then calculated the out-of-sample expected R2 of a PGI derived from a joint analysis of the candidate and supplementary phenotype summary statistics. If the expected R2 exceeded 0.01, then we used the joint-analysis output to construct a “multi-trait PGI” for the phenotype. When both single-trait and multi-trait PGIs are available, the multi-trait PGI generally has greater predictive power, but the single-trait PGI may be better suited for some applications (see Supplementary Methods).