Abstract
Many diseases exhibit populationspecific causal effect sizes with transethnic genetic correlations significantly less than 1, limiting transethnic polygenic risk prediction. We develop a new method, SLDXR, for stratifying squared transethnic genetic correlation across genomic annotations, and apply SLDXR to genomewide summary statistics for 31 diseases and complex traits in East Asians (average N = 90K) and Europeans (average N = 267K) with an average transethnic genetic correlation of 0.85. We determine that squared transethnic genetic correlation is 0.82× (s.e. 0.01) depleted in the top quintile of background selection statistic, implying more populationspecific causal effect sizes. Accordingly, causal effect sizes are more populationspecific in functionally important regions, including conserved and regulatory regions. In regions surrounding specifically expressed genes, causal effect sizes are most populationspecific for skin and immune genes, and least populationspecific for brain genes. Our results could potentially be explained by stronger geneenvironment interaction at loci impacted by selection, particularly positive selection.
Introduction
Transethnic genetic correlations are significantly less than 1 for many diseases and complex traits^{1,2,3,4,5,6}, implying that populationspecific causal disease effect sizes contribute to the incomplete portability of genomewide association study (GWAS) findings and polygenic risk scores (PRSs) to nonEuropean populations^{6,7,8,9,10,11,12}. However, current methods for estimating genomewide transethnic genetic correlations assume the same transethnic genetic correlation for all categories of SNPs^{2,5,13}, providing little insight into why causal disease effect sizes are populationspecific. Understanding the biological processes contributing to populationspecific causal disease effect sizes can help inform polygenic risk prediction in nonEuropean populations and alleviate health disparities^{6,14,15}.
Here, we introduce a new method, SLDXR, for estimating enrichment of stratified squared transethnic genetic correlation across functional categories of SNPs using GWAS summary statistics and populationmatched linkage disequilibrium (LD) reference panels (e.g. the 1000 Genomes Project (1000G)^{16}); we stratify the squared transethnic genetic correlation across functional categories to robustly handle noisy heritability estimates. SLDXR analyzes GWAS summary statistics of HapMap3^{17} SNPs with minor allele frequency (MAF) greater than 5% in both East Asian (EAS) and European (EUR) populations (regression SNPs) to draw inferences about causal effects of all SNPs with MAF greater than 5% in both populations (heritability SNPs). We confirm that SLDXR yields robust estimates in extensive simulations. We apply SLDXR to 31 diseases and complex traits with GWAS summary statistics available in both East Asian (EAS) and European (EUR) populations, leveraging recent large studies in East Asian populations from the CONVERGE consortium and Biobank Japan^{18,19,20}; we analyze a broad set of genomic annotations from the baselineLD model^{21,22,23}, as well as tissuespecific annotations based on specifically expressed gene (SEG) sets^{24}. Most results are metaanalyzed across the 31 traits to maximize power (analogous to refs. ^{21,22,23}), as we expect to see similar patterns of enrichment/depletion across traits (even though the underlying biological processes differ across traits). We also investigate traitspecific enrichments/depletions for the tissuespecific annotations (analogous to ref. ^{24}).
Results
Overview of methods
Our method (SLDXR) for estimating stratified transethnic genetic correlation is conceptually related to stratified LD score regression^{21,22} (SLDSC), a method for partitioning heritability from GWAS summary statistics while accounting for LD. SLDXR determines that a category of SNPs is enriched for transethnic genetic covariance if SNPs with high LD to that category have a higher product of Zscores than SNPs with low LD to that category. Unlike SLDSC, SLDXR models perallele effect sizes (accounting for differences in MAF between populations).
In detail, the product of Zscores of SNP j in two populations, Z_{1j}Z_{2j}, has the expectation
where N_{p} is the sample size for population p; ℓ_{×}(j, C) = ∑_{k}r_{1jk}r_{2jk}σ_{1j}σ_{2j}a_{C}(k) is the transethnic LD score of SNP j with respect to annotation C, whose value for SNP k, a_{C}(k), can be either binary or continuous; r_{pjk} is the LD (Pearson correlation) between SNP j and k in population p; σ_{pj} is the standard deviation of SNP j genotypes in population p; and θ_{C} represents the perSNP contribution to transethnic genetic covariance of the perallele causal disease effect size of annotation C. Here, r_{pjk} and σ_{pj} can be estimated from populationmatched reference panels (e.g. 1000 Genomes Project^{16}). We estimate θ_{C} for each annotation C using weighted least square regression. Subsequently, we estimate the transethnic genetic covariance of each binary annotation C (ρ_{g}(C)) by summing transethnic genetic covariance of each SNP in annotation C as \({\sum }_{j\in C}\left({\sum }_{C^{\prime} }{a}_{C^{\prime} }(j){\theta }_{C^{\prime} }\right)\), using coefficients (\({\theta }_{C^{\prime} }\)) for all binary and continuousvalued annotations \(C^{\prime}\) included in the analysis; the heritabilities in each population (\({h}_{g1}^{2}(C)\) and \({h}_{g2}^{2}(C)\)) are estimated analogously. We then estimate the stratified squared transethnic genetic correlation, defined as
We define the enrichment/depletion of squared transethnic genetic correlation as \({\lambda }^{2}(C)=\frac{{r}_{g}^{2}(C)}{{r}_{g}^{2}}\), where \({r}_{g}^{2}\) is the genomewide squared transethnic genetic correlation; λ^{2}(C) can be metaanalyzed across traits with different \({r}_{g}^{2}\). SLDXR analyzes GWAS summary statistics of common HapMap3^{17} SNPs (regression SNPs) to estimate λ^{2}(C) for (causal effects of) all common SNPs (heritability SNPs). Further details (quantities estimated, analytical bias correction, shrinkage estimator to reduce standard errors, estimation of standard errors, significance testing, and factors impacting power) of the SLDXR method are provided in the Methods section and the Supplementary Notes; we have publicly released opensource software implementing the method (see “Code availability”).
We apply SLDXR to 62 annotations (defined in both EAS and EUR populations) from our baselineLDX model (“Methods”, Supplementary Data 1, Supplementary Figs. 1, 2), primarily derived from the baselineLD model^{21,22,23} (v1.1), and 53 SEG annotations (Supplementary Data 2). We have publicly released all baselineLDX model annotations and LD scores for EAS and EUR populations (see “Data availability”).
Simulations
We evaluated the accuracy of SLDXR in simulations using genotypes that we simulated using HAPGEN2^{25} from phased haplotypes of 481 EAS and 489 EUR individuals from the 1000 Genomes Project^{16}, preserving populationspecific MAF and LD patterns (18,418 simulated EASlike and 36,836 simulated EURlike samples, after removing genetically related samples, the ratio of sample sizes similar to empirical data; ~2.5 million SNPs on chromosomes 1–3) (“Methods”); we did not have access to individuallevel EAS data at sufficient sample size to perform simulations with real genotypes. For each population, we randomly selected a subset of 500 simulated samples to serve as the reference panel for estimating LD scores. We performed both null simulations (heritable trait with functional enrichment but no enrichment/depletion of squared transethnic genetic correlation; λ^{2}(C) = 1) and causal simulations (λ^{2}(C) ≠ 1). In our main simulations, we randomly selected 10% of the SNPs as causal SNPs in both populations, set genomewide heritability to 0.5 in each population, and adjusted genomewide genetic covariance to attain a genomewide r_{g} of 0.60 (unless otherwise indicated). In the null simulations, we used heritability enrichments from analyses of real traits in EAS samples to specify perSNP causal effect size variances and covariances. In the causal simulations, we directly specified perSNP causal effect size variances and covariances to attain λ^{2}(C) ≠ 1 values from analyses of real traits, as these were difficult to attain using the heritability and transethnic genetic covariance enrichments from analyses of real traits.
First, we assessed the accuracy of SLDXR in estimating genomewide transethnic genetic correlation (r_{g}); we note that SLDXR does not use the shrinkage estimator for genomewide estimates. Across a wide range of simulated r_{g} values (0.0 to 1.0), SLDXR yielded approximately unbiased estimates and wellcalibrated jackknife standard errors (Supplementary Table 1, Supplementary Fig. 3).
Second, we assessed the accuracy of SLDXR in estimating λ^{2}(C) in quintiles of the 8 continuousvalued annotations of the baselineLDX model. We performed both null simulations (λ^{2}(C) = 1) and causal simulations (λ^{2}(C) ≠ 1). Results are reported in Fig. 1a and Supplementary Data 3–8. In both null and causal simulations, SLDXR yielded approximately unbiased estimates of λ^{2}(C) for most annotations, validating our analytical bias correction. As a secondary analysis, we tried varying the SLDXR shrinkage parameter, α, which has a default value of 0.5. In null simulations, results remained approximately unbiased; in causal simulations, reducing α led to less precise (but less biased) estimates of λ^{2}(C), whereas increasing α biased results towards the null (λ^{2}(C) = 1), demonstrating a biasvariance tradeoff in the choice of α (Supplementary Fig. 4, Supplementary Data 4, 7). Results were similar at other values of the proportion of causal SNPs (1% and 100%; Supplementary Data 3, 5, 6, 8). We also confirmed that SLDXR produced wellcalibrated jackknife standard errors (Supplementary Data 3–8).
