Figure 1.

MUSSEL workflow

(Step 0) Apply LDpred2 to each of the K training populations (ancestry groups) to obtain estimated causal SNP proportions ($p_k,k=1,\dots ,K$) and heritability ($h_k^2,k=1,\dots ,K$) parameters based on the tuning set; these parameters will be used to specify the prior distributions and tuning-parameter settings for Bayesian learning with MUSS. (Step 1) MUSS: jointly model all training populations to obtain a total of (L $\times$ K) PRS models under L different tuning-parameter settings for $\mathrm{Pr}\left({\delta }_{1j},\dots ,{\delta }_{Kj}\right)$ (functions of $p_k$ s) and ${\rho }_{k_1{k}_2}$ s across K training populations. (Step 2) for each target population, conduct ensemble learning (EL) via a super learner (SL) algorithm with a set of base learners (e.g., elastic net regression, ridge regression, and linear regression) to train an “optimal” linear combination of the (L $\times$ K) PRS models from the MUSS step to obtain the final MUSSEL model. The prediction performance of the final PRS derived using MUSSEL should be evaluated on an independent testing set.