  In observational studies, instrumental variable (IV) methods are commonly
applied when there exists some unmeasured covariates. In Mendelian
Randomization (MR), constructing an allele score by using many single
nucleotide polymorphisms (SNPs) is often implemented; however, there are risks
estimating biased causal effects by including some invalid IVs. Invalid IVs are
candidates of IVs associated with some unobserved variables. To solve this
problem, we propose a novel strategy in this paper: using Negative Control
Outcomes (NCOs) as auxiliary variables. By using NCOs, we can essentialy select
only valid IVs and exclude invalid IVs without any information of IV
candidates. We also propose the new two-step estimating procedure and prove the
semiparametric efficiency. We demonstrate the superior performance of the
proposed estimator compared with existing estimators via simulation studies.
