  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.
