Bio Causal Genomics Genetic Correlation

Version Compatibility

Reference examples tested with: LDSC v1.0.1+ (Python 3; prefer abdenlab/ldsc-python3 v2.0.0 -- belowlab/ldsc v3.0.1 README states the --h2 / --rg / --h2-cts CLI is broken; use Docker jtb114/ldsc:latest for the belowlab fallback; original bulik/ldsc is Python 2.7 unmaintained since 2019), HDL 1.4.0+ (R; GitHub zhenin/HDL), LAVA 0.1.0+ (R; GitHub josefin-werme/LAVA), HESS 0.5.4+ (Python; huwenboshi/hess), Popcorn 1.0+ (Python; brielin/Popcorn), GCTA 1.94+ (GREML-bivariate), baselineLD_v2.2 / eur_w_ld_chr LD-score panels from alkesgroup.broadinstitute.org/LDSCORE, UKB-array SVD eigen reference for HDL.

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

If code throws an LD-score "category not found" error, an HDL reference-panel mismatch, or a LAVA locus-ID lookup failure, introspect the installed LD-score column headers and the supplied partitioning file rather than retrying with default flags.

Genetic Correlation

"Estimate the genetic correlation between two traits from GWAS summary statistics" -> Decompose the bivariate genetic architecture into a single global rg (cross-trait LDSC, HDL), per-locus local rg (LAVA, rho-HESS, HDL-L), or cross-population rg (Popcorn). Genetic correlation is the central cross-trait statistic in causal genomics: it quantifies shared etiology, motivates CHP-aware MR sensitivity when high, gates LCV's gcp partial-causation parameter, and feeds into multi-trait analysis frameworks (MTAG, GenomicSEM). Tool choice is a decision about the regime (sumstats vs individual-level; global vs local; same-ancestry vs trans-ancestry) and the sample-overlap structure between input GWAS.

• CLI (LDSC, robust to overlap): 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
• R (HDL, lower variance, requires independent samples): HDL.rg(gwas1.df, gwas2.df, LD.path = 'UKB_array_SVD_eigen90_extraction', N0 = 0)
• R (LAVA, local rg per locus): process.input() -> run.univ() -> run.bivar(input, locus_id) over ~2495 LDetect-derived loci
• CLI (rho-HESS, locus-level): hess.py --local-rhog t1.sumstats.gz t2.sumstats.gz --bfile <ref> --partition <part>.bed --chrom <chr>
• CLI (Popcorn, trans-ancestry): popcorn fit -v 1 --cfile cross_pop_scores.txt --sfile1 pop1.txt --sfile2 pop2.txt out

Algorithmic Taxonomy

Methodology evolves; benchmark consensus shifts. Verify against the alkesgroup LDSC tutorial (current as of release), Werme 2022 LAVA paper + GitHub, and Speed 2020 Nat Genet model-comparison work before locking a primary method. When a claim depends on the model assumption (e.g. enrichment in shared loci), report at least two methods (e.g. LDSC global + LAVA local).

Cross-Trait LDSC Intercept: Sample Overlap is Absorbed, Not a Bias

The most common postdoc-level misreading: Treating a non-zero cross-trait LDSC intercept as evidence of bias in the rg estimate.

The bivariate LDSC regression has the form: E[Z1 Z2] = sqrt(N1 N2) * rg * h2-product / M * LD_score + rho_overlap

The intercept (rho_overlap) ABSORBS the contribution of sample overlap (correlated trait residuals on shared individuals). The slope (which carries rg) is unbiased even when overlap is non-zero. A non-zero intercept is the expected signature of sample overlap and is informative (it estimates phenotypic correlation among overlapping individuals), but it does NOT indicate that rg is contaminated.

Operational rule: Report the intercept alongside rg. When intercept is non-zero, document the overlap inferred (intercept = rho_phenotypic * sqrt(N_shared / N1 / N2) approximately) but do not discount rg. HDL, in contrast, assumes truly independent samples and does become biased above ~5% overlap; switch to LDSC under any non-trivial overlap.

