Sparse dimensionality reduction approaches in Mendelian randomization with highly correlated exposures

  1. Vasileios Karageorgiou  Is a corresponding author
  2. Dipender Gill
  3. Jack Bowden
  4. Verena Zuber
  1. University of Exeter, United Kingdom
  2. Imperial College London, United Kingdom

Abstract

Multivariable Mendelian randomization (MVMR) is an instrumental variable technique that generalizes the MR framework for multiple exposures. Framed as a linear regression problem, it is subject to the pitfall of multi-collinearity. The bias and efficiency of MVMR estimates thus depends heavily on the correlation of exposures. Dimensionality reduction techniques such as principal component analysis (PCA) provide transformations of all the included variables that are effectively uncorrelated. We propose the use of sparse PCA (sPCA) algorithms that create principal components of subsets of the exposures with the aim of providing more interpretable and reliable MR estimates. The approach consists of three steps. We first apply a sparse dimension reduction method and transform the variant-exposure summary statistics to principal components. We then choose a subset of the principal components based on data-driven cutoffs, and estimate their strength as instruments with an adjusted F-statistic. Finally, we perform MR with these transformed exposures. This pipeline is demonstrated in a simulation study of highly correlated exposures and an applied example using summary data from a genome-wide association study of 97 highly correlated lipid metabolites. As a positive control, we tested the causal associations of the transformed exposures on CHD. Compared to the conventional inverse-variance weighted MVMR method and a weak-instrument robust MVMR method (MR GRAPPLE), sparse component analysis achieved a superior balance of sparsity and biologically insightful grouping of the lipid traits.

Data availability

The GWAS summary statistics for the metabolites (http://www.computationalmedicine.fi/data/NMR_GWAS/) and CHD(http://www.cardiogramplusc4d.org/) are publicly available. We provide code for the SCA function, the simulation study and related documentation on github (https://github.com/vaskarageorg/SCA_MR/).

Article and author information

Author details

  1. Vasileios Karageorgiou

    University of Exeter, Exeter, United Kingdom
    For correspondence
    vk282@exeter.ac.uk
    Competing interests
    No competing interests declared.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-7173-9967
  2. Dipender Gill

    Department of Epidemiology and Biostatistics, Imperial College London, London, United Kingdom
    Competing interests
    Dipender Gill, is a part-time employee of Novo Nordisk.
  3. Jack Bowden

    University of Exeter, Exeter, United Kingdom
    Competing interests
    No competing interests declared.
  4. Verena Zuber

    Department of Epidemiology and Biostatistics, Imperial College London, London, United Kingdom
    Competing interests
    No competing interests declared.

Funding

State Scholarships Foundation

  • Vasileios Karageorgiou

Expanding Excellence in England

  • Vasileios Karageorgiou
  • Jack Bowden

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Reviewing Editor

  1. Siming Zhao, Dartmouth College, United States

Version history

  1. Received: May 6, 2022
  2. Preprint posted: June 16, 2022 (view preprint)
  3. Accepted: April 18, 2023
  4. Accepted Manuscript published: April 19, 2023 (version 1)
  5. Version of Record published: May 30, 2023 (version 2)

Copyright

© 2023, Karageorgiou et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.

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  1. Vasileios Karageorgiou
  2. Dipender Gill
  3. Jack Bowden
  4. Verena Zuber
(2023)
Sparse dimensionality reduction approaches in Mendelian randomization with highly correlated exposures
eLife 12:e80063.
https://doi.org/10.7554/eLife.80063

Share this article

https://doi.org/10.7554/eLife.80063

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