  Mendelian randomization uses genetic variants to make causal inferences about
the effect of a risk factor on an outcome. With fine-mapped genetic data, there
may be hundreds of genetic variants in a single gene region any of which could
be used to assess this causal relationship. However, using too many genetic
variants in the analysis can lead to spurious estimates and inflated Type 1
error rates. But if only a few genetic variants are used, then the majority of
the data is ignored and estimates are highly sensitive to the particular choice
of variants. We propose an approach based on summarized data only (genetic
association and correlation estimates) that uses principal components analysis
to form instruments. This approach has desirable theoretical properties: it
takes the totality of data into account and does not suffer from numerical
instabilities. It also has good properties in simulation studies: it is not
particularly sensitive to varying the genetic variants included in the analysis
or the genetic correlation matrix, and it does not have greatly inflated Type 1
error rates. Overall, the method gives estimates that are not so precise as
those from variable selection approaches (such as using a conditional analysis
or pruning approach to select variants), but are more robust to seemingly
arbitrary choices in the variable selection step. Methods are illustrated by an
example using genetic associations with testosterone for 320 genetic variants
to assess the effect of sex hormone-related pathways on coronary artery disease
risk, in which variable selection approaches give inconsistent inferences.