HDL Bias Under Sample Overlap

The mirror image trap: Running HDL on two GWAS that share controls or come from the same biobank.

HDL maximizes a likelihood that assumes independence of the two trait residuals after marginalizing genetics. With sample overlap, the residual correlation is non-zero and the likelihood is misspecified; bias is typically toward the rg estimate that corresponds to phenotypic correlation in the overlapping subset.

Operational rule: Use HDL only when sample overlap < 5%. When in doubt about overlap (e.g. two UKB-derived GWAS), compute LDSC intercept first; if intercept is materially non-zero, switch to LDSC for the primary rg estimate.

Relationship to MR Causal Inference

Genetic correlation between an exposure and an outcome is a screening statistic, not a causal claim. High |rg| has three biological explanations:

LCV's gcp parameter (O'Connor & Price 2018 Nat Genet 50:1728) attempts to distinguish partial from full causation: gcp = 0 is pure correlation (no causation in tested direction), gcp = 1 is full causation, 0 < gcp < 1 is partial causation. LCV uses the LDSC-style bivariate moments and is complementary to instrument-based MR.

Operational rule for any MR analysis where |rg| > 0.3: The IVW + Egger + MR-PRESSO triple is insufficient because all three are blind to CHP (Morrison 2020 Nat Genet 52:740). Add CAUSE (if sig SNPs >= 100) or LHC-MR. See causal-genomics/pleiotropy-detection for the full CHP-aware battery.

Decision Tree by Scenario

Per-Method Failure Modes

Cross-trait LDSC intercept misread as bias

Trigger: Reader (collaborator, reviewer) sees a non-zero LDSC intercept and reports the rg as "biased by sample overlap".

Mechanism: The bivariate LDSC model partitions covariance between traits into a slope (rg-driven, scales with LD score) and an intercept (overlap-driven, constant in LD score). The slope is what carries rg, and it remains unbiased regardless of intercept value (Bulik-Sullivan 2015 Nat Genet 47:1236, Methods). Confusing the intercept with bias on the slope is a routine misinterpretation.

Symptom: Reviewer comment requesting "correction for sample overlap" when LDSC was already used; collaborator suggesting switching to HDL because intercept is non-zero.

Fix: Report rg with SE and the intercept as a separate statistic; cite Bulik-Sullivan 2015 Methods explicitly; do NOT switch to HDL (which is the wrong direction since HDL is the method that breaks under overlap, not LDSC).

HDL bias with sample overlap

Trigger: Running HDL on two GWAS that share > 5% of individuals (e.g. two UKB-derived GWAS, two MVP-derived GWAS, GWAS reusing controls).

Mechanism: HDL likelihood assumes independent trait residuals after marginalizing genetics. Overlap induces non-zero residual correlation; the likelihood is misspecified and the estimate is pulled toward phenotypic correlation in the shared subset (Ning 2020 Nat Genet 52:859 Supplement).

Symptom: HDL rg differs substantially from cross-trait LDSC rg; HDL CI is narrower than expected from N alone; LDSC intercept (which absorbs overlap) is materially non-zero.

Fix: Compute LDSC intercept first as an overlap diagnostic; if non-zero, switch to LDSC as primary. HDL remains valid only when the two GWAS draw from non-overlapping cohorts (verify by cohort identifier, not just by file source).

Non-EUR ancestry mismatch with EUR LD scores

Trigger: Running LDSC on a non-EUR GWAS (or admixed sample) with the default eur_w_ld_chr/ reference.

Mechanism: LD scores are ancestry-specific; mean LD per SNP differs across populations and bivariate moments use the wrong null. h2 and rg estimates are systematically biased; intercept can be inflated.

Symptom: LDSC ratio is unusually high (>0.2); per-chromosome estimates wildly heterogeneous; total h2 mismatches independent estimates from the same cohort.

Fix: Use ancestry-matched LD scores from alkesgroup (eas_w_ld_chr, afr_w_ld_chr) or compute custom LD scores from in-sample LD reference. For trans-ancestry rg, switch to Popcorn.

