The MTAG results for SNP j are obtained in three steps: (i) estimate the variance-covariance matrix of the GWAS estimation error, ∑^j, by using a sequence of LD score regressions, (ii) estimate the variance-covariance matrix of the SNP effects, Ω^, using method of moments, and (iii) for each SNP, substitute these estimates into equation (1). We have made available for download a Python command line tool that runs our MTAG estimation procedure (see URLs). Because each of the above steps has a closed-form solution, genome-wide analyses using the MTAG software run quickly (Online Methods).