Third, we assessed the accuracy of SLDXR in estimating λ^{2}(C) for the 28 main binary annotations of the baselineLDX model (inherited from the baseline model of ref. ^{21}). We discarded λ^{2}(C) estimates with the highest standard errors (top 5%), as estimates with large standard errors (which are particularly common for annotations of small size) are uninformative for evaluating unbiasedness of the estimator (in analyses of real traits, traitspecific estimates with large standard errors are retained, but contribute very little to metaanalysis results, and would be interpreted as inconclusive when assessing traitspecific results). Results are reported in Fig. 1b and Supplementary Data 4, 7. In null simulations, SLDXR yielded unbiased estimates of λ^{2}(C), further validating our analytical bias correction. In causal simulations, estimates were biased towards the null (λ^{2}(C) = 1)—particularly for annotations of small size (proportion of SNPs < 1%)—due to our shrinkage estimator; increasing the shrinkage parameter above its default value of 0.5 further biased the estimates towards the null (λ^{2}(C) = 1) in causal simulations (Supplementary Data 6–8). To ensure robust estimates, we focus on the 20 main binary annotations of large size (>1% of SNPs) in analyses of real traits (see below); although results for these annotations may still be biased towards the null, we emphasize that SLDXR is unbiased in null data. Results were similar at other values of the proportion of causal SNPs (1% and 100%; Supplementary Data 3, 5, 6, 8). We also confirmed that SLDXR produced wellcalibrated jackknife standard errors (Supplementary Data 3–8) and conservative pvalues (Supplementary Fig. 7, Supplementary Data 3–8).
Fourth, we performed additional null simulations in which causal variants differed across the two populations (Methods). SLDXR yielded robust estimates of λ^{2}(C), wellcalibrated standard errors and conservative pvalues in these simulations (Supplementary Fig. 11, Supplementary Data 11).
Fifth, we performed additional null simulations with annotationdependent MAFdependent genetic architectures^{26,27,28}, defined as architectures in which the level of MAFdependence is annotationdependent, to ensure that estimate of λ^{2}(C) remains unbiased. We disproportionately sampled lowfrequency causal variants from the top quintile of background selection statistic, and set the variance of perallele effect sizes of a causal SNP to be inversely proportional to its maximum MAF across both populations (Methods). Results are reported in Supplementary Figs. 8–10, and Supplementary Data 9–10. SLDXR yielded nearly unbiased estimates of λ^{2}(C) for the 28 binary functional annotations (Supplementary Fig. 8) and nearly unbiased estimates of λ^{2}(C) for most quintiles of continuously valued annotations (Supplementary Fig. 9); estimates were slightly biased estimates in the top and bottom quintile of the average level of LD annotation and the recombinationrate annotation, likely due to less accurate reference LD scores at SNPs with extreme levels of LD. We repeated these simulations with five MAF bin annotations added to the baselineLDX model and obtained similar results (Supplementary Figs. 8a, 9b), supporting our decision not to include MAF bin annotations into the baselineLDX model.
Sixth, we performed additional null simulations, in which we increased or decreased the reference panel size from 500 to 250 or 1000, to assess the impact of reference panel size on the accuracy of SLDXR (Methods). We simulated GWAS summary statistics based on the baselineLDX model as well as the model with annotationdependent MAFdependent genetic architectures. We determined that the small systematic biases in null simulations of continuousvalued annotations were on the same order of magnitude as for 500 reference samples (Supplementary Figs. 12, 13 and Supplementary Data 12 for 250 reference samples; Supplementary Figs. 14, 15 and Supplementary Data 13 for 1000 reference samples). We also performed simulations in which we reduced the simulated GWAS sample size by half, from N_{EAS} = 18K, N_{EUR} = 37K to N_{EAS} = 9K, N_{EUR} = 18K (while fixing the reference panel size at 500). We again determined that the small systematic biases were generally on the same order of magnitude as for N_{EAS} = 18K, N_{EUR} = 37K (although estimates were less stable and sometimes subject to larger biases, likely because our analytical bias correction starts to break down when the GWAS has low power) (Supplementary Figs. 16, 17 and Supplementary Data 14). Although it was not computationally feasible to perform simulations at larger GWAS sample sizes, these analyses do not provide a reason to believe that the small systematic biases that we observed in some of our null simulations of continuously valued annotations would substantially increase at larger GWAS sample sizes.
In summary, SLDXR produced approximately unbiased estimates of enrichment/depletion of squared transethnic genetic correlation in null simulations, and conservative estimates in causal simulations of both quintiles of continuousvalued annotations and binary annotations.
Analysis of baselineLDX model annotations across 31 diseases and complex traits
We applied SLDXR to 31 diseases and complex traits with summary statistics in East Asians (average N = 90K) and Europeans (average N = 267K) available from Biobank Japan, UK Biobank, and other sources (Supplementary Table 2 and Methods). First, we estimated the transethnic genetic correlation (r_{g}) (as well as populationspecific heritabilies) for each trait. Results are reported in Supplementary Fig. 18 and Supplementary Table 2. The average r_{g} across 31 traits was 0.85 (s.e. 0.01) (average \({r}_{g}^{2}\) = 0.72 (s.e. 0.02)). 28 traits had r_{g} < 1, and 11 traits had r_{g} significantly less than 1 after correcting for 31 traits tested (P < 0.05/31); the lowest r_{g} was 0.34 (s.e. 0.07) for Major Depressive Disorder (MDD), although this may be confounded by different diagnostic criteria in the two populations^{29}. Several other complex traits, including Age at Menopause (r_{g} = 0.57 (s.e. 0.09)) and LDL (r_{g} = 0.66 (s.e. 0.11)) also had low transethnic r_{g}, likely due to pervasive geneenvironment interaction across the genome. These estimates were consistent with estimates obtained using Popcorn^{2} (Supplementary Fig. 19) and those reported in previous studies^{2,5,6}. We note that our estimates of transethnic genetic correlation for 31 complex traits are higher than those reported for gene expression traits^{2} (average estimate of 0.32, increasing to 0.77 when restricting the analysis to gene expression traits with (cis) heritability greater than 0.2 in both populations), which are expected to have different genetic architectures.
Second, we estimated the enrichment/depletion of squared transethnic genetic correlation (λ^{2}(C)) in quintiles of the 8 continuousvalued annotations of the baselineLDX model, metaanalyzing results across traits; these annotations are moderately correlated (Fig. 2a and Supplementary Data 1). We used the default shrinkage parameter (α = 0.5) in all analyses. Results are reported in Fig. 2b and Supplementary Data 15. We consistently observed a depletion of \({r}_{g}^{2}(C)\) (λ^{2}(C) < 1, implying more populationspecific causal effect sizes) in functionally important regions. For example, we estimated λ^{2}(C) = 0.82 (s.e. 0.01) for SNPs in the top quintile of background selection statistic (defined as 1 − McVicker B statistic/1000^{30}; see ref. ^{22}); λ^{2}(C) estimates were less than 1 for 29/31 traits, including 2 traits (Height and EGFR) with twotailed p < 0.05/31. The background selection statistic quantifies the genetic distance of a site to its nearest exon; regions with high background selection statistic have higher perSNP heritability, consistent with the action of selection, and are enriched for functionally important regions^{22}. We observed the same pattern for CpG content and SNPspecific F_{st} (which are positively correlated with background selection statistic; Fig. 2a) and the opposite pattern for nucleotide diversity (which is negatively correlated with background selection statistic). We also estimated λ^{2}(C) = 0.87 (s.e. 0.03) for SNPs in the top quintile of average LLD (which is positively correlated with background selection statistic), although these SNPs have lower perSNP heritability due to a competing positive correlation with predicted allele age^{22}. We caution that average LLD was the annotation most susceptible to bias in our simulations; see “Simulations”. Likewise, we estimated λ^{2}(C) = 0.84 (s.e. 0.02) for SNPs in the bottom quintile of recombination rate (which is negatively correlated with background selection statistic), although these SNPs have average perSNP heritability due to a competing negative correlation with average LLD^{22}. However, λ^{2}(C) < 1 estimates for the bottom quintile of GERP (NS) (which is positively correlated with both background selection statistic and recombination rate) and the middle quintile of predicted allele age are more difficult to interpret. For all annotations analyzed, heritability enrichments did not differ significantly between EAS and EUR, consistent with previous studies^{20,31}. Results were similar at a more stringent shrinkage parameter value (α = 1.0; Supplementary Fig. 20), and for a metaanalysis across a subset of 20 approximately independent traits (Methods; Supplementary Fig. 21).
