Modeling Linkage Disequilibrium Increases Accuracy of Polygenic Risk Scores

Abstract

Polygenic risk scores have shown great promise in predicting complex disease risk and will become more accurate as training sample sizes increase. The standard approach for calculating risk scores involves linkage disequilibrium (LD)-based marker pruning and applying a p value threshold to association statistics, but this discards information and can reduce predictive accuracy. We introduce LDpred, a method that infers the posterior mean effect size of each marker by using a prior on effect sizes and LD information from an external reference panel. Theory and simulations show that LDpred outperforms the approach of pruning followed by thresholding, particularly at large sample sizes. Accordingly, predicted R(2) increased from 20.1% to 25.3% in a large schizophrenia dataset and from 9.8% to 12.0% in a large multiple sclerosis dataset. A similar relative improvement in accuracy was observed for three additional large disease datasets and for non-European schizophrenia samples. The advantage of LDpred over existing methods will grow as sample sizes increase.

Figure 1

Prediction Accuracy of P+T Applied to Simulated Genotypes with and without LD The performance of P+T, PRSs based on LD-pruned SNPs (r² < 0.2) followed by p value thresholding with an optimized threshold, when applied to simulated genotypes with and without LD. The prediction accuracy, as measured by squared correlation between the true phenotypes and the PRSs (prediction R²), is plotted as a function of the training sample size. The results are averaged over 1,000 simulated traits with 200,000 simulated genotypes, where the fraction of causal variants p was allowed to vary. In (A), the simulated genotypes are unlinked. In (B), the simulated genotypes are linked; we simulated independent batches of 100 markers while fixing the squared correlation between adjacent variants in a batch at 0.9.

Figure 2

Comparison of Four Prediction Methods Applied to Simulated Traits Prediction accuracy of the four different methods listed in Table S1 when applied to simulated traits with WTCCC genotypes. The four subfigures correspond to p = 1 (A), p = 0.1 (B), p = 0.01 (C), and p = 0.001 (D) for the fraction of simulated causal markers with (non-zero) effect sizes sampled from a Gaussian distribution. To aid interpretation of the results, we plot the accuracy against the effective sample size, defined as $N_{\text{eff}}=\left(N/M_{\text{sim}}\right)M$, where N = 10,786 is the training sample size, M = 376,901 is the total number of SNPs, and $M_{\text{sim}}$ is the actual number of SNPs used in each simulation: 376,901 (all chromosomes), 112,185 (chromosomes 1–4), 61,689 (chromosomes 1 and 2), and 30,004 (chromosome 1). The effective sample size is the sample size that maintains the same N/M ratio if all SNPs are used.

Figure 3

Comparison of Methods Applied to Seven WTCCC Disease Datasets The prediction accuracy of different methods as estimated from 5-fold cross-validation in seven WTCCC disease datasets: type 1 diabetes (T1D), rheumatoid arthritis (RA), Crohn disease (CD), bipolar disease (BD), type 2 diabetes (T2D), hypertension (HT), and coronary artery disease (CAD). The Nagelkerke prediction R² is shown on the y axis (see Table S2 for other metrics). LDpred significantly improved the prediction accuracy for the immune-related diseases T1D, RA, and CD (see main text).

Figure 4

Comparison of Methods Training on Large GWAS Summary Statistics for Five Different Diseases The prediction accuracy is shown for five different diseases: schizophrenia (SCZ), multiple sclerosis (MS), breast cancer (BC), type 2 diabetes (T2D), and coronary artery disease (CAD). The risk scores were trained with large GWAS summary-statistics datasets and used for predicting disease risk in independent validation datasets. The Nagelkerke prediction R² is shown on the y axis (see Table S5 for other metrics). Compared to LD pruning + thresholding (P+T), LDpred improved the prediction R² by 11%–25%. SCZ results are shown for the SCZ-MGS validation cohort used in recent studies, but LDpred also produced a large improvement for the independent SCZ-ISC validation cohort (Table S5).