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Valid estimation of a causal effect using instrumental variables requiresthat all of the instruments are independent of the outcome conditional on therisk factor of interest and any confounders. In Mendelian randomization studieswith large numbers of genetic variants used as instruments, it is unlikely thatthis condition will be met. Any given genetic variant could be associated witha large number of traits, all of which represent potential pathways to theoutcome which bypass the risk factor of interest. Such pleiotropy can beaccounted for using standard multivariable Mendelian randomization with allpossible pleiotropic traits included as covariates. However, the estimatorobtained in this way will be inefficient if some of the covariates do not trulysit on pleiotropic pathways to the outcome. We present a method which usesregularization to identify which out of a set of potential covariates need tobe accounted for in a Mendelian randomization analysis in order to produce anefficient and robust estimator of a causal effect. The method can be used inthe case where individual-level data are not available and the analysis mustrely on summary-level data only. It can also be used in the case where thereare more covariates under consideration than instruments, which is not possibleusing standard multivariable Mendelian randomization. We show the results ofsimulation studies which demonstrate the performance of the proposedregularization method in realistic settings. We also illustrate the method inan applied example which looks at the causal effect of urate plasmaconcentration on coronary heart disease.

An efficient and robust approach to Mendelian randomization with measured pleiotropic effects in a high-dimensional setting