causal-genomics-heritability-partitioning

name	causal-genomics-heritability-partitioning
description	Estimate SNP heritability and partition it across functional annotations, cell types, and loci from GWAS summary statistics or individual-level genotypes. Implements LDSC, stratified LDSC with the baseline-LD model, Finucane 2018 cell-type prioritization, LDAK SumHer, HDL, HESS local heritability, BOLT-REML, GCTA-GREML, graphREML, and Popcorn cross-population genetic correlation. Use when computing total h2_SNP from summary stats, partitioning heritability across functional categories, prioritizing trait-relevant tissues or cell types from ENCODE/Roadmap chromatin marks, reconciling LDSC vs LDAK enrichment estimates, computing local heritability with HESS, estimating genetic correlation between traits, or producing publication-grade enrichment with calibrated sensitivity to model assumptions.
tool_type	mixed
primary_tool	ldsc

Version Compatibility

Reference examples tested with: LDSC v1.0.1+ (Python 3 fork; prefer abdenlab/ldsc-python3 v2.0.0 which retains the working --h2 / --rg / --h2-cts CLI -- belowlab/ldsc v3.0.1 explicitly broke that CLI per its README and is best run via Docker jtb114/ldsc:latest), LDAK 6.0+, BOLT-LMM 2.4.1+, GCTA 1.94+, HESS 0.5.4+, HDL 1.4.0+ (R; GitHub zhenin/HDL), Popcorn 1.0+ (Python; brielin/Popcorn), baselineLD_v2.2 annotations (alkesgroup.broadinstitute.org/LDSCORE).

Before using code patterns, verify installed versions match. If versions differ:

• Python: pip show <package> then python -c 'import <module>; help(<module>)'
• R: packageVersion('<pkg>') then ?function_name
• CLI: <tool> --version then <tool> --help

LDSC's official repository (bulik/ldsc) is Python 2.7 only and unmaintained since 2019; use the Python 3 community forks. If code throws ImportError, AttributeError, or a "category not found" error in the LD score file, introspect the installed binary and the actual LD-score column headers rather than retrying.

Heritability Partitioning

"Estimate SNP heritability and partition it across functional categories, cell types, and loci" -> Decompose h2_SNP from GWAS summary statistics (or individual-level genotypes) into contributions from baseline annotations (coding, conserved, regulatory), tissue-specific chromatin marks, and per-locus components, then reconcile model-dependent enrichment estimates across LDSC and LDAK. Tool choice is a decision about the regime (summary-stat vs individual-level; one-trait vs two-trait genetic correlation; total vs partitioned vs local) and the model assumption about how per-SNP heritability scales with LD, MAF, and functional annotation (GCTA model vs LDAK-Thin vs baseline-LD).

• CLI (h2 from sumstats, EUR): ldsc.py --h2 trait.sumstats.gz --ref-ld-chr eur_w_ld_chr/ --w-ld-chr eur_w_ld_chr/ --out h2
• CLI (functional partitioning): ldsc.py --h2 trait.sumstats.gz --ref-ld-chr baselineLD.,<annot>. --frqfile-chr 1000G.EUR.QC. --w-ld-chr weights. --overlap-annot --print-coefficients --out part
• CLI (cell-type prioritization, Finucane 2018): ldsc.py --h2-cts trait.sumstats.gz --ref-ld-chr-cts <cts_file>.ldcts --w-ld-chr weights. --out cts
• CLI (cross-trait rg): ldsc.py --rg t1.sumstats.gz,t2.sumstats.gz --ref-ld-chr eur_w_ld_chr/ --w-ld-chr eur_w_ld_chr/ --out rg
• CLI (LDAK alternative): ldak --sum-hers <out> --summary trait.txt --tagfile ldak.thin.<build>.tagging --check-sums NO
• R (HDL): HDL::HDL.rg(gwas1.df, gwas2.df, LD.path = 'UKB_array_SVD_eigen90_extraction')
• CLI (local h2): HESS step1 hess.py --local-hsqg trait.sumstats.gz --chrom <chr> --bfile <ref> --partition-file <part>.bed --out hess_<chr>

