  Mendelian randomization is the use of genetic variants to make causal
inferences from observational data. The field is currently undergoing a
revolution fuelled by increasing numbers of genetic variants demonstrated to be
associated with exposures in genome-wide association studies, and the public
availability of summarized data on genetic associations with exposures and
outcomes from large consortia. A Mendelian randomization analysis with many
genetic variants can be performed relatively simply using summarized data.
However, a causal interpretation is only assured if each genetic variant
satisfies the assumptions of an instrumental variable. To provide some
protection against failure of these assumptions, robust methods for
instrumental variable analysis have been proposed. Here, we develop three
extensions to instrumental variable methods using: i) robust regression, ii)
the penalization of weights from candidate instruments with heterogeneous
causal estimates, and iii) L1 penalization. Results from a wide variety of
robust methods, including the recently-proposed MR-Egger and median-based
methods, are compared in an extensive simulation study. We demonstrate that two
methods, robust regression in an inverse-variance weighted method and a simple
median of the causal estimates from the individual variants, have considerably
improved Type 1 error rates compared with conventional methods in a wide
variety of scenarios when up to 30% of the genetic variants are invalid
instruments. While the MR-Egger method gives unbiased estimates when its
assumptions are satisfied, these estimates are less efficient than those from
other methods and are highly sensitive to violations of the assumptions.
Methods that make different assumptions should be used routinely to assess the
robustness of findings from applied Mendelian randomization investigations with
multiple genetic variants.
