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Related Experiment Video

Updated: Apr 21, 2026

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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The many weak instruments problem and Mendelian randomization.

Neil M Davies1, Stephanie von Hinke Kessler Scholder, Helmut Farbmacher

  • 1Medical Research Council Integrative Epidemiology Unit, University of Bristol, Barley House, Oakfield Grove, Bristol, BS8 2BN, U.K.; School of Social and Community Medicine, University of Bristol, Barley House, Oakfield Grove, Bristol, BS8 2BN, U.K.

Statistics in Medicine
|November 11, 2014
PubMed
Summary
This summary is machine-generated.

Instrumental variable (IV) methods can be biased with many weak instruments. The continuously updating estimator (CUE) and allele scores provide consistent causal effect estimates, with CUE offering a robust statistical tool for complex IV analyses.

Keywords:
ALSPACMendelian randomizationallele scorescontinuously updating estimatorheightmany weak instruments

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Last Updated: Apr 21, 2026

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Area of Science:

  • Biostatistics
  • Econometrics
  • Genetics

Background:

  • Instrumental variable (IV) methods are crucial for estimating causal effects.
  • Bias can arise in IV estimates when employing numerous weak instruments.
  • Weak instruments have limited association with the exposure of interest.

Purpose of the Study:

  • To introduce and evaluate techniques for reducing bias in IV estimates with many weak instruments.
  • To develop methods for estimating corrected standard errors in such scenarios.
  • To compare the performance of different IV estimators.

Main Methods:

  • Simulation studies to assess estimator performance under various conditions.
  • Empirical application estimating the effect of height on lung function.
  • Utilized genetic variants as instrumental variables for height.
  • Compared two-stage least squares (2SLS), limited information maximum likelihood (LIML), and continuously updating estimator (CUE).
  • Evaluated allele scores (weighted and unweighted) as single instruments.

Main Results:

  • Two-stage least squares (2SLS) showed bias with many weak instruments.
  • Limited information maximum likelihood (LIML) and continuously updating estimator (CUE) were unbiased with corrected standard errors.
  • CUE and allele scores yielded consistent causal effect estimates.
  • Allele scores were more efficient in the empirical example.
  • CUE with corrected standard errors proved a valuable tool for many weak instruments.

Conclusions:

  • Continuously updating estimator (CUE) and allele scores offer reliable methods for causal inference with weak instruments.
  • CUE provides a statistically robust approach, especially when population weights for allele scores are unknown or for joint risk factor analysis.
  • Corrected standard errors enhance the accuracy of CUE in complex IV settings.