On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments
Open accessAbstract
We investigate the behavior of the Lasso for selecting invalid instruments in linear instrumental variables models for estimating causal effects of exposures on outcomes, as proposed recently by Kang et al. Invalid instruments are such that they fail the exclusion restriction and enter the model as explanatory variables. We show that for this setup, the Lasso may not consistently select the invalid instruments if these are relatively strong. We propose a median estimator that is consistent when less than 50% of the instruments are invalid, and its consistency does not depend on the relative strength of the instruments, or their correlation structure. We show that this estimator can be used for adaptive Lasso estimation, with the resulting estimator having oracle properties. The methods are applied to a Mendelian randomization study to estimate the causal effect of body mass index (BMI) on diastolic blood pressure, using data on individuals from the UK Biobank, with 96 single nucleotide polymorphisms as potential instruments for BMI. Supplementary materials for this article are available online.
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Recent methods such as sisVIVE and adaptive LASSO provide MR estimates that are robust to pleiotropy under certain assumptions.
“Recent methods such as sisVIVE71 and adaptive LASSO72 provide MR estimates that are robust to pleiotropy under certain assumptions.”
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- Authors
- Windmeijer, F., Farbmacher, H., Davies, N., & Davey Smith, G.
- Affiliations
- University of Bristol (GB)
- Max Planck Society (DE)
- MRC Integrative Epidemiology Unit, Bristol, United Kingdom
- Corresponding author
- Windmeijer, Frank
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2018-11-13
- Volume
- 114
- Issue
- 527
- Pages
- 1339-1350
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- PMC
- PMC6817329
- OpenAlex
- W2900183310
- Cited by
- 144
- References
- 48
- Citations by year
- 2026: 10 · 2025: 20 · 2024: 16 · 2023: 18 · 2022: 19 · 2021: 17 · 2020: 25 · 2019: 8 · 2018: 8 · 2017: 1 · 2016: 2
- FWCI
- 12.03
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Journal of the American Statistical Association (publishedVersion, other-oa)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Bristol Research (University of Bristol) (publishedVersion, other-oa)
- RePEc: Research Papers in Economics (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion, other-oa)
- Figshare (submittedVersion, cc-by)
- Econstor (Econstor) (submittedVersion)
- mediaTUM (Technical University of Munich) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Figshare (cc-by)
- Funders
- Fritz Thyssen Stiftung
- Medical Research Council (MC_UU_12013, MCUU12013/1, MC_PC_17228, MC_UU_00011/1, MC_UU_00011, MC_UU_12013/9)
- Economic and Social Research Council (ES/N000757/1)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
- Keywords
- LASSO, invalid instruments, instrumental variables, exclusion restriction, variable selection consistency, median estimator, adaptive LASSO, oracle property, Mendelian randomization, body mass index, diastolic blood pressure, single nucleotide polymorphisms
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