Statistical Methods for cis-Mendelian Randomization

Mendelian randomization is the use of genetic variants to assess the existence of a causal relationship between a risk factor and an outcome of interest. In this paper we focus on Mendelian randomization analyses with many correlated variants from a single gene region, and particularly on cis-Mendelian randomization studies which uses protein expression as a risk factor. Such studies must rely on a small, curated set of variants from the studied region; using all variants in the region requires inverting an ill-conditioned genetic correlation matrix and results in numerically unstable causal effect estimates. We review methods for variable selection and causal effect estimation in cis-Mendelian randomization, ranging from stepwise pruning and conditional analysis to principal components analysis, factor analysis and Bayesian variable selection. In a simulation study, we show that the various methods have a comparable performance in analyses with large sample sizes and strong genetic instruments. However, when weak instrument bias is suspected, factor analysis and Bayesian variable selection produce more reliable inference than simple pruning approaches, which are often used in practice. We conclude by examining two case studies, assessing the effects of LDL-cholesterol and serum testosterone on coronary heart disease risk using variants in the HMGCR and SHBG gene regions respectively.