Fig. 1. Schematic of MRAID.

MRAID is an MR method that infers the causal effect of an exposure on an outcome in the presence of unmeasured confounder by using SNPs as instrumental variables. MRAID first obtains an initial set of candidate SNP instruments that are marginally associated with the exposure (SNP₁, …, SNP_p) and that are in potential LD with each other (LD plot on left). MRAID imposes a sparsity assumption on the instrumental effects of the candidate SNPs to divide instruments with nonzero effects (SNP set 1) and zero effects (SNP set 2) on the exposure. Among the selected instruments (SNP set 1), MRAID assumes that a proportion of them display horizontal pleiotropic effects that are uncorrelated with instrumental effects (blue path) and that another proportion of them display horizontal pleiotropic effects that are correlated with instrumental effects (orange path). Among the nonselected instrument candidates (SNP set 2), MRAID also assumes that a proportion of them display horizontal pleiotropic effects that are uncorrelated with instrumental effects (blue path). Overall, MRAID models jointly all genome-wide significant SNPs that are in potential LD with each other and performs automated instrument selection among them to identify suitable instruments. MRAID explicitly accounts for both correlated and uncorrelated horizontal pleiotropy and relies on a likelihood framework for effective and scalable inference.