This is likely because when the number of causal variants is small and the training sample size is large, all markers in LD with the causal variant become highly statistically significant in association tests, and LDpred does not accurately adjust for the LD structure, resulting in a decrease in predictive performance. In contrast, PRS-CS and PRS-CS-auto were minimally affected in the combination of sparse genetic architectures and large training sample sizes, which demonstrates the advantage of multivariate modeling and block update of the effect sizes for genetic markers in LD. In a few scenarios where the training sample size is small, PRS-CS produced lower prediction accuracy than LDpred, but it outperformed LDpred as the sample size grows across all genetic architectures. PRS-CS-auto did not perform well when the training sample size is small and the genetic architecture is sparse (e.g., in the case of 100 causal variants and 10,000 training samples), but approached the performance of PRS-CS as the sample size increases.
