Sparse Dimensionality Reduction Approaches in Mendelian Randomization with highly correlated exposures

Abstract

ABSTRACTMultivariable 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 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 and may provide 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 118 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.Key MessagesIn multivariable MR, investigation of multiple highly correlated exposures can hinder the efficiency of the estimators and mask true associations.Dimensionality reduction approaches such as principal component analysis (PCA) appear to be effective in summarising the variant-exposure summary statistics data in an example of correlated metabolite data.Sparse PCA approaches have the additional benefit of providing interpretable PCs as only a few exposures contribute to each. This benefit is shown in simulation studies where there is a gain in accuracy over PCA.In a positive control analysis, the sparse PCs were representing biologically meaningful groups of metabolites (VLDL, LDL, HDL) and in general were associated with coronary heart disease in an anticipated mannert.