MR-LDP: a two-sample Mendelian randomization for GWAS summary statistics accounting for linkage disequilibrium and horizontal pleiotropy

The proliferation of genome-wide association studies (GWAS) has prompted the use of two-sample Mendelian randomization (MR) with genetic variants as instrumental variables (IV) for drawing reliable causal relationships between health risk factors and disease outcomes. However, the unique features of GWAS demand that MR methods account for both linkage disequilibrium (LD) and ubiquitously existing horizontal pleiotropy among complex traits, which is the phenomenon wherein a variant affects the outcome through mechanisms other than exclusively through the exposure. Therefore, statistical methods that fail to consider LD and horizontal pleiotropy can lead to biased estimates and false-positive causal relationships. To overcome these limitations, we propose a probabilistic model for MR analysis to identify the casual effects between risk factors and disease outcomes using GWAS summary statistics in the presence of LD and to properly account for horizontal pleiotropy among genetic variants (MR-LDP). MR-LDP utilizes a computationally efficient parameter-expanded variational Bayes expectation-maximization (PX-VBEM) algorithm to estimate the parameter of interest and further calibrates the evidence lower bound (ELBO) for a likelihood ratio test. We then conducted comprehensive simulation studies to demonstrate the advantages of MR-LDP over the existing methods in terms of both type-I error control and point estimates. Moreover, we used two real exposure-outcome pairs (CAD-CAD and Height-Height; CAD for coronary artery disease) to validate the results from MR-LDP compared with alternative methods, showing that our method is more efficient in using all instrumental variants in LD. By further applying MR-LDP to lipid traits and body mass index (BMI) as risk factors for complex diseases, we identified multiple pairs of significant causal relationships, including a protective effect of high-density lipoprotein cholesterol (HDL-C) on peripheral vascular disease (PVD), and a positive causal effect of body mass index (BMI) on hemorrhoids.