Large consortia often combine multiple GWAS studies into a single aggregate analysis to boost power for discovering SNP associations of small effect. Studies are combined either by jointly analyzing summary association results from each study (meta-analysis) or by re-analyzing individual-level data across all studies (mega-analysis)3. It has been shown that meta-analysis attains similar power for association as mega-analysis, with fewer privacy constraints and logistical challenges (since only summary association data is shared across studies)4. Meta-analysis is usually performed using fixed-effects approaches, which assume that true effect sizes are the same across studies. Under the assumption that causal effect sizes may differ across studies, this heterogeneity can be explicitly modeled using random-effects methods, which include an extra variance term in the model to account for heterogeneity. Traditional random-effects methods allow for heterogeneity under the null model, leading to low power even when heterogeneity is present. This motivated the development of a random-effects method based on a null model of no-heterogeneity, which increases power over traditional random-effects methods5. Under this framework, a statistical test against a null model of no-heterogeneity can be