Statistical Model Taxonomy

Method	Heritability model	Input	Output	Strength	Fails when
LDSC h2 (Bulik-Sullivan 2015 Nat Genet 47:291)	GCTA model: per-SNP h2 proportional to LD score	Sumstats + ancestry-matched LD scores	h2 estimate + intercept + ratio	Standard for sumstats; fast; calibrated EUR LD scores	N too low (mean chi-square < 1.02); non-EUR ancestry with EUR LD scores; population stratification not captured
Stratified LDSC / S-LDSC (Finucane 2015 Nat Genet 47:1228)	GCTA model with per-annotation tau coefficients	Sumstats + baseline + custom annotations	Per-annotation enrichment + tau	Reference functional partitioning method	Highly collinear annotations inflate per-tau SE; small annotation (<0.5% genome) underpowered
Baseline-LD model (Gazal 2017 Nat Genet 49:1421)	Adds LD-related and MAF-dependent annotations to baseline	Sumstats + baselineLD_v2.2.	Enrichment robust to LD-MAF confounding	Modern S-LDSC default; calibrates LD/MAF dependence	EUR-only baseline-LD v2.2 must NOT be used on non-EUR GWAS; use baseline-LD-X (Atkinson 2021 Nat Genet 53:1432) or per-ancestry baseline-LD (Atkinson/Price 2022) instead
Cell-type S-LDSC (Finucane 2018 Nat Genet 50:621)	Per-cell-type annotation marginal to baseline	Sumstats + cell-type chromatin annotations (.ldcts)	Per-cell-type p-value	Tissue / cell-type prioritization; published per-tissue ldcts files	Sample size small (mean chi-square < 1.02); annotation overlaps strongly with baseline
HDL (Ning 2020 Nat Genet 52:859)	Genome-wide eigen-decomposition likelihood	Sumstats + HDL reference panel (UKB N=336k)	h2 and rg with ~60% lower variance than LDSC	Equivalent to ~2.5x sample size for h2 / rg	Sample overlap > 5% biases the likelihood; only EUR HDL reference panel publicly available; no non-EUR HDL eigen-reference exists as of 2026 -- for non-EUR fall back to ancestry-matched cross-trait LDSC (intercept absorbs overlap; rg unbiased)
LDAK SumHer (Speed 2019 Nat Genet 51:277)	LDAK-Thin model: per-SNP h2 reweighted by MAF + LD	Sumstats + LDAK-Thin tagging file	h2 + enrichment	Alternative to LDSC; often better-fitting per cross-validation per Speed 2017 Nat Genet 49:986	Tagging file must match build / ancestry; non-EUR support limited
HESS (Shi 2016 AJHG 99:139; Shi 2017 AJHG 101:737)	Per-locus h2 via quadratic form on LD-projected effect estimates	Sumstats + LD reference + locus partition (LDetect)	Per-locus h2 + bivariate local rg	Locus-level resolution; identifies high-h2 loci for follow-up	Locus has < 1000 SNPs; LD reference must be in-sample or matched
BOLT-REML (Loh 2015 Nat Genet 47:1385)	Bayesian REML; multi-component variance	Individual-level genotypes (PLINK BED) + phenotype	h2 + per-component partition	Biobank-scale (N=500k feasible); more precise than LDSC at high N	Needs individual-level data; assumes Gaussian residual; not for case-control < 5% prevalence without LMM-BOLT
GCTA-GREML (Yang 2011 AJHG 88:76)	GRM-based REML on individual genotypes	GRM (PLINK BED) + phenotype + covariates	h2 + SE	Gold standard for individual-level data; PCGC for case-control	N <= 5000 has wide SE; case-control needs PCGC-S correction; population stratification leaks into h2
graphREML (Wang 2024 bioRxiv)	Sumstat REML using LDGM graph	Sumstats + LDGM reference	h2 + functional partition	Use when an LDGM reference exists for the ancestry AND runtime matters at biobank N (> 200k); pre-built LDGM panels currently cover EUR + EAS	Newer (2024); reference panel availability evolving; non-EUR/EAS ancestries lack pre-built LDGM
Popcorn / Popcorn-2 (Brown 2016 AJHG 99:76; Brown 2022 ext.)	Trans-ancestry genetic correlation under MAF-LD model	Sumstats + cross-population LD scores	rg trans-ancestry + h2 per population	Distinguishes shared-causal vs ancestry-specific signal	Effective N per population must be > 5000; small non-EUR cohorts unstable
Cross-model reconciliation (Gazal 2019 Nat Genet 51:1202; Hou 2019 Nat Genet 51:1244)	Joint LDSC + LDAK comparison framework	Both LDSC and LDAK outputs	Model-averaged enrichment	Quantifies model-dependent component of enrichment	Methodological / reporting practice, not a separate primary estimator

Methodology evolves; benchmark consensus shifts. Verify against current Yengo 2022 Nat Methods, Speed 2020 Nat Methods (model comparison), and the alkesgroup/Price Lab tutorial (LDSC) before locking method as primary. Per-SNP-h2 model choice is an open debate; report both LDSC and LDAK SumHer when a claim depends on model assumption.

