The GSMR paper

This paper aims to test for putative causal association between a risk factor and a disease using summary-level data from genome-wide association studies (Zhu et al. 2018 Nat. Commun.).

In this paper we developed three useful methods
1) a generalized summary--data-based Mendelian randomization approach (GSMR). cnsgenomics.com/software/gcta/#GSMR

2) a HEIDI-outlier filtering approach to remove SNPs instruments with pleiotropic effects on both exposure and outcome from the GSMR analysis. cnsgenomics.com/software/gcta/#GSMR

3) A summary-data-based covariate analysis, i.e. GWAS analysis for one trait conditioning on other traits using summary statistics. cnsgenomics.com/software/gcta/#mtCOJO

Corrigendum

In the Supplementary Note 1 (page 3 of the supplementary file),
y = x * b_xy + z_p * b_zpy + c + e_y should be changed to y = x * b_xy + z_p * b_zpy + c + e_xy
var(e_xy) should equal to var(x * b_xy + z_p * b_zpy) * (1/(R²_xy + R²_zpy) - 1) - var(c) * (1 + 2 * b_xy)