Polygenic risk scores (PRS) developed from genome-wide association studies (GWAS) can be used for risk stratification by quantifying the genetic contribution to disease, and many clinical applications have been proposed. Bayesian methods are popular for building PRS because of their natural ability to regularize models and incorporate external information. In this article, we present new theoretical results, methods, and extensive numerical studies to advance Bayesian methods for PRS applications. We identify a potential risk, under a common Bayesian PRS framework, of posterior impropriety when integrating the required GWAS summary statistics and linkage disequilibrium (LD) data from distinct sources. As a principled remedy, we propose a projection of the summary statistics that ensures compatibility between the two sources and in turn a proper behavior of the posterior. We further introduce a new PRS method, with accompanying software, under the less-explored Bayesian bridge prior to more flexibly model varying sparsity levels in effect-size distributions. We extensively benchmark it against alternative Bayesian methods using synthetic and real datasets, quantifying the impact of prior specification and LD estimation strategy. Our proposed PRS-Bridge, equipped with the projection technique and flexible prior, demonstrates the most consistent and generally superior performance across a variety of scenarios.

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