from 0.75 to 0.99 with a mean of 0.91 (Supplementary Table 4), suggesting strong genetic overlaps for the diseases between the two cohorts. We therefore meta-analyzed the data of the two cohorts to maximize power using the inverse-variance meta-analysis approach31. Because OR is free of the ascertainment bias in a case–control study, the effect size (logOR) of a SNP on disease in the general population can be approximated by that from a case–control study assuming that disease in the case–control study is defined similarly as that in the general population. Therefore, GSMR can be applied to data with SNP effects on the risk factor from a population-based study and SNP effects on the disease from an ascertained case–control study, and the estimated causative effect of risk factor on disease should be interpreted as that in the general population. We therefore included in the analysis summary data for 11 diseases from published case–control studies (n = 18,759–184,305) (Supplementary Table 5). The estimated SNP effects and standard errors (SE) for age-related macular degeneration (AMD) were not available in the summary data32, which were estimated from z-statistics using an approximate approach (Supplementary Note 3).
