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Mendelian randomization is the use of genetic variants to make causalinferences from observational data. The field is currently undergoing arevolution fuelled by increasing numbers of genetic variants demonstrated to beassociated with exposures in genome-wide association studies, and the publicavailability of summarized data on genetic associations with exposures andoutcomes from large consortia. A Mendelian randomization analysis with manygenetic variants can be performed relatively simply using summarized data.However, a causal interpretation is only assured if each genetic variantsatisfies the assumptions of an instrumental variable. To provide someprotection against failure of these assumptions, robust methods forinstrumental variable analysis have been proposed. Here, we develop threeextensions to instrumental variable methods using: i) robust regression, ii)the penalization of weights from candidate instruments with heterogeneouscausal estimates, and iii) L1 penalization. Results from a wide variety ofrobust methods, including the recently-proposed MR-Egger and median-basedmethods, are compared in an extensive simulation study. We demonstrate that twomethods, robust regression in an inverse-variance weighted method and a simplemedian of the causal estimates from the individual variants, have considerablyimproved Type 1 error rates compared with conventional methods in a widevariety of scenarios when up to 30% of the genetic variants are invalidinstruments. While the MR-Egger method gives unbiased estimates when itsassumptions are satisfied, these estimates are less efficient than those fromother methods and are highly sensitive to violations of the assumptions.Methods that make different assumptions should be used routinely to assess therobustness of findings from applied Mendelian randomization investigations withmultiple genetic variants.

Robust instrumental variable methods using multiple candidate instruments with application to Mendelian randomization