LD Score regression distinguishes confounding from polygenicity in genome-wide association studies
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Abstract
Both polygenicity (many small genetic effects) and confounding biases, such as cryptic relatedness and population stratification, can yield an inflated distribution of test statistics in genome-wide association studies (GWAS). However, current methods cannot distinguish between inflation from a true polygenic signal and bias. We have developed an approach, LD Score regression, that quantifies the contribution of each by examining the relationship between test statistics and linkage disequilibrium (LD). The LD Score regression intercept can be used to estimate a more powerful and accurate correction factor than genomic control. We find strong evidence that polygenicity accounts for the majority of the inflation in test statistics in many GWAS of large sample size.
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Results from LD Score regression favored polygenicity over stratification bias, with an LD Score intercept of 1.115 (SE=0.019) and attenuation ratio of 0.054 (SE=0.009).
“LD Score regression suggested polygenicity rather than bias from population stratification10,12, as the (default settings) LD Score intercept and attenuation ratio were estimated to be 1.115 (SE = 0.019) and 0.054 (SE = 0.009), respectively.”
From Multivariate analysis of 1.5 million people identifies genetic associations with traits related to self-regulation and addiction. (2021) · cites this paper as [12]
The Results (Real Data; page not provided) say that LD Score regression found polygenicity contributed substantially more than bias to GWAS test-statistic inflation. Our copy does not report the claimed intercept of 1.115 (SE = 0.019) or attenuation ratio of 0.054 (SE = 0.009); its schizophrenia example instead gives an intercept of 1.07. (LLM, conf=0.87)
Experimental — accuracy not yet measuredThe LD score regression intercept was computed using LDSC v1.0.1 with baselineLD LD scores from 1000 Genomes phase 3.
“The LD score regression intercept was computed with LDSC v1.0.1 software using the ‘baselineLD’ LD scores built from 1000 Genomes phase 3 (ref. 64).”
From New insights into the genetic etiology of Alzheimer’s disease and related dementias (2022) · cites this paper as [64]
The Results (Overview of Methods) describe LD Score regression and LD Scores estimated from 1000 Genomes European samples; Online Methods (Estimation of LD Score) also mention the authors’ LDSC software package. Our copy does not identify LDSC v1.0.1, ‘baselineLD’ scores, or 1000 Genomes phase 3 as the inputs used in the citing paper’s computation. (LLM, conf=0.87)
Experimental — accuracy not yet measuredLD score regression intercepts were calculated for each GWAS and corrected standard errors were calculated by multiplying the standard error by the square root of the LD score regression intercept when the intercept was more than 1.
“LD score regression intercepts were calculated for each GWAS using LD score (v.1.0.1)45 and corrected standard errors (SEldsc) were calculated by multiplying the standard error by the square root of the LD score regression intercept in cases where the LD score regression intercept was more than 1.”
From Genomic and transcriptomic analyses of aortic stenosis enhance therapeutic target discovery and disease prediction (2026) · cites this paper as [45]
The Discussion (page unavailable) identifies LD Score regression and a command-line tool for estimating LD Scores and performing the regression. It also proposes using the regression intercept to correct inflated GWAS test statistics. Our copy does not specify multiplying standard errors by the square root of the intercept or applying that correction only when the intercept exceeds 1. (LLM, conf=0.85)
Experimental — accuracy not yet measuredIn deCODE, correction for inflation of test statistics due to relatedness and population stratification was performed using the intercept estimate (1.30) from linkage disequilibrium score regression.
“In deCODE, correction for inflation of test statistics due to relatedness and population stratification was performed using the intercept estimate (1.30) from linkage disequilibrium (LD) score regression21.”
From Consensus meta-analysis of genome-wide association studies for Alzheimer’s disease and related dementias (2026) · cites this paper as [21]
The Introduction explains that the LD Score regression intercept estimates inflation from confounding biases, including relatedness and population stratification; the Discussion proposes using it to correct test statistics. Our copy does not report a deCODE analysis, an intercept of 1.30, or that this correction was performed in deCODE. (LLM, conf=0.88)
Experimental — accuracy not yet measuredPopulation-specific LD scores based on the 1KG Project phase 3 data were used to estimate SNP-based heritability.
