A standard approach to boost association power in GWAS is to leverage LD information from a population reference panel to impute genotypes at variants not typed in the study11. Imputation is traditionally performed using individual-level data, which requires substantial computational resources and can be logistically cumbersome when new reference panels become available, particularly for large consortia combining data from multiple studies. As an alternative to imputation using individual-level data, approaches have been developed to perform imputation directly at the level of summary statistics12–18 (providing an alternative to other multivariate tests19,20). The key insight of these approaches is that LD induces correlations between z-scores, which can be modeled using a multi-variate normal (MVN) distribution with variance equal to the LD correlation matrix21 (an adjustment in the LD computation is needed for z-scores estimated using mixed models22). Thus, z-scores at untyped SNPs can be imputed from observations at typed SNPs using conditional means and variances of the MVN distribution. Imputation using summary statistics recovers >80% of the information from imputation using individual-level data at common variants14–16, and is practical and efficient since
