bio-causal-genomics-genetic-correlation

What this skill does

## 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+ / Popcorn-2 (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 / Popcorn-2). 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_eigen99_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-file <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

| Method | Model | Input | Output | Strength | Fails when |
|--------|-------|-------|--------|----------|------------|
| Cross-trait LDSC (Bulik-Sullivan 2015 Nat Genet 47:1236) | Bivariate LD-score regression; off-diagonal absorbs rg, intercept absorbs sample overlap | Sumstats + ancestry-matched LD scores | rg, SE, intercept (overlap proxy) | Robust to sample overlap (intercept absorbs it without biasing rg); fast; calibrated EUR | Mean chi-square < 1.02 in either trait (underpowered); non-EUR sumstats with EUR LD scores |
| HDL (Ning 2020 Nat Genet 52:859) | High-Definition Likelihood; eigen-decomposition of full LD with closed-form variance | Sumstats + UKB-array SVD eigen reference (EUR N=336k) | rg, SE | ~60% lower variance than LDSC; equivalent to ~2.5x sample size; preferred when both GWAS truly independent | Sample overlap > 5% biases likelihood; only public reference panel is EUR UKB-array |
| LAVA (Werme 2022 Nat Genet 54:274) | Semi-parametric local genetic correlation per locus; PC-projected SNP effects under a local null | Sumstats + LDetect partitioning (~2495 loci) | Per-locus univariate h2 + bivariate rg + p-value | Detects heterogeneous rg masked by global cancellation; conditional + partial rg supported | Locus has too few SNPs (< 50) or low local h2 (univariate p > 0.05 in either trait); LD reference mismatch |
| rho-HESS (Shi 2017 AJHG 101:737) | Quadratic form on LD-projected effect estimates per locus | Sumstats + LDetect partition + LD reference | Per-locus rho_g + bivariate local rg | Earliest locus-level rg method; complements LAVA | Locus < 1000 SNPs; LD ref must match in-sample structure |
| HDL-L (Ning 2022 ext.) | HDL likelihood applied to local windows | Sumstats + windowed LD reference | Per-window local rg | Lower variance than rho-HESS at locus level | Same sample-overlap caveat as HDL; reference-panel coverage limited |
| GREML-bivariate (Lee 2012 Bioinformatics 28:2540) | Joint REML on bivariate GRM | Individual-level genotypes + both phenotypes | rg + SE | Gold standard at individual level; better precision than sumstats methods | Needs individual-level data on overlapping individuals OR carefully matched two-cohort; population stratification leaks |
| Popcorn (Brown 2016 AJHG 99:76) | Cross-population genetic effect (rho_ge) and impact (rho_gi) correlation under MAF-LD model | Sumstats per population + cross-population LD scores | Trans-ancestry rg + per-pop h2 | Quantifies shared causal architecture across ancestries | Effective N per population < 5000; cross-population LD score reference mismatched to GWAS ancestry |
| Popcorn-2 (Galinsky 2019 ext.) | Improved Popcorn with admixture-aware LD scores | Same as Popcorn + admixture LD scores | Same outputs, lower SE | More precise on admixed cohorts; better handling of LD mismatch | Same data-volume limit as Popcorn |
| GenomicSEM `LDSC()` (Grotzinger 2019 Nat Hum Behav 3:513) | LDSC wrapper feeding into SEM | Multiple sumstats | Genetic covariance matrix + multivariable SEM | Multi-trait extension of LDSC; common-factor and bifactor models | Same per-pair limits as LDSC; SEM identification problems |
| SUPERGNOVA (Zhang 2021 Nat Commun 12:7234) | Annotation-aware LD-block local rg with eigen-decomposed kernel | Sumstats + annotation-aware LD partition | Per-locus rg + p; orthogonal philosophy from LAVA | Different LD partitioning than LDetect; useful as triangulation against LAVA | Same chi-square floor as LDSC; non-EUR coverage limited |
| KGGSEE local rg (Zhang 2022 Bioinformatics) | Heritability-based per-region rg | Sumstats + region partition | Per-region rg | Java pipeline integrates h2 partition + local rg | Less adopted than LAVA; partition file curation overhead |

Methodology evolves; benchmark consensus shifts. Verify against the alkesgroup LDSC tutorial (current as of release), Werme 2022 LAVA paper + GitHub, and Speed 2020 *Nat Methods* 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 tw