“We performed LDSC v1.0.1 (ref. 18) to estimate the SNP-based heritability of EduYears in the TWB, KoGES, EAS and EUR populations14 using population-specific LD scores based on the 1KG Project phase 3 data.”
From Shared genetic architectures of educational attainment in East Asian and European populations (2024) · cites this paper as [18]
The Results (Overview of Methods) say LD Score regression can estimate SNP-based heritability under strong assumptions, and Online Methods (Estimation of LD Score) describe LD scores derived from the 1000 Genomes European reference panel. Online Methods (Intra-European LD Score Differences) also describe scores for European subpopulations. The paper does not specify phase 3 data or report using population-specific scores for TWB, KoGES, and EAS heritability estimates. (LLM, conf=0.87)
Experimental — accuracy not yet measured
LDSC can use GWAS data to estimate SNP heritability, the proportion of phenotypic variation explained by common SNPs.
“Linkage disequilibrium (LD) score regression (LDSC) can use GWAS data to estimate SNP heritability, the proportion of phenotypic variation explained by common SNPs20,23.”
From Within-sibship genome-wide association analyses decrease bias in estimates of direct genetic effects (2022) · cites this paper as [20]
The Results (Overview of Methods; page unavailable) say the LD Score regression slope can be rescaled to estimate heritability explained by SNPs used to calculate LD Scores. But this requires strong assumptions about rare-variant effects; the paper does not present it as an unqualified estimate of the proportion of phenotypic variation explained specifically by common SNPs. (LLM, conf=0.86)
Experimental — accuracy not yet measuredA large proportion of samples in the meta-analysis were from UK-based studies such as UK Biobank and Generation Scotland, for which the LD scores, generated using 1000 Genomes project (phase 3) European samples (CEU, TSC, FIN, GBR), have been shown to fit reasonably well.
“A large proportion of samples in the meta-analysis were from UK-based studies such as UK Biobank and Generation Scotland, for which the LD scores, generated using 1000 Genomes project (phase 3) European samples (CEU, TSC, FIN, GBR), have been shown to fit reasonably well20.”
From Within-sibship genome-wide association analyses decrease bias in estimates of direct genetic effects (2022) · cites this paper as [20]
Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measuredModest inflation was observed (lambda=1.12, lambda1000=1.006), and LD score regression indicates this is arising from polygenicity (>96%) rather than confounding.
“While modest inflation was observed (lambda=1.12, lambda1000 = 1.006), LD score regression analysis 19 indicates this is arising from polygenicity (> 96%, see Methods) rather than confounding.”
From Identification of common genetic risk variants for autism spectrum disorder (2019) · cites this paper as [19]
The degree to which deviation in test statistics could be ascribed to cryptic relatedness and population stratification rather than polygenicity was measured from the LD score regression intercept.
“The degree to which the deviation in the test statistics can be ascribed to cryptic relatedness and population stratification rather than to polygenicity was measured from the intercept in LD score regression 19 (LDSC) as the ratio of (intercept1) and (mean(χ 2 )-1).”
From Identification of common genetic risk variants for autism spectrum disorder (2019) · cites this paper as [19]
The genome-wide genetic correlation for EduYears between TWB and KoGES was 0.871 (s.e. 0.073) using LDSC.
“the genome-wide genetic correlation for EduYears between TWB and KoGES was 0.871 (standard error (s.e.) 0.073) using LDSC18”
From Shared genetic architectures of educational attainment in East Asian and European populations (2024) · cites this paper as [18]
Genome-wide associations in TWB, KoGES and their meta-analysis were consistent with a highly polygenic architecture and did not indicate inflation due to potential population stratification, with LDSC intercepts from 1.029 to 1.046.
“Genome-wide associations in the TWB, KoGES and their meta-analysis were consistent with the highly polygenic architecture of educational attainment and did not indicate inflation due to potential population stratification (linkage disequilibrium score regression (LDSC)18 intercept ranged from 1.029 to 1.046).”