Decision Tree by Scenario

Scenario	Recommended	Why
Total h2 from sumstats, EUR GWAS, N > 50k	LDSC h2	Standard, fast, well-calibrated against EUR reference
Partitioned h2 by functional category	S-LDSC with baseline-LD_v2.2	Default functional partitioning; LD/MAF-robust
Tissue / cell-type prioritization	S-LDSC --h2-cts with ENCODE/Roadmap or scATAC ldcts	Designed for this; per-tissue Bonferroni-controlled
Two-trait genetic correlation from sumstats, no overlap	HDL (primary) + cross-trait LDSC (secondary)	HDL ~60% lower variance; LDSC robust under any overlap
Two-trait rg with sample overlap > 5%	Cross-trait LDSC	HDL biased by overlap; LDSC intercept absorbs overlap
Individual-level biobank h2, N > 100k	BOLT-REML	Better precision; multi-component partition
Smaller individual-level cohort, N 5-50k	GCTA-GREML	Gold-standard REML; PCGC if case-control < 20% prevalence
Local heritability and bivariate local rg	HESS	Per-locus resolution; identifies hotspots for follow-up
Trans-ancestry rg / cross-population h2	Popcorn / Popcorn-2	Designed for trans-ethnic; LD scores per population
Functional enrichment claim depends on model	Report BOTH LDSC and LDAK SumHer	Per Gazal 2019 / Hou 2019; model-dependence is real
Case-control GWAS with low prevalence	LDSC on liability scale (--samp-prev --pop-prev)	Observed-scale h2 understates liability-scale truth
Single-cell ATAC cell-type prioritization	S-LDSC with per-cluster ATAC peaks as annotations	Cross-reference atac-seq/single-cell-atac for peak generation

LDSC Intercept Interpretation (Postdoc Nuance)

The LDSC intercept is widely misinterpreted as a "confounding score". The correct interpretation:

• Intercept = 1 indicates no inflation from population structure, cryptic relatedness, or sample overlap (idealised)
• Intercept > 1 indicates SOME source of inflation, BUT polygenic background can elevate the intercept too: at very high N, polygenic signal can lift the intercept modestly without stratification
• The ratio statistic ratio = (intercept - 1) / (mean_chi2 - 1) is the fraction of inflation attributable to non-polygenic sources; a ratio of 0 means all inflation is polygenic, a ratio near 1 means most of it is stratification or overlap
• Bulik-Sullivan 2015 recommends interpreting intercept jointly with mean chi-square; intercept of 1.05 is innocuous if mean chi-square is 1.5 (ratio = 0.1) but worrying if mean chi-square is 1.05 (ratio = 1.0)

Operational rule: Always report intercept, mean chi-square, and ratio together. Do not interpret intercept in isolation. For sample-overlap diagnosis between two GWAS, use bivariate LDSC intercept, not univariate.

Intercept > 1.5 troubleshooting ladder (work in order; stop when source is found): (a) per-cohort PC adjustment was insufficient; refit GWAS with more PCs (10-20) or per-cohort separately, (b) cryptic relatedness in the GWAS cohort -- run king --related and remove pairs with kinship > 0.05 (or 0.0884 for second-degree), (c) case-control matching imbalance -- check case/control PCs separately, (d) sample-overlap with one of the contributing cohorts (especially in meta-analysis) -- check bivariate intercepts pairwise, (e) if biobank-internal, recompute the GWAS with sample-level relatedness exclusion before LDSC.

LDSC vs LDAK Reconciliation

LDSC (GCTA model) and LDAK SumHer (LDAK-Thin model) make different assumptions about how per-SNP heritability scales with LD and MAF:

• GCTA model (LDSC default): per-SNP h2 inversely proportional to local LD score; high-LD SNPs tag many causal variants
• LDAK-Thin (Speed 2017 Nat Genet 49:986-992): per-SNP h2 weighted by MAF and inversely by LD with empirical exponents; less weight on common high-LD SNPs

These give systematically different functional enrichment estimates. Speed 2019 reported that LDAK-Thin often gives lower conserved-region enrichment than baseline LDSC; conversely LDSC can over-attribute h2 to coding/conserved regions because the GCTA prior couples LD to causality. Gazal 2019 Nat Genet 51:1202-1204 and Hou 2019 Nat Genet 51:1244 reconcile the two by showing the true enrichment lies between the model-specific point estimates.

Operational rule: Whenever functional enrichment is the primary claim (e.g. "h2 is enriched in tissue T by N-fold"), report enrichment from BOTH LDSC and LDAK. Flag the model assumption. If LDSC and LDAK disagree by > 2x, treat the claim as model-dependent and cite Hou 2019. For non-enrichment claims (total h2, rg between two traits), the model dependence is smaller and LDSC alone is acceptable.