Finally, we estimated λ^{2}(C) for the 28 main binary annotations of the baselineLDX model (Supplementary Data 1), metaanalyzing results across traits (as we did not observe significant traitspecific enrichment/depletion of squared transethnic genetic correlation for these annotations due to limited power). Results are reported in Fig. 3a and Supplementary Data 16. Our primary focus is on the 20 annotations of large size (>1% of SNPs), for which our simulations yielded robust estimates; results for remaining annotations are reported in Supplementary Data 16. We consistently observed a depletion of λ^{2}(C) (implying more populationspecific causal effect sizes) within these annotations: 17 annotations had λ^{2}(C) < 1, and 5 annotations had λ^{2}(C) significantly less than 1 after correcting for 20 annotations tested (P < 0.05/20). These annotations included Conserved (λ^{2}(C) = 0.93 (s.e. 0.02)), Promoter (λ^{2}(C) = 0.85 (s.e. 0.04)) and Super Enhancer (λ^{2}(C) = 0.93 (s.e. 0.02)), each of which was significantly enriched for perSNP heritability, consistent with ref. ^{21}. For all annotations analyzed, heritability enrichments did not differ significantly between EAS and EUR (Fig. 3a), consistent with previous studies^{20,31}. Results were similar at a more stringent shrinkage parameter value (α = 1.0; Supplementary Fig. 20), and for a metaanalysis across a subset of 20 approximately independent traits (Methods; Supplementary Fig. 22). As a secondary analysis, we also estimated λ^{2}(C) across 10 MAF bin annotations; we did not observe variation in λ^{2}(C) estimates across MAF bins (Supplementary Table 3), further supporting our decision to not include MAF bin annotations in the baselineLDX model.
Since the functional annotations are moderately correlated with the 8 continuousvalued annotations (Supplementary Data 1c, Supplementary Fig. 1), we investigated whether the depletions of squared transethnic genetic correlation (λ^{2}(C) < 1) within the 20 binary annotations could be explained by the 8 continuousvalued annotations. For each binary annotation, we estimated its expected λ^{2}(C) based on values of the 8 continuousvalued annotations for SNPs in the binary annotation (Methods), metaanalyzed this quantity across traits, and compared observed vs. expected λ^{2}(C) (Fig. 3b and Supplementary Data 17). We observed strong concordance, with a slope of 0.57 (correlation of 0.61) across the 20 binary annotations. This implies that the depletions of \({r}_{g}^{2}(C)\) (λ^{2}(C) < 1) within binary annotations are largely explained by corresponding values of continuousvalued annotations.
In summary, our results show that causal disease effect sizes are more populationspecific in functionally important regions impacted by selection. Further interpretation of these findings, including the role of positive and/or negative selection, is provided in the “Discussion” section.
Analysis of SEG annotations
We analyzed 53 SEG annotations, defined in ref. ^{24} as ±100kb regions surrounding the top 10% of genes specifically expressed in each of 53 GTEx^{32} tissues (Supplementary Data 2), by applying SLDXR with the baselineLDX model to the 31 diseases and complex traits (Supplementary Table 2). We note that although SEG annotations were previously used to prioritize diseaserelevant tissues based on diseasespecific heritability enrichments^{20,24}, enrichment/depletion of squared transethnic genetic correlation (λ^{2}(C)) is standardized with respect to heritability (i.e. increase in heritability in the denominator would lead to increase in transethnic genetic covariance in the numerator (Eq. (2))), hence not expected to produce exceedingly diseasespecific signals. Thus, we first assess metaanalyzed λ^{2}(C) estimates across the 31 diseases and complex traits (traitspecific estimates are assessed below).
Results are reported in Fig. 4a and Supplementary Data 18. λ^{2}(C) estimates were less than 1 for all 53 tissues and significantly less than 1 (p < 0.05/53) for 37 tissues, with statistically significant heterogeneity across tissues (p < 10^{−20}; Methods). The strongest depletions of squared transethnic genetic correlation were observed in skin tissues (e.g. λ^{2}(C) = 0.83 (s.e. 0.02) for Skin Sun Exposed (Lower Leg)), Prostate and Ovary (λ^{2}(C) = 0.84 (s.e. 0.02) for Prostate, λ^{2}(C) = 0.86 (s.e. 0.02) for Ovary) and immunerelated tissues (e.g. λ^{2}(C) = 0.85 (s.e. 0.02) for Spleen), and the weakest depletions were observed in Testis (λ^{2}(C) = 0.98 (s.e. 0.02); no significant depletion) and brain tissues (e.g. λ^{2}(C) = 0.98 (s.e. 0.02) for Brain Nucleus Accumbens (Basal Ganglia); no significant depletion). Results were similar at less stringent and more stringent shrinkage parameter values (α = 0.0 and α = 1.0; Supplementary Figs. 23, 24 and Supplementary Data 18). A comparison of 14 bloodrelated traits and 16 other traits yielded highly consistent λ^{2}(C) estimates (R = 0.82; Supplementary Fig. 25, Supplementary Data 19), confirming that these findings were not exceedingly diseasespecific.
These λ^{2}(C) results were consistent with the higher background selection statistic^{30} in Skin Sun Exposed (Lower Leg) (R = 0.17), Prostate (R = 0.16), and Spleen (R = 0.14) as compared to Testis (R = 0.02) and Brain Nucleus Accumbens (Basal Ganglia) (R = 0.08) (Supplementary Fig. 26, Supplementary Data 2), and similarly for CpG content (Supplementary Fig. 27, Supplementary Data 2). Although these results could in principle be confounded by gene size^{33}, the low correlation between gene size and background selection statistic (R = 0.06) or CpG content (R = −0.20) (in ±100kb regions) implies limited confounding. We note the welldocumented action of recent positive selection on genes impacting skin pigmentation^{34,35,36,37,38}, the immune system^{34,35,36,37,39}, and Ovary^{40}; we are not currently aware of any evidence of positive selection impacting Prostate. We further note the welldocumented action of negative selection on fecundity and brainrelated traits^{26,28,41}, but it is possible that recent positive selection may more closely track differences in causal disease effect sizes across human populations, which have split relatively recently^{42} (see “Discussion”).
More generally, since SEG annotations are moderately correlated with the 8 continuousvalued annotations (Supplementary Fig. 28, Supplementary Data 2), we investigated whether these λ^{2}(C) results could be explained by the 8 continuousvalued annotations (analogous to Fig. 3b). Results are reported in Fig. 4b and Supplementary Data 20. We observed strong concordance, with a slope of 0.96 (correlation of 0.76) across the 53 SEG annotations. This implies that the depletions of λ^{2}(C) within SEG annotations are explained by corresponding values of continuousvalued annotations.
The strong depletion of squared transethnic genetic correlation in tissues impacted by positive selection (as opposed to negative selection) suggests a possible connection between positive selection and populationspecific causal effect sizes. To further assess this, we estimated the enrichment/depletion of squared transethnic genetic correlation in SNPs with high integrated haplotype score (iHS)^{43,44}, which quantifies the action of positive selection (“Methods”). We observed a significant depletion (λ^{2}(C) = 0.88 (s.e. 0.03)), further implicating positive selection (however, it is difficult to assess whether the iHS annotation contains unique information about λ^{2}(C) conditional on other annotations; see “Discussion”). In addition, we observed a high genomewide transethnic genetic correlation for schizophrenia (r_{g} = 0.95 (s.e. 0.04) vs. average of 0.85 (s.e. 0.01) across traits), a psychiatric disorder hypothesized to be strongly impacted by negative selection^{45,46}, suggesting that negative selection may play a limited role in populationspecific causal effect sizes. As noted above, these estimates pertain to parameters that were defined based on common variants (see “Overview of methods”); we note that although negative selection has the strongest impact on lowfrequency variants^{26}, common variants are also impacted by negative selection and can inform inferences about negative selection^{22}. The role of positive selection (as opposed to negative selection) in populationspecific causal effect sizes is discussed further in the Discussion section.
We investigated the enrichment/depletion of λ^{2}(C) in the 53 SEG annotations for each individual trait (Supplementary Data 21). We identified six significantly depleted (vs. 0 significantly enriched) traittissue pairs at pertrait p < 0.05/53. The limited number of statistically significant results was expected, due to the reduced power of traitspecific analyses; however, λ^{2}(C) estimates were generally consistent across traits. Results for BMI and height, two widely studied anthropometric traits, are reported in Fig. 5. For BMI, we observed significant depletion of squared transethnic genetic correlation (λ^{2}(C) = 0.84 (s.e. 0.05)) in Pituitary. Previous studies have highlighted the role of Pituitary in obesity^{47,48,49}; our results suggest that this tissuespecific mechanism is populationspecific. For height, we observed significant depletion of squared transethnic genetic correlation for Transformed fibroblasts (λ^{2}(C) = 0.87 (s.e. 0.03)), a connective tissue linked to human developmental disorders^{50}; again, our results suggest that this tissuespecific mechanism is populationspecific. Although Pituitary was significantly depleted for BMI but not height, and Transformed fibroblasts were significantly depleted for height but not BMI, we caution that for both tissues our λ^{2}(C) estimates did not differ significantly between BMI and height.
