On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments - PubMed (original) (raw)

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

Frank Windmeijer et al. J Am Stat Assoc. 2018.

Abstract

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.

Keywords: Causal inference; Instrumental variables estimation; Invalid instruments; Lasso; Mendelian randomization..

© 2018 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

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Figures

Figure 1.

Figure 1.

(a–c) Rejection frequencies of robust Wald tests for _H_0: β = 0 at 10% level as a function of sample size, in steps of 500. Equal strength instruments design, Post-Lasso in (a), Post-ALasso in (b). Unequal strength instruments design, Post-ALasso in (c). Based on 1000 MC replications for each sample size.

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