Fig. 1

The explanation of Mendelian randomization (MR) analysis by a directed acyclic graph. The accuracy of estimating causality using MR analyses is based on the following three assumptions: (1) The instrumental variable (IV) associates robustly with the exposure (IV assumption 1). This assumption can be satisfied in that SNPs are selected using GWAS levels (P < 5 × 10^− 8), which suggests that potential bias from weak IV should not be substantial. (2) The IV is independent of the combined influence of all confounders (IV assumption 2). For the same population and reference, we assess the correlation of linkage disequilibrium between SNPs associated robustly with exposure. If the correlation coefficient is higher, the corresponding selected SNPs will be discarded. (3) The IV is independent of the outcome given the exposure and confounders (IV assumption 3). Horizontal pleiotropy (that IVs influence the outcome through alternative pathways other than the exposure) could violate this assumption. This assumption can be checked by using MR-Egger regression