In summary, our results show that causal disease effect sizes are more populationspecific in regions surrounding SEGs.
Discussion
We developed a new method (SLDXR) for stratifying squared transethnic genetic correlation across functional categories of SNPs that yields approximately unbiased estimates in extensive simulations. By applying SLDXR to East Asian and European summary statistics across 31 diseases and complex traits, we determined that SNPs with high background selection statistic^{30} have substantially depleted squared transethnic genetic correlation (vs. the genomewide average), implying that causal effect sizes are more populationspecific. Accordingly, squared transethnic genetic correlations were substantially depleted for SNPs in many functional categories and enriched in less functionally important regions (although the power of SLDXR to detect enrichment of squared transethnic genetic correlation is limited due to depletion of heritability in less functionally important regions). In analyses of SEG annotations, we observed substantial depletion of squared transethnic genetic correlation for SNPs near skin and immunerelated genes, which are strongly impacted by recent positive selection, but not for SNPs near brain genes. We also observed traitspecific depletions of squaredtransethnic genetic correlation for SEG annotations, which indicate populationspecific disease mechanisms.
Reductions in transethnic genetic correlation have several possible underlying explanations, including geneenvironment (G × E) interaction, gene–gene (G × G) interaction, and dominance variation (but not differences in heritability across populations, which would not affect transethnic genetic correlation and were not observed in our study). Given the increasing evidence of the role of G × E interaction in complex trait architectures^{51}, and evidence that G × G interaction and dominance variation explain limited heritability^{52,53,54}, we hypothesize that depletion of squared transethnic genetic correlation in the top quintile of background selection statistic and in functionally important regions may be primarily attributable to stronger G × E interaction in these regions. Interestingly, a recent study on plasticity in Arabidopsis observed a similar phenomenon: lines with more extreme phenotypes exhibited stronger G × E interaction^{55}. Although depletion of squared transethnic genetic correlation is often observed in regions with higher perSNP heritability, which may often be subject to stronger G × E, depletion may also occur in regions with lower perSNP heritability that are subject to stronger G × E; we hypothesize that this is the case for SNPs in the top quintile of average LLD and the bottom quintile of GERP (NS) (Fig. 2).
Distinguishing between stronger G × E interaction in regions impacted by selection and stronger G × E interaction in functionally important regions as possible explanations for our findings is a challenge, because functionally important regions are more strongly impacted by selection. To this end, we constructed an annotation that is similar to the background selection statistic but does not make use of recombination rate, instead relying solely on a SNP’s physical distance to the nearest exon (“Methods”). Applying SLDXR to the 31 diseases and complex traits using a joint model incorporating baselineLDX model annotations and the nearest exon annotation, the background selection statistic remained highly conditionally informative for transethnic genetic correlation, whereas the nearest exon annotation was not conditionally informative (Supplementary Table 4). This result implicates stronger G × E interaction in regions with a reduced effective population size that are impacted by the selection, and not just proximity to functional regions, in explaining depletions of squared transethnic genetic correlation; however, we emphasize that selection acts on allele frequencies rather than causal effect sizes, and could help explain our findings only in conjunction with other explanations such as G × E interaction. Our results on SEGs implicate stronger G × E interaction near skin, immune, and ovary genes and weaker G × E interaction near brain genes, potentially implicating positive selection (as opposed to negative selection). This conclusion is further supported by the significant depletion of squared transethnic genetic correlation in the integrated haplotype score (iHS) annotation that specifically reflects positive selection, high genomewide transethnic genetic correlation for schizophrenia (Supplementary Table 2), and lack of variation in squared transethnic genetic correlation across genes in different deciles of probability of lossoffunction intolerance^{56} (Methods, Supplementary Figs. 29, 30, Supplementary Table 5). We conclude that depletions of squared transethnic genetic correlation could potentially be explained by stronger G × E interaction at loci impacted by positive selection. We caution that other explanations are also possible; in particular, evolutionary modeling using an extension of the Eyre–Walker model^{57} to two populations suggests that our results for the background selection statistic could also be consistent with negative selection (Supplementary Notes, Supplementary Figs. 31, 32, Supplementary Table 6). Additional information, such as genomic annotations that better distinguish different types of selection or data from additional diverse populations, may help elucidate the relationship between selection and populationspecific causal effect sizes.
Our study has several implications. First, PRSs in nonEuropean populations that make use of European training data^{6,9,11} may be improved by reweighting SNPs based on the expected enrichment/depletion of squared transethnic genetic correlation, helping to alleviate health disparities^{6,14,15}. For example, when applying LDpruning + pvalue thresholding methods^{58,59}, both the strength of association and transethnic genetic correlation should be accounted for when prioritizing SNPs for transethnic PRS, as our results suggest that transethnic genetic correlation is likely depleted near functional SNPs with significant pvalues (due to stronger G × E). In particular, when multiple SNPs have a similar level of significance, the SNPs enriched for transethnic genetic correlation should be prioritized. Analogously, when applying more recent methods that estimate posterior mean causal effect sizes^{60,61,62,63,64,65,66} (including functionally informed methods^{62,66}), these estimates should subsequently be weighted according to the expected enrichment/depletion for squared transethnic genetic correlation based on their functional annotations. Second, modeling populationspecific genetic architectures may improve transethnic finemapping. Our results suggest that causal effect sizes and/or causal variants are likely to differ across different populations, contrary to standard assumptions^{31,67}. Thus, incorporating information about transethnic genetic correlations in transethnic finemapping may lead to more accurate identification of both populationspecific and shared causal variants^{68}. Third, modeling populationspecific genetic architectures may also increase power in transethnic metaanalysis^{69}, e.g. by adapting MTAG^{70} to two populations (instead of two traits), leveraging transethnic (instead of crosstrait) genetic correlation between pairs of populations to improve the estimation of SNP effect sizes in both populations. Fourth, it may be of interest to stratify G × E interaction effects^{51} across genomic annotations. Fifth, modeling and incorporating environmental variables, where available, may provide additional insights into populationspecific causal effect sizes. In our simulations, we did not explicitly simulate G × E. However, G × E would induce populationspecific causal effect sizes, which we did explicitly simulate. Sixth, the SLDXR method could potentially be extended to stratify squared crosstrait genetic correlations^{71} across genomic annotations^{72}.
We note several limitations of this study that pertain to the SLDXR method. First, SLDXR is designed for populations of homogeneous continental ancestry (e.g. East Asians and Europeans) and is not currently suitable for analysis of admixed populations^{73} (e.g. African Americans or admixed Africans from UK Biobank^{74}), analogous to LDSC and its published extensions^{21,71,75}. However, a recently proposed extension of LDSC to admixed populations^{76} could be incorporated into SLDXR, enabling its application to the growing set of large studies in admixed populations^{10}. Second, SLDXR estimates of enrichment of stratified squared transethnic genetic correlation (λ^{2}(C)) are slightly downward biased in null simulations of the top quintile of the background selection statistic and average LLD annotations, especially in simulations involving annotationdependent MAFdependent genetic architectures. However, these biases are small compared to the depletions of λ^{2}(C) observed in the analysis of real traits. We further note that our estimates are unbiased in null simulations of binary annotations, implying that our results on real traits for binary annotations are robust. Third, since SLDXR applies shrinkage to reduce standard error in estimating stratified squared transethnic genetic correlation and its enrichment, estimates are conservative—true depletions of squared transethnic genetic correlation in functionally important regions may be stronger than the estimated depletions. However, we emphasize that SLDXR is approximately unbiased in null data. Fourth, the optimal value of the shrinkage parameter α may be specific to the pair of populations analyzed. In our simulations, we determined that α = 0.5 provides a satisfactory biasvariance tradeoff across a wide range of values of polygenicity and power. Thus, α = 0.5 may also be satisfactory for other pairs of populations. However, we recommend that one should ideally perform simulations on the pair of populations being analyzed to selection the optimal value of α. Fifth, it is difficult to assess whether a focal annotation contains unique information about λ^{2}(C) conditional on other annotations, as squared transethnic genetic correlation is a nonlinear quantity defined by the quotient of squared transethnic genetic covariance and the product of heritabilities in each population.