Cell-Type Prioritization (Finucane 2018)

Finucane 2018 Nat Genet 50:621 introduced cell-type-specific S-LDSC: partition heritability against ENCODE / Roadmap chromatin marks (H3K4me3, H3K27ac, H3K4me1, DNase, ATAC) tissue-by-tissue, retain per-tissue p-value adjusting for the baseline model. Trait-relevant tissue = top-ranked tissue with p < 0.05/N_tissues (Bonferroni for ~200 tissues, threshold ~2.5e-4).

Goal: Rank tissues / cell types by their per-annotation contribution to trait heritability.

Approach: Build per-cell-type LD scores from chromatin-marker BED files; compile .ldcts manifest (one row per cell type: name, ldscore prefix, control ldscore); run --h2-cts and interpret per-cell-type coefficient p-value.

# Cell-type prioritization example workflow (Finucane 2018)
# Inputs: trait.sumstats.gz (munged), <cts>.ldcts manifest, baseline annotations,
#         eur_w_ld weights, 1000G EUR frequency files

ldsc.py \
    --h2-cts trait.sumstats.gz \
    --ref-ld-chr 1000G_EUR_Phase3_baseline/baseline. \
    --ref-ld-chr-cts Multi_tissue_chromatin.ldcts \
    --w-ld-chr weights_hm3_no_hla/weights. \
    --out trait_cts
# trait_cts.cell_type_results.txt: Name, Coefficient, Coefficient_std_error, Coefficient_P_value
# Apply Bonferroni at 0.05 / nrow; top tissues are trait-relevant

Published .ldcts files cover GTEx tissues, Roadmap epigenome, immune cell types, and scATAC clusters. Custom .ldcts for novel cell types requires computing per-cell-type LD scores from a chromatin BED via ldsc.py --l2 --bfile ... --annot <cell>.annot.gz.

Quantitative Thresholds

Threshold	Source	Rationale
mean chi-square > 1.02	LDSC wiki / Bulik-Sullivan 2015	Below this, LDSC h2 estimate has huge SE; need N proportional to 1 / h2
h2 SE < 0.02	LDSC convention	Below this SE, h2 estimate is interpretable; above, treat as exploratory
h2 SE >= 0.02 OR mean chi-square < 1.02	LDSC convention	Estimate unreliable; N >= 50k is typical noise floor for h2 ~ 0.1 (scales as ~1/h2)
LDSC intercept in (1, 1.5]	Bulik-Sullivan 2015	Mild inflation acceptable; report ratio
LDSC intercept > 1.5	--	Substantial inflation; investigate stratification / overlap before interpreting h2
LDSC ratio < 0.2	Bulik-Sullivan 2015	Most inflation is polygenic; estimate is trustworthy
Stratified LDSC enrichment p < 0.05 / N_annot	Finucane 2015	Bonferroni across annotations in the baseline-LD model
S-LDSC cell-type p < 2.5e-4	Finucane 2018; ~200 tissues	Bonferroni for tissue prioritization
HESS h2 per locus needs >= 1000 SNPs	Shi 2017 AJHG 101:737	Quadratic form unstable below this density
HDL sample overlap < 5%	Ning 2020 Nat Genet 52:859	Above 5%, HDL likelihood is biased
LDAK tagging file build match	Speed 2019	hg19 vs hg38 tagging files non-interchangeable
Annotation > 0.5% of genome	Finucane 2015	Smaller categories underpowered for tau estimation
Effective N > 5000 per population (Popcorn)	Brown 2016 AJHG 99:76	Below this, trans-ancestry rg has very wide CI

LDSC Standard Workflow

Goal: Compute total h2 plus partitioned heritability across functional categories from EUR GWAS summary statistics.

Approach: Munge sumstats to LDSC format -> run --h2 for total -> run --h2 with --ref-ld-chr including baseline annotations -> --overlap-annot for enrichment p-values -> --print-coefficients for per-annotation tau.

# 1. Munge GWAS summary statistics into LDSC format
munge_sumstats.py \
    --sumstats gwas_raw.tsv \
    --N-col N \
    --snp SNP --a1 A1 --a2 A2 --p P --signed-sumstats BETA,0 \
    --merge-alleles w_hm3.snplist \
    --out trait
# Produces trait.sumstats.gz with SNP, A1, A2, Z, N columns

# 2. Total h2 (univariate; intercept, ratio, mean chi2 reported)
ldsc.py \
    --h2 trait.sumstats.gz \
    --ref-ld-chr eur_w_ld_chr/ \
    --w-ld-chr eur_w_ld_chr/ \
    --out trait_h2

# 3. Partitioned h2 with baseline-LD v2.2 model (Gazal 2017)
ldsc.py \
    --h2 trait.sumstats.gz \
    --ref-ld-chr 1000G_Phase3_baselineLD_v2.2_ldscores/baselineLD. \
    --frqfile-chr 1000G_Phase3_frq/1000G.EUR.QC. \
    --w-ld-chr 1000G_Phase3_weights_hm3_no_MHC/weights.hm3_noMHC. \
    --overlap-annot \
    --print-coefficients \
    --out trait_partitioned

Ancestry-matched LD scores (EAS, AFR, AMR) are available at alkesgroup.broadinstitute.org/LDSCORE; do NOT apply EUR LD scores to non-EUR GWAS.

