A Random Effects Model-based Method of Moments Estimation of Causal Effect in Mendelian Randomization Studies

Recent advances in genotyping technology have delivered a wealth of genetic data, which is rapidly advancing our understanding of the underlying genetic architecture of complex diseases. Mendelian Randomization (MR) leverages such genetic data to estimate the causal effect of an exposure factor on an outcome from observational studies. In this paper, we utilize genetic correlations to summarize information on a large set of genetic variants associated with the exposure factor. Our proposed approach is a generalization of the MR-inverse variance weighting (IVW) approach where we can accommodate many weak and pleiotropic effects. Our approach quantifies the variation explained by all valid instrumental variables (IVs) instead of estimating the individual effects and thus could accommodate weak IVs. This is particularly useful for performing MR estimation in small studies, or minority populations where the selection of valid IVs is unreliable and thus has a large influence on the MR estimation. Through simulation and real data analysis, we demonstrate that our approach provides a robust alternative to the existing MR methods. We illustrate the robustness of our proposed approach under the violation of MR assumptions and compare the performance with several existing approaches.