From Shared genetic architectures of educational attainment in East Asian and European populations (2024) · cites this paper as [18]
A large number of samples were from Scandinavian populations (HUNT study, FinnTwin), where LD mismatch leading to elevated LDSC intercept/ratios has been previously discussed.
“However, a large number of samples were from Scandinavian populations (HUNT study, FinnTwin), where LD mismatch leading to elevated LDSC intercept/ratios has been previously discussed20.”
From Within-sibship genome-wide association analyses decrease bias in estimates of direct genetic effects (2022) · cites this paper as [20]
The LDSC intercept has been proposed as a measure of confounding, with deviations above one argued to represent the extent of spurious inflation in GWAS test statistics.
“The LDSC intercept has been proposed as a measure of confounding, with deviations above one argued to represent the extent of spurious inflation in GWAS test statistics33.”
From Family-GWAS reveals effects of environment and mating on genetic associations (2024) · cites this paper as [33]
Inferences from LD score regression applied to GWAS results appear fairly robust to confounding due to population stratification, at least some of which is adjusted out by LDSC.
“Inferences drawn from the application of LD score regression (LDSC) to GWAS results appear to be fairly robust to confounding due to population stratification, at least some of which is adjusted out by LDSC5,33.”
From Family-GWAS reveals effects of environment and mating on genetic associations (2024) · cites this paper as [33]
Only a small share (~5%) of the inflation is attributable to bias according to LD Score regression estimates.
“According to our LD Score regression13 estimates, only a small share (~5%) of this inflation is attributable to bias (Supplementary Figure 2, Supplementary Table 1).”
From Gene discovery and polygenic prediction from a genome-wide association study of educational attainment in 1.1 million individuals (2018) · cites this paper as [13]
The LD score intercept was 1.08 (s.e. = 0.02).
“a linkage disequilibrium (LD) score intercept 17 of 1.08 (s.e.= 0.02)”
From Genome-wide association meta-analysis in 269,867 individuals identifies new genetic and functional links to intelligence (2018) · cites this paper as [17]
The LD score regression intercept for the EA GWAS is 1.66, and confounding accounts for 7% of the inflation.
“According to the LD score regression8 intercept (1.66), confounding accounts for 7% of the inflation, similar to previous GWAS of EA2”
From Polygenic prediction of educational attainment within and between families from genome-wide association analyses in 3 million individuals (2022) · cites this paper as [8]
ASD (N = 46,350) shows significant genetic correlations with other traits after Bonferroni correction for testing a total of 234 traits available at LDhub plus a handful of new phenotypes.
“Significant genetic correlations between ASD ( N = 46,350) and other traits after Bonferroni correction for testing a total of 234 traits available at LDhub with the addition of a handful of new phenotypes.”
From Identification of common genetic risk variants for autism spectrum disorder (2019) · cites this paper as [19]
The Results > Real Data passage (page unavailable) reports LD Score regression across more than 20 phenotypes, not genetic correlations for ASD. Searches for ASD, a sample of 46,350, LDhub, and the 234-trait Bonferroni correction found no passage in our copy addressing the claim. (LLM, conf=0.76)
Experimental — accuracy not yet measuredMany cardiometabolic traits are genetically correlated with one another.
“Due to the epidemiological correlation between AD and cardiometabolic traits, coupled with the fact that many cardiometabolic traits are genetically correlated with one another, additional broader-scale pleiotropic studies are warranted, and recently the field has begun to do so [4, 11].”
From Multi-trait association studies discover pleiotropic loci between Alzheimer’s disease and cardiometabolic traits (2021) · cites this paper as [11]
The Results (Real Data; page unavailable) discuss polygenicity across more than 20 phenotypes, but do not report genetic correlations between cardiometabolic traits. The Discussion (page unavailable) describes estimating genetic correlation as research in progress. Searches for cardiometabolic genetic correlations and shared genetic architecture found no passage establishing the claim. (LLM, conf=0.76)
Experimental — accuracy not yet measuredSNP-based heritability for EduYears was estimated to be 9.7% in TWB, 8.7% in KoGES and 9.0% in the EAS GWAS meta-analysis.
