On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments

Windmeijer, Frank; Farbmacher, Helmut; Davies, Neil M; Smith, George Davey

doi:10.1080/01621459.2018.1498346

Cited by 136 publications

(211 citation statements)

References 45 publications

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“…() and Windmeijer et al . () also worked on the invalid IV setting, but without making a stringent orthogonality assumption.…”

Section: Introductionmentioning

confidence: 97%

“…() and the adaptive lasso method of Windmeijer et al . (). We find that our method and that of Windmeijer et al .…”

Section: Introductionmentioning

confidence: 99%

“…We find that our method and that of Windmeijer et al . () are comparable when the 50% rule holds, whereas the median estimator suffers from coverage and optimality issues. However, when the 50% rule fails, our method dominates all these methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Confidence Intervals for Causal Effects with Invalid Instruments by Using Two-Stage Hard Thresholding with Voting

Guo

Kang

Cai

et al. 2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

201

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Summary A major challenge in instrumental variable (IV) analysis is to find instruments that are valid, or have no direct effect on the outcome and are ignorable. Typically one is unsure whether all of the putative IVs are in fact valid. We propose a general inference procedure in the presence of invalid IVs, called two‐stage hard thresholding with voting. The procedure uses two hard thresholding steps to select strong instruments and to generate candidate sets of valid IVs. Voting takes the candidate sets and uses majority and plurality rules to determine the true set of valid IVs. In low dimensions with invalid instruments, our proposal correctly selects valid IVs, consistently estimates the causal effect, produces valid confidence intervals for the causal effect and has oracle optimal width, even if the so‐called 50% rule or the majority rule is violated. In high dimensions, we establish nearly identical results without oracle optimality. In simulations, our proposal outperforms traditional and recent methods in the invalid IV literature. We also apply our method to reanalyse the causal effect of education on earnings.

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“…() and Windmeijer et al . () also worked on the invalid IV setting, but without making a stringent orthogonality assumption.…”

Section: Introductionmentioning

confidence: 97%

“…() and the adaptive lasso method of Windmeijer et al . (). We find that our method and that of Windmeijer et al .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Confidence Intervals for Causal Effects with Invalid Instruments by Using Two-Stage Hard Thresholding with Voting

Guo

Kang

Cai

et al. 2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

201

View full text Add to dashboard Cite

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“…A possible solution might be to implement a version of BMA with the genetic variants included in the regression equation for Y but this needs further investigation. Invalid instruments are also a major concern in the classical MR setting where several methods to account for this have been developed, each with their own estimation assumptions, and suitable for both summary data and individual‐level data …”

Section: Discussionmentioning

confidence: 99%

A Bayesian approach to Mendelian randomisation with dependent instruments

Shapland

Thompson

Sheehan

2018

Statistics in Medicine

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Mendelian randomisation (MR) is a method for establishing causality between a risk factor and an outcome by using genetic variants as instrumental variables. In practice, the association between individual genetic variants and the risk factor is often weak, which may lead to a lack of precision in the MR and even biased MR estimates. Usually, the most significant variant within a genetic region is selected to represent the association with the risk factor, but there is no guarantee that this variant will be causal or that it will capture all of the genetic association within the region. It may be advantageous to use extra variants selected from the same region in the MR. The problem is to decide which variants to select. Rather than selecting a specific set of variants, we investigate the use of Bayesian model averaging (BMA) to average the MR over all possible combinations of genetic variants. Our simulations demonstrate that the BMA version of MR outperforms classical estimation with many dependent variants and performs much better than an MR based on variants selected by penalised regression. In further simulations, we investigate robustness to violations in the model assumptions and demonstrate sensitivity to the inclusion of invalid instruments. The method is illustrated by applying it to an MR of the effect of body mass index on blood pressure using SNPs in the FTO gene.

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“…They hence proposed the use of “post‐lasso” estimators to reduce this bias. In the same spirit, Windmeijer et al considered post‐lasso estimators for sisVIVE in which only the SNPs identified as valid IVs in

\overset{V}{true}

are used as multiple IVs in 2SLS; they found the resulting estimator to be subject to considerably lower bias than sisVIVE. However, they also derive theoretical results that show that sisVIVE is not always consistent, in the sense that

\overset{V}{true} ↛ V

as n → ∞: in short, if the relative strengths of the valid‐IV and invalid‐IV SNPs do not satisfy the “irrepresentable condition,” then sisVIVE will not be consistent and can perform poorly.…”

Section: Estimating Causal Exposure Effectsmentioning

confidence: 99%

Assessing the robustness of sisVIVE in a Mendelian randomization study to estimate the causal effect of body mass index on income using multiple SNPs from understanding society

Bao

Clarke

Smart

2018

Statistics in Medicine

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The “some invalid, some valid instrumental variable estimator” (sisVIVE) is a lasso‐based method for instrumental variables (IVs) regression of outcome on an exposure. In principle, sisVIVE is robust to some of the IVs in the analysis being invalid, in the sense of being related to the outcome variable through pathways not mediated by the exposure. In this paper, we consider the application of sisVIVE to a Mendelian randomization study in which multiple genetic variants are used as IVs to estimate the causal effect of body mass index on personal income in the presence of unobserved confounding. In addition to analyzing data from the large‐scale longitudinal household survey Understanding Society , we conduct a simulation study to (a) assess the performance of sisVIVE in relation to that of competing robust methods like “MR‐Egger” and “MR‐Median” and (b) identify scenarios under which its absolute performance is poor. We find that sisVIVE outperforms alternative robust methods, in terms of mean‐square error, across a wide range of scenarios, but that its performance is poor in absolute terms when the presence of indirect pleiotropy leads to failure of the “InSIDE” condition, which is not explicitly required for identification. We argue that this is because the consistency criterion for sisVIVE does not identify the true causal effect when InSIDE fails.

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On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments

Cited by 136 publications

References 45 publications

Confidence Intervals for Causal Effects with Invalid Instruments by Using Two-Stage Hard Thresholding with Voting

Confidence Intervals for Causal Effects with Invalid Instruments by Using Two-Stage Hard Thresholding with Voting

A Bayesian approach to Mendelian randomisation with dependent instruments

Assessing the robustness of sisVIVE in a Mendelian randomization study to estimate the causal effect of body mass index on income using multiple SNPs from understanding society

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