We also note several limitations of this study that pertain to our analysis of real traits. First, we focused on comparisons of East Asians and Europeans, due to the limited availability of very large GWAS in other populations. For other pairs of continental populations, if differences in the environment are similar, then we would expect similar genomewide transethnic genetic correlation and similar enrichment/depletion of squared transethnic genetic correlation, based on our hypothesis that imperfect transethnic genetic correlation is primarily attributable to G × E. We also note that different sets of SNPs, with different MAF and LD patterns, would be analyzed for different pairs of populations. However, we expect that these differences would not contribute to differences in transethnic genetic correlation, if G × E is the fundamental factor impacting transethnic genetic correlation. Second, the SEG annotations analyzed in this study are defined predominantly (but not exclusively) based on gene expression measurements of Europeans^{24}. We hypothesize that results based on SEG annotations defined in East Asian populations would likely be similar, as heritability enrichment of functional annotations (predominantly defined in Europeans) are consistent across continental populations^{20,31}, despite the fact that gene expression patterns and genetic architectures of gene expression differ across diverse populations^{12,77,78}. Thus, SEG annotations derived from gene expression data from diverse populations may provide additional insights into populationspecific causal effect sizes. Third, we restricted our analyses to SNPs that were relatively common (MAF > 5%) in both populations (estimating parameters that were defined based on common SNPs), due to the lack of a large LD reference panel for East Asians. Extending our analyses to lowerfrequency SNPs may provide further insights into the role of negative selection in shaping populationspecific genetic architectures, as negative selection has the strongest impact on variants with low frequency^{26,27}. Fourth, we did not consider populationspecific variants in our analyses, due to the difficulty in defining transethnic genetic correlation for populationspecific variants^{2,5}, a more fundamental challenge than analyzing lowfrequency SNPs; a recent study^{79} has reported that populationspecific variants substantially limit transethnic genetic risk prediction accuracy. Fifth, estimates of genomewide transethnic genetic correlation may be confounded by different trait definitions or diagnostic criteria in the two populations, particularly for major depressive disorder. However, this would not impact estimates of enrichment/depletion of squared transethnic genetic correlation (λ^{2}(C)), which is defined relative to genomewide values. Sixth, we have not pinpointed the exact underlying phenomena (e.g. environmental heterogeneity coupled with geneenvironment interaction) that lead to populationspecific causal disease effect sizes at functionally important regions. Despite these limitations, our study provides an improved understanding of the underlying biology that contribute to populationspecific causal effect sizes, and highlights the need for increasing diversity in genetic studies.
Methods
Definition of stratified squared transethnic genetic correlation
We model a complex phenotype in two populations using linear models, Y_{1} = X_{1}β_{1} + ϵ_{1} and Y_{2} = X_{2}β_{2} + ϵ_{2}, where Y_{1} and Y_{2} are vectors of phenotype measurements of population 1 and population 2 with sample size N_{1} and N_{2}, respectively; X_{1} and X_{2} are meancentered but not normalized genotype matrices at M SNPs in the two populations; β_{1} and β_{2} are perallele causal effect sizes of the M SNPs; and ϵ_{1} and ϵ_{2} are environmental effects in the two populations. We assume that in each population, genotypes, causal effect sizes, and environmental effects are independent of each other. We assume that the perallele effect size of SNP j in the two populations has variance and covariance,
where a_{C}(j) is the value of SNP j for annotation C, which can be binary or continuousvalued; τ_{1C} and τ_{2C} are the net contribution of annotation C to the variance of β_{1j} and β_{2j}, respectively; and θ_{C} is the net contribution of annotation C to the covariance of β_{1j} and β_{2j}.
We define stratified transethnic genetic correlation of a binary annotation C (e.g. functional annotations^{21} or quintiles of continuousvalued annotations^{22}) as
where \({\rho }_{g}(C)={\sum }_{j\in C}{\rm{Cov}}[{\beta }_{1j},{\beta }_{2j}]={\sum }_{j\in C}{\sum }_{C^{\prime} }{a}_{C^{\prime} }(j){\theta }_{C^{\prime} }\) is the transethnic genetic covariance of annotation C; and \({h}_{gp}^{2}(C)={\sum }_{j\in C}{\rm{Var}}[{\beta }_{pj}]={\sum }_{j\in C}{\sum }_{C^{\prime} }{a}_{C^{\prime} }(j){\tau }_{pC^{\prime} }\) is the "allelicscale heritability" (sum of perSNP variance of perallele causal effect sizes; different from heritability on the standardized scale) of annotation C in population p. Here, \(C^{\prime}\) includes all binary and continuousvalued annotations included in the analysis. Since estimates of \({h}_{gp}^{2}(C)\) can be noisy (possibly negative), we estimate squared stratified transethnic genetic correlation,
to avoid bias or undefined values in the square root. In this work, we only estimate \({r}_{g}^{2}(C)\) for SNPs with minor allele frequency (MAF) greater than 5% in both populations. To assess whether causal effect sizes are more or less correlated for SNPs in annotation C compared with the genomewide average, \({r}_{g}^{2}\), we define the enrichment/depletion of stratified squared transethnic genetic correlation as
We metaanalyze λ^{2}(C) instead of \({r}_{g}^{2}(C)\) across diseases and complex traits. For continuousvalued annotations, defining \({r}_{g}^{2}(C)\) and λ^{2}(C) is challenging, as squared correlation is a nonlinear term involving a quotient of squared covariance and a product of variances; we elected to instead estimate λ^{2}(C) for quintiles of continuousvalued annotations (analogous to ref. ^{22}). We note that the average value of λ^{2}(C) across quintiles of continuousvalued annotations is not necessarily equal to 1, as squared transethnic genetic correlation is a nonlinear quantity.
We provide a more detailed definition of the estimands in the Supplementary Notes.
SLDXR method
SLDXR is conceptually related to stratified LD score regression^{21,22} (SLDSC), a method for stratifying heritability from GWAS summary statistics, to two populations. The SLDSC method determines that a category of SNPs is enriched for heritability if SNPs with high LD to that category have higher expected χ^{2} statistic than SNPs with low LD to that category. Analogously, the SLDXR method determines that a category of SNPs is enriched for transethnic genetic covariance if SNPs with high LD to that category have higher expected product of Zscores than SNPs with low LD to that category.
SLDXR relies on the regression equation
to estimate θ_{C}, where Z_{pj} is the Zscore of SNP j in population p; ℓ_{×}(j, C) = ∑_{k}r_{1jk}r_{2jk}σ_{1j}σ_{2j}a_{C}(k) is the transethnic LD score of SNP j with respect to annotation C, whose value for SNP k, a_{C}(k), can be either binary or continuous; r_{pjk} is the LD between SNP j and k in population p; and σ_{pj} is the standard deviation of SNP j in population p. We obtain unbiased estimates of ℓ_{×}(j, C) using genotype data of 481 East Asian and 489 European samples in the 1000 Genomes Project^{16}. To account for heteroscedasticity and increase statistical efficiency, we use weighted least square regression to estimate θ_{C}. We use regression equations analogous to those described in ref. ^{21} to estimate τ_{1C} and τ_{2C}. We include only wellimputed (imputation INFO > 0.9) and common (MAF > 5% in both populations) SNPs that are present in HapMap 3^{17} (irrespective of GWAS significance level) in the regressions (regression SNPs), analogous to our previous work^{21,71,75}. We use all SNPs present in either population in 1000 Genomes^{16} to estimate transethnic LD scores ℓ_{×}(j, C) (reference SNPs; analogous to SLDSC^{21}), so that the resulting coefficients θ_{C} also pertain to these SNPs. However, we estimate \({r}_{g}^{2}(C)\) and λ^{2}(C) (see below; defined as a function of causal effect sizes) for all SNPs with MAF > 5% in both populations (heritability SNPs), accounting for tagging effects (analogous to SLDSC^{21}).
