Genome-wide association studies (GWAS) have been broadly successful in identifying genetic variants associated to complex traits and diseases, explaining a significant fraction of narrow-sense heritability and occasionally pinpointing biological mechanisms1. These studies have produced extensive databases of genetic variation (typically at the level of common single nucleotide polymorphisms (SNPs) included on genotyping arrays) in large numbers of individuals across hundreds of complex traits. Further analyses of this data can yield important insights into the genetics of complex traits, but privacy concerns and other logistical considerations often restrict access to individual-level data. On the other hand, summary association statistics, defined here as per-allele SNP effect sizes (log odds ratios for case-control traits) together with their standard errors, are often readily available and can be used to compute z-scores (per-allele effect sizes divided by their standard errors; see Figure 1); we note that in some applications, allele frequencies may also be required. A partial list of publicly available summary association statistics from large GWAS is provided in Table 1. Summary statistics also offer advantages in computational cost, which does not scale with