Cross-Trait LDSC for Genetic Correlation

Goal: Estimate genetic correlation rg between two traits with calibrated handling of sample overlap.

Approach: Munge both sumstats with identical SNP list -> run --rg with two munged files; the bivariate intercept absorbs sample overlap and the rg estimate remains unbiased.

ldsc.py \
    --rg trait1.sumstats.gz,trait2.sumstats.gz \
    --ref-ld-chr eur_w_ld_chr/ \
    --w-ld-chr eur_w_ld_chr/ \
    --out rg
# Output: rg, se, p, gcov_int (cross-trait intercept), h2_obs, h2_int per trait

The cross-trait intercept (gcov_int) is the LDSC analog of sample-overlap z-score correlation; non-zero indicates sample overlap or cryptic shared structure. LDSC rg is unbiased even with sample overlap because the bivariate intercept absorbs it. HDL is more precise but requires non-overlapping samples.

Non-zero gcov_int under known sample overlap is the correct behavior, NOT pathology. The rg estimate remains unbiased; the intercept is the overlap absorber, doing its job. Pre-empt the reviewer comment "gcov_int = 0.05 with a shared cohort is expected, not confounding evidence" by reporting gcov_int alongside rg and explaining the absorber role.

Per-Method Failure Modes

LDSC intercept misinterpretation

Trigger: Reporting intercept ~1.05 as "evidence of confounding".

Mechanism: Intercept absorbs mean chi-square inflation from any non-polygenic source PLUS some polygenic contribution at very high N. In isolation, intercept above 1 does not imply confounding.

Symptom: Methods section claims population stratification based solely on intercept value; reviewers flag the omission of ratio statistic.

Fix: Always report intercept, mean chi-square, ratio = (intercept - 1) / (mean_chi2 - 1), and h2 jointly. Interpret ratio < 0.2 as "mostly polygenic, h2 trustworthy"; ratio > 0.3 as "investigate population structure / overlap before claiming h2".

LDSC vs LDAK enrichment discordance

Trigger: Running both LDSC baseline-LD and LDAK SumHer and getting different per-annotation enrichment.

Mechanism: GCTA model (LDSC) couples per-SNP h2 to local LD; LDAK-Thin de-couples and re-weights by MAF + LD with empirical exponents. These priors differ; the data alone cannot determine which is correct.

Symptom: LDSC reports conserved-region enrichment of 25x; LDAK reports 10x; both are model-internally consistent.

Fix: Cite Gazal 2019 Nat Genet 51:1202 and Hou 2019 Nat Genet 51:1244 as the LDSC-vs-LDAK reconciliation references; report BOTH models; treat 2x or larger discordance as model-dependent. For enrichment-driven hypotheses (e.g. tissue prioritization), reconcile by reporting LDSC primary + LDAK confirmatory and emphasize directional agreement over magnitude. Do not pick the model that gives the desired answer.

HDL bias with sample overlap

Trigger: Running HDL.rg on two GWAS that share > 5% of samples (e.g. two UKB traits, or UKB + FinnGen with overlapping recruitment).

Mechanism: HDL's eigen-decomposition likelihood treats the two traits as independent samples; sample-correlation in residuals biases the likelihood (typically inflates rg toward 1).

Symptom: HDL rg substantially different from cross-trait LDSC rg; HDL z-score very large compared to LDSC z; suspicious for high-correlation trait pairs.

Fix: Use cross-trait LDSC instead (intercept absorbs overlap). If both must be used, restrict HDL to unambiguously non-overlapping cohorts (e.g. UKB-only trait1 vs FinnGen-only trait2 with no shared individuals confirmed via individual ID exchange or IBD).

LDSC with non-EUR ancestry and EUR LD scores

Trigger: Applying default EUR LD scores from alkesgroup.broadinstitute.org/LDSCORE/eur_w_ld_chr/ to an EAS, AFR, or AMR GWAS.

Mechanism: LD-score regression assumes the LD-score covariate matches the GWAS population's LD structure. Cross-ancestry application produces biased h2 (typically underestimates) and inflated intercept.

Symptom: h2 estimate < 0.05 despite trait being known-heritable from twin / family studies; intercept > 1.2 with non-polygenic mean chi-square; ratio > 0.5.