Let \({\hat{\tau }}_{1C}\), \({\hat{\tau }}_{2C}\), and \({\hat{\theta }}_{C}\) be the estimates of τ_{1C}, τ_{2C}, and θ_{C}, respectively. For each binary annotation C, we estimate the stratified heritability of annotation C in each population, \({h}_{g1}^{2}(C)\) and \({h}_{g2}^{2}(C)\), and transethnic genetic covariance, ρ_{g}(C), as
respectively, restricting to causal effects of SNPs with MAF > 5% in both populations (heritability SNPs), using coefficients (\({\tau }_{1C^{\prime} }\), \({\tau }_{2C^{\prime} }\), and \({\theta }_{C^{\prime} }\)) of both binary and continuousvalued annotations. We estimate genomewide transethnic genetic correlation as \({\hat{r}}_{g}=\frac{{\hat{\rho }}_{g}({\mathcal{C}})}{\sqrt{{\hat{h}}_{g1}^{2}({\mathcal{C}}){\hat{h}}_{g1}^{2}({\mathcal{C}})}}\), where \({\mathcal{C}}\) represents the set of all SNPs with MAF > 5% in both populations. We then estimate \({r}_{g}^{2}(C)\) as
where \({\tilde{r}}_{g}^{2}(C)=\frac{{\hat{\rho }}_{g}^{2}(C){\rm{Var}}[{\hat{\rho }}_{g}(C)]}{{\hat{h}}_{g1}^{2}(C){\hat{h}}_{g2}^{2}(C){\rm{Cov}}[{\hat{h}}_{g1}^{2}(C),{\hat{h}}_{g2}^{2}(C)]}\). The correction to \({\tilde{r}}_{g}^{2}(C)\) in Eq. (9) is necessary for obtaining an unbiased estimate of \({r}_{g}^{2}(C)\), as computing quotients of two random variables introduces bias (Supplementary Notes). (We do not constrain the estimate of \({r}_{g}^{2}(C)\) to its plausible range of [−1, 1], as this would introduce bias.) Subsequently, we estimate enrichment of stratified squared transethnic genetic correlation as
where \({\tilde{\lambda }}^{2}(C)=\frac{\hat{{r}_{g}^{2}(C)}}{\hat{{r}_{g}^{2}}}\), the ratio between estimated stratified (\({\hat{r}}_{g}^{2}(C)\)) and genomewide (\({\hat{r}}_{g}^{2}\)) squared transethnic genetic correlation. We use block jackknife over 200 nonoverlapping and equally sized blocks to obtain the standard error of all estimates. The standard error of λ^{2}(C) primarily depends on the total allelicscale heritability of SNPs in the annotation (sum of perSNP variances of causal perallele effect sizes), which appears as the denominator (\({h}_{1g}^{2}(C){h}_{2g}^{2}(C)\)) in the estimation of a stratified squared transethnic genetic correlation (\({r}_{g}^{2}(C)\)); if this denominator is small, estimation of \({r}_{g}^{2}(C)\) becomes noisy. The standard error of λ^{2}(C) indirectly depends on the size of the annotation, because larger annotations tend to have larger total heritability. However, estimates of λ^{2}(C) for a large annotation may have a large standard error if the annotation is depleted for heritability.
To assess the informativeness of each annotation in explaining disease heritability and transethnic genetic covariance, we define standardized annotation effect size on heritability and transethnic genetic covariance for each annotation C analogous to ref. ^{22},
where \({\tau }_{1C}^{* }\), \({\tau }_{2C}^{* }\), and \({\theta }_{C}^{* }\) represent proportionate change in perSNP heritability in population 1 and 2 and transethnic genetic covariance, respectively, per standard deviation increase in annotation C; τ_{1C}, τ_{2C}, and θ_{C} are the corresponding unstandardized effect sizes, defined in Eq. (3); and σ_{C} is the standard deviation of annotation C.
We provide a more detailed description of the method, including derivations of the regression equation and unbiased estimators of the LD scores, in the Supplementary Notes.
SLDXR shrinkage estimator
Estimates of \({r}_{g}^{2}(C)\) can be imprecise with large standard errors if the denominator, \({h}_{g1}^{2}(C){h}_{g2}^{2}(C)\), is close to zero and noisily estimated. This is especially the case for annotations of small size (<1% SNPs). We introduce a shrinkage estimator to reduce the standard error in estimating \({r}_{g}^{2}(C)\).
Briefly, we shrink the estimated perSNP heritability and transethnic genetic covariance of annotation C towards the genomewide averages, which are usually estimated with smaller standard errors, prior to estimating \({r}_{g}^{2}(C)\). In detail, let M_{C} be the number of SNPs in annotation C, we shrink \(\frac{{\hat{h}}_{1g}^{2}(C)}{{M}_{C}}\), \(\frac{{\hat{h}}_{2g}^{2}(C)}{{M}_{C}}\), and \(\frac{{\hat{\rho }}_{g}(C)}{{M}_{C}}\) towards \(\frac{{\hat{h}}_{1g}^{2}}{M}\), \(\frac{{\hat{h}}_{2g}^{2}}{M}\), and \(\frac{{\hat{\rho }}_{g}}{M}\), respectively, where \({\hat{h}}_{g1}^{2}\), \({\hat{h}}_{g2}^{2}\), \({\hat{\rho }}_{g}\) are the genomewide estimates, and M the total number of SNPs. We obtain the shrinkage as follows. Let \({\gamma }_{1}=1/\left(1+\alpha \frac{{\rm{Var}}\left[{\hat{h}}_{g1}^{2}(C)\right]}{{\rm{Var}}\left[{\hat{h}}_{g1}^{2}\right]}\frac{M}{{M}_{C}}\right)\), \({\gamma }_{2}=1/\left(1+\alpha \frac{{\rm{Var}}\left[{\hat{h}}_{g2}^{2}(C)\right]}{{\rm{Var}}\left[{\hat{h}}_{g2}^{2}\right]}\frac{M}{{M}_{C}}\right)\), and \({\gamma }_{3}=1/\left(1+\alpha \frac{{\rm{Var}}\left[{\hat{\rho }}_{g}(C)\right]}{{\rm{Var}}\left[{\hat{\rho }}_{g}\right]}\frac{M}{{M}_{C}}\right)\) be the shrinkage obtained separately for \({\hat{h}}_{g1}^{2}(C)\), \({\hat{h}}_{g2}^{2}(C)\) and \({\hat{\rho }}_{g}(C)\), respectively, where α ∈ [0, 1] is the shrinkage parameter adjusting magnitude of shrinkage. We then choose the most stringent shrinkage, \(\gamma =\min \{{\gamma }_{1},{\gamma }_{2},{\gamma }_{3}\}\), as the final shared shrinkage for both heritability and transethnic genetic covariance.
We shrink heritability and transethnic genetic covariance of annotation C using γ as, \({\bar{h}}_{g1}^{2}(C)={M}_{C}\left(\gamma \frac{{\hat{h}}_{g1}^{2}(C)}{{M}_{C}}+(1\gamma )\frac{{\hat{h}}_{g1}^{2}}{M}\right)\), \({\bar{h}}_{g2}^{2}(C)={M}_{C}\left(\gamma \frac{{\hat{h}}_{g2}^{2}(C)}{{M}_{C}}+(1\gamma )\frac{{\hat{h}}_{g2}^{2}}{M}\right)\), and \({\bar{\rho }}_{g}(C)={M}_{C}\left(\gamma \frac{{\hat{\rho }}_{g}(C)}{{M}_{C}}+(1\gamma )\frac{{\hat{\rho }}_{g}}{M}\right)\), where \({\bar{h}}_{g1}^{2}(C)\), \({\bar{h}}_{g2}^{2}(C)\), and \({\bar{\rho }}_{g}(C)\) are the shrunk counterparts of \({\hat{h}}_{g1}^{2}(C)\), \({\hat{h}}_{g2}^{2}(C)\), and \({\hat{\rho }}_{g}(C)\), respectively. We shrink \({\hat{r}}_{g}^{2}(C)\) by substituting \({\hat{h}}_{g1}^{2}(C)\), \({\hat{h}}_{g2}^{2}(C)\), and \({\hat{\rho }}_{g}(C)\) with \({\bar{h}}_{g1}^{2}(C)\), \({\bar{h}}_{g2}^{2}(C)\), \({\bar{\rho }}_{g}(C)\), respectively, in Eq. (9), to obtain its shrunk counterpart, \({\bar{r}}_{g}^{2}(C)\). Finally, we shrink \({\hat{\lambda }}^{2}(C)\), by plugging in \({\bar{r}}_{g}^{2}(C)\) in Eq. (10) to obtain its shrunk counterpart, \({\bar{\lambda }}^{2}(C)\). We recommend α = 0.5 as the default shrinkage parameter value, as this value provides robust estimates of λ^{2}(C) in simulations. We note that SLDXR does not use the shrinkage estimator when estimating genomewide r_{g} and \({r}_{g}^{2}\).
Significance testing
To assess whether an annotation C is enriched or depleted of squared transethnic genetic correlation for a trait, we test the null hypothesis \({\hat{\lambda }}^{2}(C)=1\). Since \({\hat{\lambda }}^{2}(C)\) is not normally distributed^{80}, we instead test the equivalent null hypothesis \({\hat{D}}^{2}(C)={\hat{\rho }}_{g}^{2}(C){\hat{r}}_{g}^{2}{\hat{h}}_{g1}^{2}(C){\hat{h}}_{g1}^{2}(C)=0\), where \({\hat{r}}_{g}^{2}\) is the genomewide squared transethnic genetic correlation. We obtain test statistic as \(\frac{{\hat{D}}^{2}(C)}{s.e.[{\hat{D}}^{2}(C)]}\), and obtain pvalue under tdistribution with B − 1 degrees of freedom, where B is the number of jackknife blocks. Since the \({\hat{D}}^{2}(C)\) statistic does not involve division by \({\hat{h}}_{g1}^{2}(C){\hat{h}}_{g1}^{2}(C)\), we do not apply any shrinkage to \({\hat{D}}^{2}(C)\).
