Making the Most of Clumping and Thresholding for Polygenic Scores

Abstract

Polygenic prediction has the potential to contribute to precision medicine. Clumping and thresholding (C+T) is a widely used method to derive polygenic scores. When using C+T, several p value thresholds are tested to maximize predictive ability of the derived polygenic scores. Along with this p value threshold, we propose to tune three other hyper-parameters for C+T. We implement an efficient way to derive thousands of different C+T scores corresponding to a grid over four hyper-parameters. For example, it takes a few hours to derive 123K different C+T scores for 300K individuals and 1M variants using 16 physical cores. We find that optimizing over these four hyper-parameters improves the predictive performance of C+T in both simulations and real data applications as compared to tuning only the p value threshold. A particularly large increase can be noted when predicting depression status, from an AUC of 0.557 (95% CI: [0.544-0.569]) when tuning only the p value threshold to an AUC of 0.592 (95% CI: [0.580-0.604]) when tuning all four hyper-parameters we propose for C+T. We further propose stacked clumping and thresholding (SCT), a polygenic score that results from stacking all derived C+T scores. Instead of choosing one set of hyper-parameters that maximizes prediction in some training set, SCT learns an optimal linear combination of all C+T scores by using an efficient penalized regression. We apply SCT to eight different case-control diseases in the UK biobank data and find that SCT substantially improves prediction accuracy with an average AUC increase of 0.035 over standard C+T.

Keywords: C+T; PRS; UK Biobank; clumping and thresholding; complex traits; polygenic risk scores; stacking.

Figure 1

Results of the Six Simulation Scenarios with Well-Imputed Variants Scenarios are (100) 100 random causal variants; (10K) 10,000 random causal variants; (1M) all 1M variants are causal variants; (2chr) 100 variants of chromosome 1 are causal and all variants of chromosome 2, with half of the heritability for both chromosomes; (err) 10,000 random causal variants, but 10% of the GWAS effects are reported with an opposite effect; (HLA) 7,105 causal variants in a long-range LD region of chromosome 6. Mean and 95% CI of 10⁴ non-parametric bootstrap replicates of the mean AUC of 10 simulations for each scenario. The blue dotted line represents the maximum achievable AUC for these simulations (87.5% for a prevalence of 10% and an heritability of 50%; see Equation 3 of Wray et al.³⁰). See corresponding values in Table S1.

Figure 2

Results of the Real Data Applications with Large Training Size AUC values on the test set of UKBB (mean and 95% CI from 10⁴ bootstrap samples). Training SCT and choosing optimal hyper-parameters for C+T and lassosum use 63%–90% of the individuals reported in Table 1. See corresponding values in Table S2.