Polygenic risk scores (PRS) have shown promise in predicting human complex traits and diseases. Here, we present PRS-CS, a polygenic prediction method that infers posterior effect sizes of single nucleotide polymorphisms (SNPs) using genome-wide association summary statistics and an external linkage disequilibrium (LD) reference panel. PRS-CS utilizes a high-dimensional Bayesian regression framework, and is distinct from previous work by placing a continuous shrinkage (CS) prior on SNP effect sizes, which is robust to varying genetic architectures, provides substantial computational advantages, and enables multivariate modeling of local LD patterns. Simulation studies using data from the UK Biobank show that PRS-CS outperforms existing methods across a wide range of genetic architectures, especially when the training sample size is large. We apply PRS-CS to predict six common complex diseases and six quantitative traits in the Partners HealthCare Biobank, and further demonstrate the improvement of PRS-CS in prediction accuracy over alternative methods.

Polygenic prediction has shown promise in identifying individuals at high risk for complex diseases, and may become clinically useful as the predictive performance of polygenic risk scores (PRS) improves. Here, we present PRS-CS, a novel polygenic prediction method that infers posterior SNP effect sizes using GWAS summary statistics and an external linkage disequilibrium (LD) reference panel. PRS-CS utilizes a highdimensional Bayesian regression framework, and is distinct from previous work by placing a continuous shrinkage (CS) prior on SNP effect sizes, which is robust to varying genetic architectures, provides substantial computational advantages, and enables multivariate modeling of local LD patterns. Simulation studies using data from the UK Biobank show that PRS-CS outperforms existing methods across a wide range of effect size distributions, especially when the training sample size is large. We apply PRS-CS to predict six complex diseases and six quantitative traits in the Partners HealthCare Biobank, and further demonstrate the improvement of PRS-CS in prediction accuracy over alternative methods.

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The scarcity of suitable proxies for asymmetric information has impeded empirical research from providing reliable evidence on whether information risk shapes equity pricing. In reexamining this unresolved question, we rely on firms’ geographic distance from financial centers to gauge information asymmetry. We provide strong, robust evidence supporting the prediction that equity financing is cheaper for firms nearer central locations, implying that investors rationally require more compensation when information asymmetry is worse. The equity pricing role of geographic proximity is economically large, with our coefficient estimates translating into firms located within 100 kilometers of the city center of the nearest of six major financial centers, or in their metropolitan statistical areas, enjoying equity financing costs that are seven basis points lower. Our inferences are insensitive to measuring both the cost of equity capital and distance in several ways, controlling for corporate governance quality, and addressing endogeneity. Collectively, our analysis suggests that investors discount the price that they pay for their securities to reflect the greater information asymmetry that ensues when firms are far from major financial centers.

We consider the problem of modeling conditional independence structures in heterogeneous data in the presence of additional subject-level covariates -termed Graphical Regression. We propose a novel specification of a conditional (in)dependence function of covariates -which allows the structure of a directed graph to vary flexibly with the covariates; imposes sparsity in both edge and covariate selection; produces both subject-specific and predictive graphs; and is computationally tractable. We provide theoretical justifications of our modeling endeavor, in terms of graphical model selection consistency. We demonstrate the performance of our method through rigorous simulation studies. We illustrate our approach in a cancer genomics-based precision medicine paradigm, where-in we explore gene regulatory networks in multiple myeloma taking prognostic clinical factors into account to obtain both populationlevel and subject-level gene regulatory networks.

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Summary Gene regulatory networks represent the regulatory relationships between genes and their products and are important for exploring and defining the underlying biological processes of cellular systems. We develop a novel framework to recover the structure of nonlinear gene regulatory networks using semiparametric spline-based directed acyclic graphical models. Our use of splines allows the model to have both flexibility in capturing nonlinear dependencies as well as control of overfitting via shrinkage, using mixed model representations of penalized splines. We propose a novel discrete mixture prior on the smoothing parameter of the splines that allows for simultaneous selection of both linear and nonlinear functional relationships as well as inducing sparsity in the edge selection. Using simulation studies, we demonstrate the superior performance of our methods in comparison with several existing approaches in terms of network reconstruction and functional selection. We apply our methods to a gene expression dataset in glioblastoma multiforme, which reveals several interesting and biologically relevant nonlinear relationships.