“At the genome-wide level, we first showed that the SNP-based heritability for EduYears was estimated to be 9.7% in TWB, 8.7% in KoGES and 9.0% in the EAS GWAS meta-analysis”
From Shared genetic architectures of educational attainment in East Asian and European populations (2024) · cites this paper as [18]
The Results (Overview of Methods; page unavailable) explain how an LD Score regression slope can be used to estimate SNP heritability under strong assumptions. The passages found do not report EduYears heritability estimates for TWB, KoGES, or an EAS GWAS meta-analysis; searches for those cohorts and the three percentages found no matching result. (LLM, conf=0.76)
Experimental — accuracy not yet measuredThe three contributing cohorts showed strong pairwise genetic correlations: PGC_139k-23andMe_307k rG = 0.85, UK Biobank-PGC_139k rG = 0.87, and UK Biobank-23andMe_307k rG = 0.85.
“There was a strong genetic correlation between each of these cohorts. The rG between PGC_139k and 23andMe_307k was 0.85 (s.e = 0.03). The UK Biobank had a rG of 0.87 (s.e = 0.04) with PGC_139k. A similar rG was also found between UK Biobank and 23andMe_307k (0.85, s.e = 0.03).”
From Genome-wide meta-analysis of depression identifies 102 independent variants and highlights the importance of the prefrontal brain regions (2019) · cites this paper as [10]
LDSC estimated the SNP-based heritability of depression at 0.089 (s.e. 0.003) on the liability scale.
“The estimate of the SNP-based heritability of depression within our meta-analysis was 0.089 (0.003) on the liability scale using LDSC regression 10.”
From Genome-wide meta-analysis of depression identifies 102 independent variants and highlights the importance of the prefrontal brain regions (2019) · cites this paper as [10]
LDSC regression estimated a genomic inflation factor of 1.63 and an intercept of 1.015 (s.e. 0.011) before inflation correction.
“Linkage Disequilibrium Score (LDSC) regression 10 produced a genomic inflation factor (λGC) estimate of 1.63 with an intercept of 1.015 (0.011) prior to inflation correction”
From Genome-wide meta-analysis of depression identifies 102 independent variants and highlights the importance of the prefrontal brain regions (2019) · cites this paper as [10]
Genomic inflation was controlled using LDSC regression intercepts for each contributing cohort and the final meta-analysis.
“Linkage disequilibrium score (LDSC) regression intercepts 10 were used for genomic inflation control of the three contributing cohorts and the final meta-analysis results.”
From Genome-wide meta-analysis of depression identifies 102 independent variants and highlights the importance of the prefrontal brain regions (2019) · cites this paper as [10]
LDSC regression estimates indicated that the majority of inflation was due to polygenic signal, with intercept close to 1 (1.026, s.e.m. = 0.006).
“univariate linkage disequilibrium score (LDSC) regression12,13 estimates indicated that the majority of this inflation was due to a polygenic signal, with the intercept being close to 1 (1.026, s.e.m. = 0.006).”
From Genetic meta-analysis of diagnosed Alzheimer’s disease identifies new risk loci and implicates Aβ, tau, immunity and lipid processing (2019) · cites this paper as [13]
LDSC regression was performed to calculate the LD score regression intercept and derive a heritability estimate for the inverse-variance weighted meta-analysis summary statistics.
“In addition, we performed LDSC regression via LD Hub v.1.9.0 (refs. 12,13) to calculate the LD score regression intercept and derive a heritability estimate for the inverse-variance weighted meta-analysis summary statistics.”
From Genetic meta-analysis of diagnosed Alzheimer’s disease identifies new risk loci and implicates Aβ, tau, immunity and lipid processing (2019) · cites this paper as [13]
Loci associated with human osteocyte transcriptome signature gene orthologs contribute to the heritability of OA at any site (P = 1.6 × 10−7), at the knee (P = 1.9 × 10−6), hip (P = 4.5 × 10−3) and hip and/or knee (P = 3.2 × 10−6).
“LDSC-SEG analysis60,61 showed that loci associated with human osteocyte transcriptome signature gene orthologs contribute to the heritability of OA at any site (P = 1.6 × 10−7), at the knee (P = 1.9 × 10−6), hip (P = 4.5 × 10−3) and hip and/or knee (P = 3.2 × 10−6).”
