Polygenic prediction, which exploits genome-wide genetic markers to estimate the genetic liability to a complex human disease or trait, is likely to become useful in clinical care and contribute to personalized medicine. As a high-dimensional regression problem that requires regularization, a majority of the existing methods that jointly model genetic markers across the genome employ Bayesian approaches and assign a discrete mixture prior on SNP effect sizes. Although intuitively appealing, this class of priors generates daunting computational challenges: the model space grows exponentially with the number of markers, which is difficult to fully explore, and more importantly, discrete mixture priors do not allow for block update of effect sizes and thus hinder accurate LD adjustment in polygenic prediction. LDpred4 partially addressed this issue by making several simplifying assumptions to the posterior distribution and using marginal posterior without LD to approximate the true posterior. However, our simulation studies suggest that this approximation may be inaccurate.