BaselineLDX model
We include a total of 54 binary functional annotations in the baselineLDX model. These include 53 annotations introduced in ref. ^{21}, which consists of 28 main annotations including conserved annotations (e.g. Coding, Conserved) and epigenomic annotations (e.g. H3K27ac, DHS, Enhancer) derived from ENCODE^{81} and Roadmap^{82}, 24 500basepairextended main annotations, and 1 annotation containing all SNPs. We note that although chromatin accessibility can be populationspecific, the fraction of such regions is small^{83}. Following ref. ^{22}, we created an additional annotation for all genomic positions with number of rejected substitutions^{84} greater than 4. Further information for all functional annotations included in the baselineLDX model is provided in Supplementary Data 1a.
We also include a total of 8 continuousvalued annotations in the baselineLDX model. First, we include 5 continuousvalued annotations introduced in ref. ^{22} (see “Data availability”), without modification: background selection statistic^{30}, CpG content (within a ± 50 kb window), GERP (number of substitutation) score^{84}, nucleotide diversity (within a ± 10 kb window), and Oxford map recombination rate (within a ± 10 kb window)^{85}. Second, we include 2 minor allele frequency (MAF) adjusted annotations introduced in ref. ^{22}, with modification: level of LD (LLD) and predicted allele age. We created analogous annotations applicable to both East Asian and European populations. To create an analogous LLD annotation, we estimated LD scores for each population using LDSC^{75}, took the average across populations, and then quantilenormalized the average LD scores using 10 average MAF bins. We call this annotation “average level of LD”. To create analogous predicted allele age annotation, we quantilenormalized allele age estimated by ARGweaver^{86} across 54 multiethnic genomes using 10 average MAF bins. Finally, we include 1 continuousvalued annotation based on F_{ST} estimated by PLINK2^{87}, which implements the Weir & Cockerham estimator of F_{ST}^{88}. Further information for all continuousvalued annotations included in the baselineLDX model is provided in Supplementary Data 1b.
Simulations
We used simulated East Asian (EAS) and European (EUR) genotype data to assess the performance of our method, as we did not have access to real EAS genotype data at a sufficient sample size to perform simulations with real genotypes. We simulated genotype data for 100,000 EastAsianlike and 100,000 Europeanlike individuals using HAPGEN2^{25} (see “Code availability”), which preserves populationspecific MAF and LD patterns, starting from phased haplotypes of 481 East Asians and 489 Europeans individuals available in the 1000 Genomes Project^{16} (see “Data availability”), restricting to ~2.5 million SNPs on chromosome 1 – 3 with minor allele count greater than 5 in either population. Since the direct output of HAPGEN2 includes substantial relatedness^{2}, we used PLINK2^{87} (see “Code availability”) to remove simulated individuals with genetic relatedness greater than 0.05, resulting in 35,378 EASlike and 36,836 EURlike individuals. From the filtered set of individuals, we randomly selected 500 individuals in each simulated population to serve as reference panels. We used 18,418 EASlike and 36,836 EURlike individuals to simulate GWAS summary statistics, capturing the imbalance in sample size between EAS and EUR GWAS in the analysis of real traits. In our secondary simulations, we also decreased or increased the reference panel size or decreased the GWAS sample size, to evaluate the robustness of our method with respect to reference panel size and GWAS sample size.
We performed both null simulations, where enrichment of squared transethnic genetic correlation, λ^{2}(C), is 1 across all functional annotations, and causal simulations, where λ^{2}(C) varies across annotations, under various degrees of polygenicity (1%, 10%, and 100% causal SNPs). In the null simulations, we set τ_{1C}, τ_{2C}, θ_{C} to be the metaanalyzed τ_{C} in realdata analyses of EAS GWASs, and followed Eq. (3) to obtain a variance, Var[β_{1j}] and Var[β_{2j}], and covariance, Cov[β_{1j}, β_{2j}], of perSNP causal effect sizes β_{1j}, β_{2j}, setting all negative perSNP variance and covariance to 0. In the causal simulations, we directly specified perSNP causal effect size variances and covariances using selfdevised τ_{1C}, τ_{2C}, and θ_{C} coefficients, to attain λ^{2}(C) ≠ 1, as these were difficult to attain using the coefficients from analyses of real traits.
We randomly selected a subset of SNPs to be causal for both populations, and set Var[β_{1j}], Var[β_{2j}], and Cov[β_{1j}, β_{2j}] to be 0 for all remaining noncausal SNPs. We scaled the transethnic genetic covariance to attain a desired genomewide r_{g}. Next, we drew causal effect sizes of each causal SNP j in the two populations from the bivariate Gaussian distribution,
and scaled the drawn effect sizes to match the desired total heritability and transethnic genetic covariance. We also performed null simulations in which imperfect genomewide transethnic genetic correlation is due to populationspecific causal variants. In these simulations, we randomly selected 10% of the SNPs to be causal in each population, with 80% of causal variants in each population shared with the other population, and sampled perfectly correlated causal effect sizes for shared causal variants using Eq. (12). We simulated the genetic component of the phenotype in population p as X_{p}β_{p}, where X_{p} is columncentered genotype matrix, and drew environmental effects, ϵ_{p}, from the Gaussian distribution, \(N\left(0,1{\rm{Var}}[{{\bf{X}}}_{p}{{\boldsymbol{\beta }}}_{p}]\right)\), such that the total phenotypic variance in each population is 1. Finally, we simulated GWAS summary association statistics for population p, Z_{p}, as \({Z}_{pj}=\frac{{{\bf{X}}}_{pj}^{{\mathtt{T}}}{{\bf{Y}}}_{p}}{\sqrt{{N}_{p}}{\sigma }_{pj}}\), where σ_{pj} is the standard deviation of SNP j in population p. We have publicly released Python code for simulating GWAS summary statistics for 2 populations (see “Code availability”). Fifth, we performed additional null simulations with annotationdependent MAFdependent genetic architectures^{26,27,28}, defined as architectures in which the level of MAFdependence is annotationdependent.
We also performed null simulations with annotationdependent MAFdependent genetic architectures^{26,27,28}, defined as architectures in which the level of MAFdependence is annotationdependent, to assess the impact on estimates of enrichment of stratified squared transethnic genetic correlation, (λ^{2}(C)). In these simulations, we set the variance of causal effect size of each SNP j in both populations to be proportional to \({[{p}_{j,\text{max}}(1{p}_{j,\text{max}})]}^{\alpha }\), where p_{j,max} is the maximum MAF of SNP j in the two populations. (We elected to use maximum MAF because a SNP that is rare in one population but common in the other is less likely to be impacted by negative selection.) We set α to − 0.38, as previously estimated for 25 UK Biobank diseases and complex traits in ref. ^{28}. We sampled causal effect sizes using Eq. (12), with Var[β_{1j}], Var[β_{2j}], and Cov[β_{1j}, β_{2j}] scaled to attain a desired genomewide heritability and transethnic genetic correlation. We randomly selected 10% of SNPs to be causal in both populations. Additionally, in the top quintile of background selection statistic, we selected 1.8 × more lowfrequency causal variants (p_{j,max} < 0.05) than common variants (p_{j,max} ≥ 0.05), capturing the action of negative selection across lowfrequency and common variants^{27}.