From Osteocyte transcriptome mapping identifies a molecular landscape controlling skeletal homeostasis and susceptibility to skeletal disease (2021) · cites this paper as [61]
LD Score intercepts were near 1.00 (range: 0.98-1.02), indicating that the genomic inflation was due to a polygenic architecture rather than inflation due to uncorrected population structure.
“Estimation of the LD Score intercepts, using LD score regression26, revealed intercepts near 1.00 (range: 0.98–1.02), indicating that the genomic inflation was due to a polygenic architecture rather than inflation due to uncorrected population structure.”
From GWAS identifies 14 loci for device-measured physical activity and sleep duration (2018) · cites this paper as [26]
Genetic correlations between men and women were strong, ranging from 0.92 for overall activity to 0.97 for sleep duration.
“Genetic correlations32 of trait architectures as measured using LD score regression26 showed strong correlation between men and women; correlations ranged from 0.92 for overall activity to 0.97 for sleep duration (Supplementary Fig. 6).”
From GWAS identifies 14 loci for device-measured physical activity and sleep duration (2018) · cites this paper as [26]
Sensitivity analysis using LD score regression on the overall activity trait showed no need to include principal components of ancestry as covariates in the linear mixed models (lambda = 1.20 vs. 1.20, LD intercept = 1.0085 vs. 1.0092, genome-wide genetic correlation Rg = 0.99).
“Sensitivity analysis using LD score regression26 on the overall activity trait showed we did not need to include principal components of ancestry as covariates in our linear mixed models (lambda = 1.20 vs. 1.20, LD intercept = 1.0085 vs. 1.0092, genome-wide genetic correlation (Rg) = 0.99).”
From GWAS identifies 14 loci for device-measured physical activity and sleep duration (2018) · cites this paper as [26]
SNP-heritability methods calculate heritability from SNP array data and provide assessments based on genome-wide genotypes, improving on traditional heritability measurements.
“Second, several methods can calculate the heritability of a trait using SNP array data (Bulik-Sullivan et al., 2015; Yang et al., 2011). These provide assessments of heritability based on genome-wide genotypes, and improves upon traditional heritability measurements given their basis in direct genetic measurements.”
From Defining the genetic, genomic, cellular, and diagnostic architectures of psychiatric disorders (2019) · cites this paper as Bulik-Sullivan et al., 2015
LDSC genetic correlations above 1 are possible and occurred when testing the same sample with similar phenotypes or smaller FinnGen samples against large samples.
“Some of the genetic correlations from the LD score regression were greater than one; genetic correlation from LDSC does not bound to one,13 and the instances with values higher than one occurred when testing in the same sample with similar phenotype (rg 1.07, SE=0.0343) between MDD and SR-Depression within MVP), or between the somewhat smaller FinnGen sample and the large PGC/UKB broad depression”
From Bi-ancestral depression GWAS in the Million Veteran Program and meta-analysis in >1.2 million individuals highlight new therapeutic directions (2021) · cites this paper as [13]
Phenotypes with heritability z-scores ≥ 4 were considered suitable for genetic correlation against MDD-META.
“Phenotypes with heritability z-scores ≥ 4 were considered suitable for genetic correlation against MDD-META. 13”
From Bi-ancestral depression GWAS in the Million Veteran Program and meta-analysis in >1.2 million individuals highlight new therapeutic directions (2021) · cites this paper as [13]
SNP heritability calculated using LD Score Regression ranged from 4.2% for DrnkWk to 8.0% for CigDay.
“SNP heritability calculated using LD Score Regression17 ranged from 4.2% for DrnkWk to 8.0% for CigDay (Figure 3; Supplementary Table 13)”
From Association studies of up to 1.2 million individuals yield new insights into the genetic etiology of tobacco and alcohol use (2019) · cites this paper as [17]
No statistically significant genetic correlation was observed between endometriosis and 199 common complex traits based on LD score regression analysis using LD hub.
“We did not observe statistically significant genetic correlation between endometriosis and 199 common complex traits, based on LD score regression analysis25 using LD hub26.”
