger models. The thesis investigated the use of multivariate Bayesian models with hierarchical priors (BayesLasso, Horseshoe, and Horseshoe+) that account for high-throughput data. Simulations showed these models produced consistent estimates in the presence of pleiotropy and invalid instruments. This thesis also investigated weighted and conditional quantile estimators. Quantile models were shown to produce less bias estimates in simulations.
This thesis has described and reviewed the MR approach and then developed and assessed Bayesian methods for genotype summary level data for application in MR analyses. This research shows how prior distributions can be used to make MR models more robust to the standard IV assumptions.