Sparse dimensionality reduction approaches in Mendelian randomization with highly correlated exposures
- University of Exeter, United Kingdom
- 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
Vasileios Karageorgiou
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.
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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