The GWAS meta-analysis was conducted using chi-square statistics based upon an imputation-quality aware fixed effect meta-analysis approach. Two sided p-values were calculated. The MTAG and GenomicSEM analysis test statistics was conducted using the GWAS meta-analysis results, and two-sided p-values were similarly calculated from chi-square distribution. The pleiotropic analysis was conducted based upon an empirical Bayes approach. The prior distribution for the effect sizes were assumed to follow a mixture distribution: with a point mass at 0 (representing the possibility the locus is not associated with the trait) and a normal distribution (representing the possibility that the locus is associated). The hyper-parameters were estimated by maximizing the marginal likelihood. The method properly accounts for the local genetic correlation and residual correlation between phenotypes. The posterior probability of association for each locus was estimated for each possible combination of 5 phenotypes, and the combination with the highest PPA was reported for each locus.
