To evaluate PRS approaches, we constructed PRSs in an independent validation dataset based on SNPs and weights according to the training dataset. Let the PRS for participant i in the validation dataset be PRSi=∑j∈S^gijα^j where S^ is the selected set of SNPs (which is likely different than the true causal set S), and α^j is the estimated effect of the jth SNP is the set. We considered two measures for evaluation. For simulation studies we used the Root Mean Squared Prediction Error (RMSPE), computed by (2)RMSPE=[1nv∑i=1nv(yi−PRSi)2]1∕2, across the nv individuals in the validation dataset. In data analysis, we computed the variance explained by each PRS in a regression model adjusted for sex, age, and the first five principal components (PCs) of genetic ancestry. This was calculated by first fitting a model with these covariates, but without the PRS, and obtaining the residual variance denoted by σ^02, then fitting a model that also included the PRS and obtaining the residual variance σ^g2. The estimated percent variance explained is 100 × (σ^02−σ^g2)∕σ^02.
