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In observational studies, instrumental variable (IV) methods are commonlyapplied when there exists some unmeasured covariates. In MendelianRandomization (MR), constructing an allele score by using many singlenucleotide polymorphisms (SNPs) is often implemented; however, there are risksestimating biased causal effects by including some invalid IVs. Invalid IVs arecandidates of IVs associated with some unobserved variables. To solve thisproblem, we propose a novel strategy in this paper: using Negative ControlOutcomes (NCOs) as auxiliary variables. By using NCOs, we can essentialy selectonly valid IVs and exclude invalid IVs without any information of IVcandidates. We also propose the new two-step estimating procedure and prove thesemiparametric efficiency. We demonstrate the superior performance of theproposed estimator compared with existing estimators via simulation studies.

Valid Instrumental Variables Selection Methods using Negative Control Outcomes and Constructing Efficient Estimator