Fix: Use ancestry-matched LD scores (EAS, AFR, AMR available at the same Alkes group URL). If multi-ancestry meta-analysis, use Popcorn or trans-ancestry MAMA framework rather than LDSC on the combined sumstats.

Stratified LDSC with collinear annotations

Trigger: Adding a custom annotation that overlaps heavily with an existing baseline category (e.g. "active promoter" against "promoter").

Mechanism: Per-annotation tau coefficients are estimated jointly via multivariable regression; collinearity inflates per-tau SE and can flip the sign of marginal effect.

Symptom: Custom annotation tau has very large SE, p-value > 0.5; baseline categories that were significant become non-significant.

Fix: Test annotations marginal to the baseline by including baseline-LD_v2.2 plus the new annotation only; never test multiple highly correlated annotations jointly; report VIF of annotation matrix; use the joint enrichment of {baseline + new} category not per-tau.

HESS locus instability at sparse SNP density

Trigger: Running HESS at a locus with < 1000 LD-pruned SNPs (e.g. centromere-adjacent region).

Mechanism: HESS quadratic form on projected effect estimates is unstable at low SNP density; matrix conditioning explodes.

Symptom: Locus h2 estimate negative or > 0.5 (unphysical); standard error very large; subsequent loci stable.

Fix: Require >= 1000 SNPs per locus; use LDetect partition (Berisa & Pickrell 2016 Bioinformatics 32:283) which targets ~1700 loci genome-wide; discard sparse loci or merge with neighbors.

Case-control LDSC observed vs liability scale

Trigger: Reporting LDSC h2 from a case-control GWAS on the observed (0/1) scale.

Mechanism: Observed-scale h2 depends on case fraction in the GWAS sample, not population prevalence; comparisons across studies require liability-scale transformation.

Symptom: h2 looks tiny (0.02) for a known-heritable disease; differs across studies with different case fractions.

Fix: Always supply --samp-prev <case_fraction> and --pop-prev <population_lifetime_prevalence> to LDSC; report h2 on liability scale. Without these flags, LDSC defaults to observed scale. Lee 2011 (AJHG 88:294) conversion: h2_liab = h2_obs * K(1-K)^2 / (P(1-P) * z^2), where K = population prevalence, P = sample case proportion, z = standard-normal density at the quantile (1-K). LDSC applies this via --samp-prev/--pop-prev; verify K and P are assigned correctly (K is population, P is sample). Skipping the conversion typically yields a 2-10x underestimate vs the liability-scale truth.

LDAK SumHer Pipeline

Goal: Alternative h2 and functional enrichment estimate using the LDAK-Thin model for reconciliation with LDSC.

Approach: Reformat sumstats to LDAK input -> run ldak --sum-hers against the pre-computed LDAK-Thin tagging file -> compare to LDSC.

# 1. LDAK requires header: Predictor A1 A2 n Z (Z optional; can use beta + se instead)
# Reference LDAK-Thin tagging files at dougspeed.com/pre-computed-tagging-files
ldak --sum-hers trait_sumher \
    --summary trait_ldak.txt \
    --tagfile bld.ldak.thin.hapmap.gbr.tagging \
    --check-sums NO

# 2. Partitioned with BLD-LDAK annotations
# BaselineLD.zip provides 86 continuous annotations covering coding/conserved/regulatory
# bins; download from dougspeed.com/bldldak and extract to ./BaselineLD/BaselineLD{1..86}.
# LDAK uses --annotation-number + --annotation-prefix (continuous) or
# --partition-number + --partition-prefix (binary). No --category-file flag exists.
ldak --sum-hers trait_bld --summary trait_ldak.txt \
    --tagfile bld.ldak.thin.hapmap.gbr.tagging \
    --annotation-number 86 \
    --annotation-prefix BaselineLD/BaselineLD \
    --check-sums NO

Pre-computed tagging files exist for GBR (HapMap reference); other ancestries require building tagging file via --calc-tagging. LDAK SumHer outputs h2 estimate, per-category h2 share, and enrichment with Z-scores.

HESS Local h2 Pipeline

Goal: Estimate per-locus heritability genome-wide using LDetect partition.

Approach: Step 1 computes quadratic forms per locus from LD reference; step 2 estimates h2; output per-locus h2 with SE.

# HESS step 1: per-chromosome local h2 quadratic forms (run per chromosome)
for chr in {1..22}; do
    hess.py \
        --local-hsqg trait.sumstats.gz \
        --chrom $chr \
        --bfile 1000G_EUR_chr${chr} \
        --partition-file LDetect_EUR_chr${chr}.bed \
        --out hess_chr${chr}
done

# HESS step 2: aggregate across chromosomes and estimate h2
hess.py \
    --prefix hess_chr \
    --out trait_local_h2 \
    --tot-hsqg <total_h2_estimate> <total_h2_SE>
# Provide total h2 and SE from LDSC for the global constraint

LDetect partition files (Berisa & Pickrell 2016) are available pre-computed for EUR/EAS/AFR at https://bitbucket.org/nygcresearch/ldetect-data. HESS detects high-h2 loci suitable for fine-mapping prioritization.

