Efficient Estimation and Applications of Cross-Validated Genetic Predictions to Polygenic Risk Scores and Linear Mixed Models

Abstract

Large-scale cohorts with combined genetic and phenotypic data, coupled with methodological advances, have produced increasingly accurate genetic predictors of complex human phenotypes called polygenic risk scores (PRSs). In addition to the potential translational impacts of identifying at-risk individuals, PRS are being utilized for a growing list of scientific applications, including causal inference, identifying pleiotropy and genetic correlation, and powerful gene-based and mixed-model association tests. Existing PRS approaches rely on external large-scale genetic cohorts that have also measured the phenotype of interest. They further require matching on ancestry and genotyping platform or imputation quality. In this work, we present a novel reference-free method to produce a PRS that does not rely on an external cohort. We show that naive implementations of reference-free PRS either result in substantial overfitting or prohibitive increases in computational time. We show that our algorithm avoids both of these issues and can produce informative in-sample PRSs over a single cohort without overfitting. We then demonstrate several novel applications of reference-free PRSs, including detection of pleiotropy across 246 metabolic traits and efficient mixed-model association testing.

Keywords: BLUP; PCA; PRS; linear mixed model; polygenic risk score.

FIG. 1.

Independence of cvBLUPs and nongenetic factors. Correlations of genetic predictions, BLUPs and cvBLUPs, true genetic factors Zb, and independent environmental factors $\epsilon$ in a simulation of a continuous phenotype with $h^2\approx 50\%$, 1000 subjects, and 1000 independent SNPs having random effect sizes. BLUPs are correlated with $\epsilon$, while cvBLUPs are not. Lines and p-values are from linear regression fits. R² values: A:0.21, B:0.0019, C:0.64, D:0.38. BLUPs, Best Linear Unbiased Predictors; cvBLUPs, cross-validated Best Linear Unbiased Predictors; SNP, single-nucleotide polymorphism.

FIG. 2.

Cross-trait correlations with cvBLUPs. Correlations of phenotypes (rows) and genetic predictions (cvBLUPs, columns) across 246 phenotypes. Many cvBLUPs are strongly correlated with additional phenotypes.