Summary statistics for 31 diseases and complex traits
We analyzed GWAS summary statistics of 31 diseases and complex traits, primarily from UK Biobank^{74}, Biobank Japan^{20}, and CONVERGE^{18}. All summary statistics were based on genotyping arrays with imputation to an appropriate LD reference panel (e.g. Haplotype Reference Consortium^{89} and UK10K^{90} for UK Biobank^{74}, the 1000 Genomes Project^{16} for Biobank Japan^{20}), except those of the MDD GWAS in the East Asian population, which was based on lowcoverage whole genome sequencing data^{18}. These include: atrial fibrillation (AF)^{91,92}, age at menarche(AMN)^{93,94}, age at menopause (AMP)^{93,94}, basophil count(BASO)^{20,95}, body mass index (BMI)^{20,96}, blood sugar(BS)^{20,96}, diastolic blood pressure (DBP)^{20,96}, eosinophil count(EO)^{20,96}, estimated glomerular filtration rate (EGFR)^{20,97}, hemoglobin A1c(HBA1C)^{20,96}, height (HEIGHT)^{96,98}, high density lipoprotein (HDL)^{20,96}, hemoglobin (HGB)^{20,95}, hematocrit (HTC)^{20,95}, low density lipoprotein (LDL)^{20,96}, lymphocyte count(LYMPH)^{20,96}, mean corpuscular hemoglobin (MCH)^{20,96}, mean corpuscular hemoglobin concentration (MCHC)^{20,95}, mean corpuscular volume (MCV)^{20,95}, major depressive disorder (MDD)^{18,99}, monocyte count (MONO)^{20,96}, neutrophil count(NEUT)^{20,95}, platelet count (PLT)^{20,96}, rheumatoid arthritis(RA)^{100}, red blood cell count (RBC)^{20,96}, systolic blood pressure (SBP)^{20,96}, schizophrenia (SCZ)^{101}, type 2 diabetes (T2D)^{102,103}, total cholesterol (TC)^{20,96}, triglyceride (TG)^{20,96}, and white blood cell count (WBC)^{20,96}. Further information for the GWAS summary statistics analyzed is provided in Supplementary Table 2. In our main analyses, we performed randomeffect metaanalysis to aggregate results across all 31 diseases and complex traits. To test if the metaanalyzed \({\hat{\lambda }}^{2}(C)\) is significantly different from 1, we computed a test statistic as \(\frac{{\hat{\lambda }}^{2}(C)1}{s.e.({\hat{\lambda }}^{2}(C))}\), where \(s.e.({\hat{\lambda }}^{2}(C))\) is the standard error of metaanalyzed \({\hat{\lambda }}^{2}(C)\), and obtained a pvalue under the normal distribution. We also defined a set of 20 approximately independent diseases and complex traits with crosstrait \({r}_{g}^{2}\) (estimated using crosstrait LDSC^{71}) less than 0.25 in both populations: AF, AMN, AMP, BASO, BMI, EGFR, EO, HBA1C, HEIGHT, HTC, LYMPH, MCHC, MCV, MDD, NEUT, PLT, RA, SBP, TC, TG.
Expected enrichment of stratified squared transethnic genetic correlation from 8 continuousvalued annotations
To obtain expected enrichment of squared transethnic genetic correlation of a binary annotation C, λ^{2}(C), from 8 continuousvalued annotations, we first fit the SLDXR model using these 8 annotations together with the base annotation for all SNPs, yielding coefficients, \({\tau }_{1C^{\prime} }\), \({\tau }_{2C^{\prime} }\), and \({\theta }_{C^{\prime} }\), for a total of 9 annotations. We then use Eq. (3) to obtain perSNP variance and covariance of causal effect sizes, β_{1j} and β_{1j}, substituting τ_{1C}, τ_{2C}, θ_{C} with \({\tau }_{1C^{\prime} }\), \({\tau }_{2C^{\prime} }\), and \({\theta }_{C^{\prime} }\), respectively. We apply shrinkage with default parameter setting (α = 0.5), and use Eqs. (9) and (10) to obtain expected stratified squared transethnic genetic correlation, \({r}_{g}^{2}(C)\), and subsequently λ^{2}(C).
Analysis of SEG annotations
We obtained 53 SEG annotations, defined in ref. ^{24} as ±100kbasepair regions surrounding genes specifically expressed in each of 53 GTEx^{32} tissues. A list of the SEG annotations is provided in Supplementary Data 2. Correlations between SEG annotations and the 8 continuousvalued annotations are reported in Supplementary Fig. 28 and Supplementary Data 2. Most SEG annotations are moderately correlated with the background selection statistic and CpG content annotations.
To test whether there is heterogeneity in enrichment of squared transethnic genetic correlation, λ^{2}(C), across the 53 SEG annotations, we first computed the average λ^{2}(C) across the 53 annotations, \({\bar{\lambda }}^{2}(C)\), using fixedeffect metaanalysis. We then computed the test statistic \(\mathop{\sum }\nolimits_{i = 1}^{53}\frac{{\left({\hat{\lambda }}^{2}({C}_{i}){\bar{\lambda }}^{2}({C}_{i})\right)}^{2}}{{\rm{Var}}[{\hat{\lambda }}^{2}({C}_{i})]}\), where C_{i} is the ith SEG annotation, and \({\hat{\lambda }}^{2}({C}_{i})\) the estimated λ^{2}(C). We computed a pvalue for this test statistic based on a χ^{2} distribution with 53 degrees of freedom.
Analysis of distance to nearest exon annotation
We created a continuousvalued annotation, named “distance to nearest exon annotation”, based on a SNP’s physical distance (number of base pairs) to its nearest exon, using 233,254 exons defined on the UCSC genome browser^{104} (see “Data availability”). This annotation is moderately correlated with the background selection statistic annotation^{22} (R = −0.21), defined as (1  McVicker B statistic/1000), where the McVicker B statistic quantifies a site’s genetic distance to its nearest exon^{30}. We have publicly released this annotation (see “Data availability”).
To assess the informativeness of functionally important regions versus regions impacted by selection in explaining the depletions of squared transethnic genetic correlation, we applied SLDXR on the distance to nearest exon annotation together with the baselineLDX model annotations. We used both enrichment of squared transethnic genetic correlation (λ^{2}(C)) and standardized annotation effect size (\({\tau }_{1C}^{* }\), \({\tau }_{2C}^{* }\), and \({\theta }_{C}^{* }\)) to assess informativeness.
Analysis of probability of lossoffunction intolerance decile gene annotations
We created 10 annotations based on genes in deciles of the probability of being lossoffunction intolerant (pLI) (see “Data availability”), defined as the probability of assigning a gene into haplosufficient regions, where proteintruncating variants are depleted^{56}. Genes with high pLI (e.g. >0.9) have highly constrained functionality, and therefore mutations in these genes are subject to negative selection. We included SNPs within a 100kbbasepair window around each gene, following ref. ^{24}. A correlation heat map between pLI decile gene annotations and the 8 continuousvalued annotations is provided in Supplementary Fig. 29. All pLI decile gene annotations are moderately correlated with the background selection statistic and CpG content annotations.
Analysis of the integrated haplotype score annotation
We created a binary annotation (proportion of SNPs: 6.3%) that includes all SNPs whose maximum absolute value of the integrated haplotype score (iHS)^{43,44} (see “Data availability”) across all 1000 Genomes Project EAS and EUR subpopulations are greater than 2.0, the recommended threshold to detect positive selection in ref. ^{43}. This annotation is positively correlated with the top quintile of the background selection statistic annotation (R = 0.077). We note that although the iHS is a recombinationrateadjusted quantity to detect the action of recent positive selection, it may also capture actions of negative selection^{43,44}.
Reporting summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article.
Data availability
All baselineLDX model annotations and other annotations used in this work are available at https://data.broadinstitute.org/alkesgroup/SLDXR/. We used exon definitions from the UCSC Genome Browser (https://genome.ucsc.edu/). We used gene pLI scores from the Exome Aggregation Consortium (ExAC) (https://exac.broadinstitute.org/). The integrated haplotype scores (iHS) are available at http://coruscant.itmat.upenn.edu/data/JohnsonEA_iHSscores.tar.gz. The 1000 Genomes Project Phase 3 data are available at https://www.internationalgenome.org/. The baselineLD model annotations are available at https://alkesgroup.broadinstitute.org/LDSCORE/.
Code availability
Python code implementing SLDXR is available at https://github.com/huwenboshi/sldxr. Python code for simulating GWAS summary statistics under the baselineLDX model is available at https://github.com/huwenboshi/sldxrsim. Python code implementing the twopopulation EyreWalker model is available at https://github.com/huwenboshi/twopopulationEyreWalkermodel. Python code for creating the distance to nearest exon annotation is available at https://github.com/huwenboshi/distancetonearestexon. We used HAPGEN2 (https://mathgen.stats.ox.ac.uk/genetics_software/hapgen/hapgen2.html) to simulated genotype data. We used PLINK2 (https://www.coggenomics.org/plink/2.0/) to remove related individuals in the simulated genotype data.
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Acknowledgements
The authors are grateful to L. O’Connor, H. Finucane, D. Kassler, S. Mallick, N. Patterson, B. Neale, R. Walters, A. Martin, B. Brown, F. Hormozdiari, M. Hujoel, K. Burch, and B. Pasaniuc for helpful discussions. This research was conducted using the UK Biobank Resource under Application 16549 and was funded by NIH grants R01 HG006399, U01 HG009379, R37 MH107649, R01 MH101244, and R01 CA222147.
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H.S. and A.L.P. designed the experiments. H.S. performed the experiments. H.S., S.G., M.K., E.M.K., A.P.S., and A.L.P. analyzed the data. H.S. and A.L.P. wrote the paper with assistance from all authors.
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Shi, H., Gazal, S., Kanai, M. et al. Populationspecific causal disease effect sizes in functionally important regions impacted by selection. Nat Commun 12, 1098 (2021). https://doi.org/10.1038/s41467021212861
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DOI: https://doi.org/10.1038/s41467021212861
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