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

Frank Windmeijer1,2, Helmut Farbmacher3, Neil Davies2,4

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Summary
This summary is machine-generated.

The Lasso may miss strong invalid instruments in causal inference. A new median estimator consistently identifies invalid instruments, enabling robust causal effect estimation, even in Mendelian randomization studies.

Keywords:
Causal inferenceInstrumental variables estimationInvalid instrumentsLassoMendelian randomization.

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Area of Science:

  • Econometrics
  • Biostatistics
  • Genetics

Background:

  • Instrumental variables (IV) models are crucial for estimating causal effects.
  • The Lasso is a method used for variable selection in statistical models.
  • Invalid instruments violate the exclusion restriction, potentially biasing causal effect estimates.

Purpose of the Study:

  • To investigate the performance of the Lasso in selecting invalid instruments within linear IV models.
  • To propose a novel, consistent estimator for causal effects when invalid instruments are present.
  • To demonstrate the utility of the proposed estimator in Mendelian randomization (MR) studies.

Main Methods:

  • Analysis of Lasso behavior with invalid instruments in linear IV models.
  • Development of a median-based estimator for causal effects.
  • Application of the median estimator for adaptive Lasso estimation to achieve oracle properties.
  • Utilizing UK Biobank data for a Mendelian randomization study on BMI and diastolic blood pressure.

Main Results:

  • The Lasso may fail to consistently select strong invalid instruments.
  • The proposed median estimator demonstrates consistency when less than 50% of instruments are invalid.
  • Consistency of the median estimator is independent of instrument strength and correlation structure.
  • Adaptive Lasso estimation using the median estimator yields an estimator with oracle properties.

Conclusions:

  • The Lasso is not always reliable for invalid instrument selection in IV analysis.
  • The novel median estimator offers a consistent approach to causal effect estimation in the presence of invalid instruments.
  • The proposed method is applicable to real-world genetic epidemiology studies, such as MR analyses.