by environmental factors. The results remain unchanged when we removed SNPs in the major histocompatibility complex (MHC) region (Supplementary Fig. 21). The result, however, could be biased if there are SNPs that have strong pleiotropic effects on both risk factor and disease. For example, the result for LDL-c and Alzheimer’s disease could have been biased due to 16 pleiotropic SNPs (Fig. 4). There are three lines of evidence that our results are not driven by pleiotropy between risk factor and disease. First, as demonstrated in the example above, we have used the HEIDI-outlier approach that removes instruments with strong putative pleiotropic effects (Figs. 3 and 4) and we have confirmed by simulation that the GSMR estimate is unbiased in the presence of LD (Supplementary Table 1; Supplementary Fig. 1). After the HEIDI-outlier filtering, the instruments selected for risk factors did not show strong associations with the diseases except for those highly related diseases and traits (e.g., lipids and dyslipidemia, blood pressures, and hypertensive disease) (Supplementary Fig. 18). Note that the test-statistics decreased slightly after filtering SNPs by HEIDI-outlier (Supplementary Fig. 22), indicating that the result from the analysis with HEIDI-outlier filtering is more conservative. Second, the estimates of bxy were
