We conducted bi-directional MR analysis for four traits: years of education (EDY)62, body mass index (BMI)29, coronary artery disease (CAD)63, and schizophrenia (SCZ)19. We denote z as a genetic variant (i.e., a SNP) that is significantly associated with x, an exposure or putative causal trait for y (the disease/trait outcome). The effect size of x on y can be estimated using a two-step least squares (2SLS)109 approach: b̂xy = b̂zy / b̂zx, where b̂zx is the estimated effect size for the SNP-trait association the exposure trait, and b̂zy is the effect size estimated for the same SNP in the GWAS of the outcome trait.