Global rg masks local rg variation

Trigger: Two traits with biologically plausible shared etiology return global rg ~ 0 in cross-trait LDSC.

Mechanism: Global rg averages over the genome; loci with positive local rg can cancel against loci with negative local rg, particularly for traits with antagonistic pleiotropy (e.g. autoimmune vs infectious-disease susceptibility), or when shared etiology is confined to a small fraction of the genome.

Symptom: Well-powered (mean chi-square >> 1.02) global LDSC rg near zero with wide CI overlapping zero, while domain biology, prior co-occurrence studies, or shared-pathway analyses strongly suggest shared etiology.

Fix: Run LAVA over the standard ~2495 LDetect loci; per-locus Bonferroni-significant rg at any locus is evidence of localized shared etiology. Annotate hit loci with overlapping GWAS catalog signals and pathway/tissue enrichment.

Cross-population rg below 1 even at causal level

Trigger: Computing rg between same-trait GWAS in two ancestries (e.g. EUR T2D vs EAS T2D).

Mechanism: Even when the trait has the same biological definition, causal variant identity and effect sizes can differ across populations due to gene-environment interaction, allele-frequency divergence, and population-specific epistasis. Popcorn 2016 demonstrated that rg(cross-pop) < 1 is common and biologically real, not a methodological artifact.

Symptom: Trans-ancestry rg point estimate around 0.6-0.9 with CI excluding 1 for a trait expected to be "the same disease".

Fix: Use Popcorn (within-pop LDSC is invalid for cross-pop rg); interpret rg(cross-pop) < 1 as quantifying population-specific architecture rather than as bias; report rho_ge (effect correlation) and rho_gi (impact correlation) separately.

Same-Trait Cross-Cohort rg as Consistency Check

Use case: Meta-analysis QC -- two same-trait GWAS (e.g. UKB IBD vs FinnGen IBD) yield rg < 1 with CI excluding 1. This is distinct from the cross-population analog above (handled by Popcorn); here both cohorts are same-ancestry but different studies.

Interpretation: (a) population-substructure differences, (b) phenotype-definition heterogeneity (e.g. different ICD coding, self-report vs registry), (c) genuine biology (founder effects in isolates like FinnGen).

Decision rule: rg ~ 0.9-1.0 with CI overlapping 1 -> consistent enough to meta-analyze; rg ~ 0.7-0.9 -> moderate heterogeneity, consider sensitivity meta with random effects; rg < 0.7 -> re-examine phenotype definitions before meta-analyzing.

Low chi-square mean (underpowered GWAS)

Trigger: Mean chi-square in either input GWAS is below 1.02 (heuristic LDSC threshold).

Mechanism: LDSC, HDL, and LAVA all depend on bivariate moments of Z-scores against LD score; weak signal means the slope is dominated by noise.

Symptom: LDSC rg SE > 0.2; intercept estimates fluctuate across chromosome; HDL convergence warnings; LAVA returns p > 0.05 at most loci.

Fix: Meta-analyze contributing cohorts to push effective N to ~50k or higher before running rg; if meta-analysis is not feasible, report rg as exploratory; do NOT switch methods to "salvage" power, the problem is upstream of method choice.

LAVA univariate filter ignored

Trigger: Reporting LAVA bivariate rg at a locus where the univariate local h2 is non-significant in one or both traits.

Mechanism: LAVA's bivariate test is only valid at loci with detectable local heritability in BOTH traits. Without local h2 signal in at least one trait, the bivariate test is unidentified and can return spurious significant rg.

Symptom: LAVA bivariate p < 0.05 at loci where univariate h2 p > 0.05 for one trait; rg estimates near +/- 1 (boundary cases).

Fix: Filter loci on univ.p < 0.05 / N_loci (Bonferroni for ~2495 loci) in BOTH traits before running run.bivar(); report only at filtered loci. This is the documented LAVA workflow in Werme 2022 Supplement and the GitHub vignette.