selected instruments for diseases from the disease GWAS data (i.e., GWS SNPs for the disease, hence the instruments used in the reverse-GSMR analysis were distinct from those used in the forward-GSMR analysis). The false positive rate of reverse-GSMR is well calibrated as demonstrated by simulation under the null that there is no reverse effect (Supplementary Fig. 19). We performed a reverse-GSMR analysis of the risk factors and diseases for which there was a significant association in the forward-GSMR analysis above (Supplementary Note 7). We identified 10 significant reverse effects (i.e., the effect of disease on risk factor) in the community data and 4 in the case–control data at a FWER of 0.05 (Preverse-GSMR < 1.0 × 10−3) (Supplementary Table 13). The estimates of reverse effects were very small compared with those of the forward effects. To avoid an underpowered test, we limited the reverse-GSMR analysis to diseases with more than 10 instruments. Given the fact that some of the small estimates of reverse effects were highly significant (Supplementary Table 13), it is unlikely that the large difference in the estimated effect size between the forward and reverse analyses is due to the lack of power in the reverse analysis. We
