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Title: Sparse dimensionality reduction approaches in Mendelian randomization for highly correlated exposures Authors:  Vasilis Karageorgiou - University of Exeter (United Kingdom) [presenting]
Dipender Gill - Imperial College (United Kingdom)
Jack Bowden - University of Exeter (United Kingdom)
Verena Zuber - Imperial College London (United Kingdom)
Abstract: Multivariable Mendelian randomization (MVMR) is an instrumental variable technique that generalizes the MR framework for multiple exposures. It is subject to the pitfall of multi-collinearity. The efficiency of MVMR estimates thus depends on the correlation of exposures. Dimensionality reduction techniques such as principal component analysis (PCA) provide transformations of the included variables such that they are effectively uncorrelated. We propose the use of sparse PCA (sPCA) algorithms for obtaining uncorrelated transformations of the exposures and can consequently provide more reliable summary-level estimates. The approach consists of three steps. We first apply a sparse dimensionality method and transform the SNP-exposure summary statistics into latent components. We choose a smaller number of latent components based on data-driven cutoffs, and estimate their strength as combined instruments with a novel F-statistic. Finally, we perform two-sample MR using the 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 on 118 highly correlated metabolites. As a positive control, we tested the causal effects of the transformed exposures on coronary heart disease. Compared to the conventional inverse-variance weighted MVMR method, sparse component analysis achieved a better balance of sparsity and a biologically insightful grouping of the traits.