HDL Genetic Correlation (R)

Goal: Genetic correlation with ~60% lower variance than LDSC when samples are non-overlapping.

Approach: Reformat sumstats to HDL input -> download UKB reference panel eigen-decomposition -> run HDL.rg.

library(HDL)

# Sumstats need columns: SNP, A1, A2, b (beta), se, N
gwas1 <- read.table('trait1.txt', header = TRUE, stringsAsFactors = FALSE)
gwas2 <- read.table('trait2.txt', header = TRUE, stringsAsFactors = FALSE)

LD.path <- 'UKB_array_SVD_eigen90_extraction'

rg_result <- HDL.rg(gwas1.df = gwas1, gwas2.df = gwas2, LD.path = LD.path,
                    Nref = 335265, output.file = 'hdl_rg.log',
                    eigen.cut = 'automatic')

# rg_result: rg, rg.se, p, h2_1, h2_2, gen.cov

HDL UKB reference (UKB_array_SVD_eigen90_extraction) requires non-overlapping samples; if either GWAS is from UKB, HDL is biased.

Common Errors

Error / symptom	Cause	Solution
LDSC h2 negative	Trait truly null heritable; or LD scores ancestry-mismatched	Verify mean chi-square > 1.02; switch to ancestry-matched LD; report as null
munge_sumstats.py drops > 50% of SNPs	Allele mismatch with HapMap3 SNPlist; or A1/A2 swapped	Inspect drop reasons; pre-harmonize alleles; check rsID format
LDSC intercept > 1.5	Population stratification, cryptic relatedness, or extensive sample overlap	Report jointly with ratio; investigate per-cohort PC adjustment
Stratified LDSC enrichment > 100x	Tiny annotation (<0.1% genome) underpowered	Set annotation size floor >= 0.5%; report joint enrichment of larger composite category
LDAK h2 markedly different from LDSC h2	Model assumption divergence (GCTA vs LDAK-Thin)	Per Gazal 2019 / Hou 2019; report both and flag model-dependence
HDL rg = NA or numerical error	Sumstat format wrong; or eigen.cut too aggressive	Use eigen.cut='automatic'; check column names exactly
HESS locus h2 negative	< 1000 SNPs in locus; LD ref-stat mismatch	Drop locus or merge with neighbor; ensure LD ref matches GWAS ancestry
--samp-prev/--pop-prev not supplied for case-control	LDSC defaults to observed scale	Always supply both for case-control; report liability-scale h2
Cell-type S-LDSC: no tissue p < 2.5e-4	Trait underpowered for tissue prioritization (mean chi-square low)	Pool with related traits via MTAG; or report no tissue distinguishable
LDAK tagging file: build mismatch	Using hg19 tagging on hg38 GWAS sumstats	Tagging files are build-specific; download matched build
BOLT-REML "matrix not positive definite"	GRM has duplicated individuals or extreme relatedness	Pre-filter to unrelated < 0.05 kinship; or use REML method-of-moments instead
munge_sumstats.py: missing N column	Per-SNP N column not supplied	Pass --N <Ntot> (numeric total) OR --N-col N (column name); pick one
munge_sumstats.py: all SNPs drop silently	A1/A2 flipped relative to HM3 reference (--merge-alleles)	Verify allele coding matches w_hm3.snplist; pre-harmonize or swap A1 <-> A2
munge_sumstats.py drops multi-allelic SNPs	Expected behavior (LDSC requires biallelic)	Document the drop count in methods; not a fix
Sign of Z reversed across studies	--signed-sumstats BETA,0 vs --signed-sumstats Z,0 confusion	Use BETA,0 for additive effect sign convention, Z,0 for Z-score; never both; verify direction with a known sentinel SNP

Tool Install Notes

# LDSC Python 3 fork (official bulik/ldsc is Python 2.7, unmaintained since 2019)
# IMPORTANT: belowlab/ldsc v3.0.1 broke the --h2 / --rg / --h2-cts CLI per its README.
# For a working CLI matching the flags below, use abdenlab/ldsc-python3 (v2.0.0)
# OR run belowlab/ldsc via Docker: `docker pull jtb114/ldsc:latest`.
git clone https://github.com/abdenlab/ldsc-python3.git   # working CLI
cd ldsc-python3
conda env create -f environment.yml   # creates ldsc conda env with deps pinned
conda activate ldsc

