A robust penalized-regression-based method for multivariable Mendelian randomization using GWAS summary statistics

Abstract Mendelian randomization (MR) is a statistical approach to inferring the causal relationships from genome-wide association studies (GWAS) by using genetic variants as instrumental variables (IVs). As IVs, the selected genetic variants should be solely associated with the exposure of interest, and have no associations with confounders and the studied outcome except through the exposure. Sometimes the selected genetic variants have effects on the outcome through other pathways, a phenomenon known as horizontal pleiotropy, which makes the selected variants violate IV assumptions. Two different approaches have been proposed to address this issue: one is to improve robustness to pleiotropic effects, and the other one is to generalize univariate exposure to multivariate cases so that we can incorporate possible pathways into MR analysis. Compared to pleiotropy-robust methods, multivariable Mendelian randomization (MVMR) can uncover the exposures having direct effects on the outcome. However, measuring all possible pathways from genetic variants to the outcome in MVMR analysis is difficult. Although MVMR methods with robustness to unmeasured pleiotropy have been proposed recently, they are statistically inefficient as a result of ignoring correlations among exposures and distributions of effect sizes. Given the limitations from both directions, we propose a novel method named MVMR-PRESS that can infer causal relationships between multivariate exposures and the outcome with robustness to horizontal pleiotropic effects from unconsidered pathways. MVMR-PRESS estimates causal effects by using a Penalized Regression on Summary Statistics from GWAS considering both correlations among exposures and distributions of effect sizes. One merit of MVMR-PRESS is that samples in GWAS of different exposures can have overlaps, which allows us to include GWAS summary statistics from the same cohort or consortium. Simulation experiments showed that our method achieved the smallest bias and highest power compared to existing pleiotropy-robust MR and MVMR methods while the type 1 error rate was well-controlled. Applying MVMR-PRESS to publicly available GWAS summary statistics demonstrated that body mass index (BMI), height (HT), and low-density lipoprotein cholesterol (LDL) have significant causal effects on coronary artery disease (CAD), and BMI and high-density lipoprotein cholesterol (HDL) were causally related to type 2 diabetes (T2D). On the contrary, the causal estimates of triglycerides (TG), HDL, and total cholesterol (TC) on CAD, and the estimates of HT, LDL, TG, and TC on T2D were non-significant. In addition, we found no evidence suggesting BMI, HT, and lipid levels have causal effects on inflammatory bowel disease (IBD) and schizophrenia (SCZ).