Meta-analysis is essential to combine the results of genome-wide association studies (GWASs). Recent large-scale meta-analyses have combined studies of different ethnicities, environments and even studies of different related phenotypes. These differences between studies can manifest as effect size heterogeneity. We previously developed a modified random effects model (RE2) that can achieve higher power to detect heterogeneous effects than the commonly used fixed effects model (FE). However, RE2 cannot perform meta-analysis of correlated statistics, which are found in recent research designs, and the identified variants often overlap with those found by FE.