relative increase of 135.9% (from 0.027 to 0.063) and 95.3% (from 0.032 to 0.063) in the median liability R2, respectively. In addition, PRS-CSx provided consistent, although relatively small, improvement over LDpred2-mult (relative increase in median R2: 8.7%) and PRS-CS-mult (relative increase in median R2: 5.9%), suggesting that in practice PRS-CSx can increase predictive power over Bayesian “mult” methods even for highly polygenic architecture (Fig. 4a; Supplementary Table 17), a scenario where the benefit of the coupled prior was reduced in simulations (Extended Data Fig. 1; Supplementary Table 2). Other performance metrics, including Nagelkerke’s R2, odds ratio (OR) per standard deviation change of PRS, and OR comparing top 10% with bottom 10% of the PRS distribution, showed a consistent pattern (Supplementary Table 17). Finally, PRS-CSx can more accurately identify individuals at high/low schizophrenia risk than alternative methods, showing a 2.9, 3.5 and 4.2-fold increase in the proportion of schizophrenia cases across the 6 testing cohorts when contrasting the top 10%, 5% or 2% of the PRS distribution with the bottom 10%, 5% or 2%, respectively (Fig. 4b; Supplementary Table 18).
