Robust Inference in High-Dimensional Multivariable Mendelian Randomization with Potentially Invalid Instruments

• Activity Number: 216 - Recent Advances in Nonparametric and Semiparametric Methods for Complex Data
• Type: Invited
• Date/Time: Tuesday, August 9, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Journal of Nonparametric Statistics
• Author(s): Lan Wang* and Yunan Wu and Baolin Wu and Yixuan Ye and Hongyu Zhao
• Companies: University of Miami and University of Taxas at Dallas and University of Minnesota and Yale University and Yale University
• Keywords: causal effects; confidence interval; high-dimensional data; inference; invalid instruments; Mendelian randomization

Abstract

We consider a new framework for Mendelian Randomization analysis with multivariate exposures and high-dimensional confounders and genetic instruments based on individual-level data without specifying an exposure model. We propose a novel confidence interval for the causal effects in the challenging setting where many instruments may have direct effects on the outcome and/or be correlated with an unmeasured confounder. The validity of the confidence intervals is established under relatively weak conditions without requiring the prior knowledge of a subset of valid instruments. The new procedure explores the sparsity of the outcome model and requires weaker conditions for identifying the causal effects with potentially invalid instruments or many weak instruments. We also extend the approach to nonlinear outcome models with Poisson-type responses. Numerically, we demonstrate that the new method has satisfactory performance and is robust to invalid instruments. The proposed method is illustrated on two real data examples from the UK Biobank.