  When genetic variants in a gene cluster are associated with a disease
outcome, the causal pathway from the variants to the outcome can be difficult
to disentangle. For example, the chemokine receptor gene cluster contains
genetic variants associated with various cytokines. Associations between
variants in this cluster and stroke risk may be driven by any of these
cytokines. Multivariable Mendelian randomization is an extension of standard
univariable Mendelian randomization to estimate the direct effects of related
exposures with shared genetic predictors. However, when genetic variants are
clustered, a Goldilocks dilemma arises: including too many highly-correlated
variants in the analysis can lead to ill-conditioning, but pruning variants too
aggressively can lead to imprecise estimates or even lack of identification. We
propose multivariable methods that use principal component analysis to reduce
many correlated genetic variants into a smaller number of orthogonal components
that are used as instrumental variables. We show in simulations that these
methods result in more precise estimates that are less sensitive to numerical
instability due to both strong correlations and small changes in the input
data. We apply the methods to demonstrate the most likely causal risk factor
for stroke at the chemokine gene cluster is monocyte chemoattractant protein-1.