From Meta-analysis identifies five novel loci associated with endometriosis highlighting key genes involved in hormone metabolism (2017) · cites this paper as [25]
If all genetic variants are valid instruments and the relationships between all variables are linear and homogeneous for all individuals in the population, then the variant-specific estimates all target the same causal parameter, and there is no more heterogeneity between them than expected by chance alone.
“If all genetic variants are valid instruments and the relationships between all variables (genetic variants, exposure and outcome) are linear and homogeneous for all individuals in the population, then we would expect the variant-specific estimates (that is, the ratio estimates based on each variant in turn) to all target the same causal parameter, and for there to be no more heterogeneity between”
From Guidelines for performing Mendelian randomization investigations (2020) · cites this paper as [13]
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Biological insights from 108 schizophrenia-associated genetic loci
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Self-citationA meta-analysis of genome-wide association studies identifies 17 new Parkinson's disease risk loci
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- Authors
- Schizophrenia Working Group of the Psychiatric Genomics Consortium, Bulik-Sullivan, B. K., Loh, P.-R., Finucane, H. K., Ripke, S., Yang, J., Patterson, N., Daly, M. J., Price, A. L., & Neale, B. M.
- Affiliations
- Broad Institute (US)
- Harvard University (US)
- The University of Queensland (AU)
- Corresponding author
- Neale, Benjamin M
- ORCID
- Venue
- Nature Genetics
- Published
- 2015-02-02
- Volume
- 47
- Issue
- 3
- Pages
- 291-295
- ISSN
- 1061-4036 (ISSN-L)
- 1546-1718
- PMC
- PMC4495769
- OpenAlex
- W2153860431
- Cited by
- 5,559
- References
- 52
- Citations by year
- 2026: 620 · 2025: 852 · 2024: 805 · 2023: 634 · 2022: 612 · 2021: 558 · 2020: 394 · 2019: 392 · 2018: 312 · 2017: 200 · 2016: 120 · 2015: 50 · 2014: 3
- FWCI
- 155.57
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nature Genetics (publishedVersion)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion)
- PubMed (publishedVersion)
- VU Research Portal (publishedVersion)
- PubMed Central (acceptedVersion)
- eScholarship (California Digital Library) (submittedVersion)
- Lirias (KU Leuven) (submittedVersion, other-oa)
- Pure Amsterdam UMC (submittedVersion, other-oa)
- EPubDev Repository (submittedVersion)
- UWA Profiles and Research Repository (UWA) (submittedVersion)
- Data Archiving and Networked Services (DANS) (submittedVersion)
- Adelaide Research & Scholarship (AR&S) (University of Adelaide) (submittedVersion)
- Lancaster EPrints (Lancaster University) (submittedVersion)
- UCL Discovery (University College London) (submittedVersion)
- ORCA Online Research @Cardiff (Cardiff University) (submittedVersion)
- The HKU Scholars Hub (University of Hong Kong) (submittedVersion)
- Institutional Research Information System (Università degli Studi di Trento) (submittedVersion)
- GRO (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Research Portal (Queen's University Belfast) (submittedVersion)
- RUNE (Research UNE) (submittedVersion)
- NOVA (University of Newcastle Australia) (submittedVersion)
- Funders
- National Institutes of Health (5u01mh094432-04)
- Medical Research Council (MR/L023784/2, MR/L010305/1, MR/L023784/1)
- National Institute of Mental Health (U01 MH094432, U01MH094421, R01MH085548, R01 MH094421, R01MH101244)
- National Human Genome Research Institute (R01HG006399, F32HG007805)
- National Cancer Institute (R03CA173785)
- National Center for Research Resources (UL1RR025758)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Mapping and Diversity in Plants and Animals
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic and phenotypic traits in livestock
- Keywords
- LD score regression, polygenicity, confounding, linkage disequilibrium, cryptic relatedness, population stratification, genomic control, summary statistics, polygenic traits
- MeSH terms
- Computer Simulation, Humans, Regression Analysis, Linkage Disequilibrium, Genome, Human, Sample Size, Polymorphism, Single Nucleotide, Genome-Wide Association Study
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