for the remaining LD not removed by the clumping analysis. There were m = 84, 43, 159, 141, 101, 28, and 29 SNPs for BMI, WHRadjBMI, HDL-c, LDL-c, TG, SBP and DBP, respectively, after clumping. These SNP instruments are nearly independent as demonstrated by the distribution of LD scores computed from the instruments for each trait (Supplementary Fig. 7). We only included in the analysis the near-independent SNPs for the ease of directly comparing the results from GSMR with those from other methods that do not account for LD (e.g., MR-Egger). Our simulation result suggests that the gain of power by including SNPs in LD is limited (Supplementary Fig. 8). Moreover, although the GSMR approach accounts for LD, including many SNPs in moderate to high LD often results in the V matrix being non-invertible (Methods).
