Colocalization analysis

Version Compatibility

Reference examples tested with: coloc 5.2.3+, susieR 0.12.35+, hyprcoloc 1.0+ (GitHub jrs95/hyprcoloc), SMR 1.3.1+ (CLI, cnsgenomics.com), eCAVIAR 2.2+ (compiled from caviar/eCAVIAR repo), PWCoCo 1.0+ (jwr-git/pwcoco), moloc 0.1+ (clagiamba/moloc), SharePro_coloc 7.0+ (zhwm/SharePro_coloc), R >= 4.1.

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

• R: packageVersion('coloc'); check ?coloc.abf, ?coloc.susie, ?runsusie
• CLI: smr --version, pwcoco --help, sharepro_coloc.py --help

If code throws AttributeError, NULL list elements, or Error in coloc.abf: dataset must have..., introspect the installed package signature and adapt the example rather than retrying.

Colocalization Analysis

"Test whether my GWAS signal and an eQTL share the same causal variant" -> Compute Bayesian posterior probabilities over five hypotheses (H0 neither, H1 trait-1-only, H2 trait-2-only, H3 distinct causal variants, H4 shared causal variant) to discriminate true causal overlap from LD-driven coincidence, then run sensitivity analysis over the p12 prior.

• R (single-causal, fastest): coloc::coloc.abf(dataset1, dataset2, p12=5e-6) -> coloc::sensitivity(res, 'H4 > 0.75')
• R (multi-causal, needs LD): runsusie(d1) -> runsusie(d2) -> coloc.susie(s1, s2) -> per-credible-set PP
• R (many traits, single-causal cluster): hyprcoloc::hyprcoloc(effect.est = betas_mat, effect.se = ses_mat, trait.names = ..., snp.id = ...) -> trait clusters
• CLI (causality vs linkage): smr --bfile ref --gwas-summary g.ma --beqtl-summary eqtl.besd --out smr -> SMR p + HEIDI p
• CLI (allelic heterogeneity): eCAVIAR eCAVIAR -l ld1 -l ld2 -z z1 -z z2 -o out -c 2 -> CLPP per SNP
• CLI (conditional): PWCoCo conditions on each independent signal via GCTA-COJO then runs pairwise coloc.abf

Algorithmic Taxonomy

Method	Model	Inputs	Output	Strength	Fails when
coloc.abf (Giambartolomei 2014)	Single causal variant per locus; Bayesian ABF	beta+varbeta or p+MAF; sample sizes; type/s/sdY	PP.H0-H4	Fast (~1s/locus), no LD required, mature, widely-cited	2+ causal variants in moderate LD -> PP.H3 inflates spuriously; assumes a single causal per trait
coloc.susie (Wallace 2021)	Multi-causal via SuSiE; per-credible-set pairwise coloc	Summary stats + ancestry-matched LD matrix	PP.H4 per (CS1, CS2) pair	Handles allelic heterogeneity; principled CS framework	Sensitive to LD-mismatch; sample-size-LD mismatch -> spurious credible sets; needs in-sample or matched LD
SMR + HEIDI (Zhu 2016)	Tests pleiotropy (one variant -> both traits) vs linkage (two variants in LD)	GWAS .ma; eQTL .besd; LD reference (plink bfile)	SMR p (significance) + HEIDI p (null = shared causal)	Distinguishes shared-causal from linkage at a top SNP; standard for eQTLGen / GTEx integration	Fails to discriminate when LD between causal SNPs > 0.7 (HEIDI loses power); HEIDI requires >= 10 SNPs near top
eCAVIAR / CLPP (Hormozdiari 2016)	Fine-mapping-aware; computes Colocalization Posterior Probability per SNP	Z-scores; LD matrices per trait	CLPP per SNP; per-locus sum	Handles allelic heterogeneity natively; per-SNP resolution	Computationally heavy at -c > 3 causal variants; CLPP thresholds debated (0.01 vs 0.1)
PWCoCo (Robinson 2022)	Pairwise conditional via GCTA-COJO conditioning	Summary stats + individual-level LD bfile	Per-conditional-signal coloc.abf results	Cleanly handles AH at top GWAS hit + secondary signals	Needs individual-level reference; sensitive to COJO collinearity threshold
moloc (Giambartolomei 2018)	Multi-trait extension of coloc.abf (3-5 traits)	Per-trait summary stats	15 (3-trait) / 31 (4-trait) / 63 (5-trait) hypothesis PPs	First principled multi-omic coloc	Hypothesis count = 2^k - 1 explodes; >= 6 traits computationally infeasible; minimally updated since 2019
HyPrColoc (Foley 2021)	Many-trait cluster-based; iterative branch-and-bound under single-causal	Beta + SE matrices SNPs x traits	Trait clusters sharing a causal variant	Scales to 50+ traits; identifies cluster substructure	Inherits single-causal assumption from coloc.abf; clusters can fragment under AH
SharePro_coloc (Wang 2024)	Variational effect-group joint model	Beta + SE; LD per ancestry	Effect-group level PP	Handles multi-causal + multi-ancestry jointly; faster than coloc.susie at scale	Newer (2024); benchmarks evolving; trickier installation
Wallace 2020 / 2025 variant-specific priors	Function-aware p12 (e.g. up-weight coding/promoter SNPs)	Same as coloc.abf + per-SNP prior weights	PP.H0-H4 with non-uniform prior	Improves discovery when functional annotation is informative	Annotation choice is a methodological lever; report sensitivity

