  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. Here, we focus on two-sample summary-data Mendelian randomization
analyses with many correlated variants from a single gene region, and
particularly on cis-Mendelian randomization studies which use 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 estimation in cis-Mendelian randomization with summary-level
data, 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 inferences 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.
