through imputation of gene expression when GWAS at an individual level is available16(see Discussion). However, a critical limitation is that large-scale GWAS data are typically only publicly available at the level of summary association statistics (e.g. individual SNP effect sizes)2–4. To capitalize on the largest GWAS to date (typically available only at the summary level), we extended our approach to impute the expression-trait association statistics directly from GWAS summary statistics (Methods). In contrast to expression imputation from individual-level data16, imputation of expression-trait association from GWAS summary statistics can exploit publically available data from hundreds of thousands of samples. Linear predictors naturally extend to indirect imputation of the standardized effect of the cis-genetic component on the trait starting from only the GWAS association statistics2–4 (Methods). This allowed us to increase the effective sample size for expression-trait association testing to hundreds of thousands of individuals. By focusing only on the genetic component of expression, we avoid instances of expression-trait associations that are not a consequence of genetic variation but are driven by variation in trait (Figure 2). Our approach can be conceptualized as a test for significant cis-genetic correlation between expression and trait (see Results).
