The key assumption of MTAG is that all SNPs share the same variance-covariance matrix of effect sizes across traits. This assumption is strong and is violated in many circumstances, most intuitively in scenarios where some SNPs influence only a subset of the traits. Even if this assumption is not satisfied, however, we show analytically that MTAG is a consistent estimator and that its effect estimates always have a lower genome-wide mean squared error than the corresponding single-trait GWAS estimates. Hence, polygenic scores constructed from MTAG results are expected to outperform GWAS-based predictors very generally.