# LDAK 6+
wget http://dougspeed.com/wp-content/uploads/ldak6.linux_.zip
unzip ldak6.linux_.zip && chmod +x ldak6.linux

# Pre-computed reference resources (one-time download)
# EUR LD scores (HapMap3 SNPs)
wget https://alkesgroup.broadinstitute.org/LDSCORE/eur_w_ld_chr.tar.bz2
# Baseline-LD v2.2 (Gazal 2017)
wget https://alkesgroup.broadinstitute.org/LDSCORE/1000G_Phase3_baselineLD_v2.2_ldscores.tgz
# 1000G EUR frequency files
wget https://alkesgroup.broadinstitute.org/LDSCORE/1000G_Phase3_frq.tgz
# Weights
wget https://alkesgroup.broadinstitute.org/LDSCORE/1000G_Phase3_weights_hm3_no_MHC.tgz
# Multi-tissue chromatin ldcts (Finucane 2018)
wget https://alkesgroup.broadinstitute.org/LDSCORE/Multi_tissue_chromatin_1000Gv3_ldscores.tgz

# HDL
remotes::install_github('zhenin/HDL/HDL')
# HDL UKB reference (downloads ~5 GB)
# https://github.com/zhenin/HDL/wiki/Reference-panels

# HESS (Python 2 by default; Python 3 fork: huwenboshi/hess Python 3 branch)
git clone https://github.com/huwenboshi/hess.git
pip install -r hess/requirements.txt

# BOLT-LMM / BOLT-REML
wget https://alkesgroup.broadinstitute.org/BOLT-LMM/downloads/BOLT-LMM_v2.4.1.tar.gz

# GCTA
wget https://yanglab.westlake.edu.cn/software/gcta/bin/gcta-1.94.1-linux-kernel-3-x86_64.zip

# Popcorn
pip install popcorn-stats   # OR git clone https://github.com/brielin/Popcorn

References

• Bulik-Sullivan BK et al 2015 Nat Genet 47:291 (LDSC)
• Bulik-Sullivan BK et al 2015 Nat Genet 47:1236 (cross-trait LDSC genetic correlation)
• Finucane HK et al 2015 Nat Genet 47:1228 (stratified LDSC baseline)
• Gazal S et al 2017 Nat Genet 49:1421 (baseline-LD model)
• Finucane HK et al 2018 Nat Genet 50:621 (cell-type S-LDSC)
• Speed D et al 2017 Nat Genet 49:986-992 (LDAK-Thin model)
• Speed D et al 2019 Nat Genet 51:277 (SumHer)
• Gazal S et al 2019 Nat Genet 51:1202-1204 (LDSC vs LDAK reconciliation, model-dependence)
• Hou K et al 2019 Nat Genet 51:1244 (heritability accuracy and h2 model comparison)
• Ning Z et al 2020 Nat Genet 52:859 (HDL)
• Shi H et al 2016 AJHG 99:139 (HESS univariate)
• Shi H et al 2017 AJHG 101:737 (HESS bivariate local rg)
• Loh PR et al 2015 Nat Genet 47:1385 (BOLT-REML)
• Yang J et al 2011 AJHG 88:76 (GCTA-GREML)
• Brown BC et al 2016 AJHG 99:76 (Popcorn trans-ancestry rg)
• Berisa T & Pickrell JK 2016 Bioinformatics 32:283 (LDetect locus partition)
• Wang Q et al 2024 bioRxiv (graphREML)

Related Skills

• causal-genomics/mendelian-randomization - h2 / rg-aware instrument selection and one-sample-equivalent design decisions
• causal-genomics/colocalization-analysis - Per-locus shared-causal evidence complementary to HESS local h2
• causal-genomics/fine-mapping - Credible-set construction at high-h2 HESS loci
• causal-genomics/pleiotropy-detection - Cross-trait pleiotropy via LCV / LHC-MR using LDSC outputs
• causal-genomics/genomic-sem - Genomic SEM extends LDSC rg to multivariate structural models
• causal-genomics/transcriptome-wide-association - TWAS uses partitioned-h2 weights for gene-level testing
• atac-seq/differential-accessibility - Per-cell-type chromatin annotations as S-LDSC input
• atac-seq/single-cell-atac - scATAC peaks per cluster as Finucane 2018 .ldcts annotations
• chip-seq/peak-calling - ENCODE / Roadmap chromatin marks for cell-type prioritization
• population-genetics/association-testing - GWAS source summary statistics for LDSC munging
• population-genetics/linkage-disequilibrium - LD reference panels for HESS / coloc.susie
• workflows/gwas-pipeline - Upstream GWAS pipeline feeding sumstats to LDSC