For each trait, we assess the gain in average power from MTAG relative to the GWAS results by the increase in the mean χ2-statistic. We use this increase to calculate how much larger the GWAS sample size would have to be to attain an equivalent increase in expected χ2 (Online Methods). We find that the MTAG analysis of DEP, NEUR, and SWB yielded gains equivalent to augmenting the original samples sizes by 27%, 55%, and 55%. The resulting GWAS-equivalent sample sizes are thus 449,649 for DEP, 260,897 for NEUR, and 600,834 for SWB.