Methodology evolves; verify the current Open Targets Genetics, eQTL Catalogue, and FinnGen colocalization pipelines before locking parameters. Open Targets uses coloc.abf at PP.H4 >= 0.75 with p12 = 1e-5; FinnGen uses coloc.susie at PP.H4 >= 0.8 with in-sample LD.

Decision Tree by Scenario

Scenario	Recommended method	Why
GWAS + single-tissue eQTL, top GWAS variant looks single-signal	coloc.abf + sensitivity()	Fast, no LD needed, well-validated; single-causal assumption typically holds at clean loci
GWAS + eQTL, conditional analysis shows 2+ independent signals	coloc.susie OR PWCoCo	Multi-causal handling; coloc.susie if summary-stats LD available, PWCoCo if individual-level reference accessible
GWAS + multi-tissue eQTL (e.g. all 49 GTEx tissues)	coloc.abf per tissue + HyPrColoc across tissues	Per-tissue PP.H4 gives tissue-specific causality; HyPrColoc identifies tissue clusters sharing the variant
GWAS + eQTL + sQTL + mQTL (3-5 omics)	moloc (k <= 5) OR HyPrColoc	moloc gives explicit hypothesis posterior; HyPrColoc scales but loses hypothesis structure
Many GWAS traits at one locus (pleiotropic hub)	HyPrColoc	Designed for many-trait clustering; coloc.abf pairwise scales as k^2
Top SNP has only modest GWAS p; is it the same causal as eQTL?	SMR + HEIDI	SMR tests pleiotropy/causality; HEIDI rejects shared-causal -> linkage
Want per-SNP credibility under allelic heterogeneity	eCAVIAR (CLPP)	Per-SNP CLPP integrates fine-mapping with coloc
MHC / HLA region (chr6:25-35 Mb)	HLA-coloc (Lagou 2024) OR exclude MHC	Long-range LD breaks single-causal assumption; standard PP.H4 not interpretable
Trans-eQTL / GWAS pair	coloc.abf with p12 lowered to 5e-6 or 1e-6	Shared causality is biologically rare; default p12=1e-5 over-favours H4
Ancestry-mismatched GWAS vs eQTL	SharePro_coloc OR ancestry-matched coloc.susie	LD differs across ancestries; using EUR LD on AFR z-scores produces spurious credible sets
Very small eQTL (N < 200)	None reliably; flag locus underpowered	All methods report H0/H1/H2 dominance; report PP transparently and gather larger reference (eQTLGen N~31k, GTEx v8)

Per-Method Failure Modes

coloc.abf -- PP.H3 inflation under multiple causal variants

Trigger: Locus has 2+ independent causal signals in moderate LD (r2 ~ 0.3-0.6).

Mechanism: The single-causal-variant assumption forces the model to allocate posterior mass to H3 (distinct causal variants) whenever the per-SNP Bayes factors for the two top SNPs do not align.

Symptom: Visual co-localization in LocusZoom looks convincing, but result$summary['PP.H3.abf'] dominates over PP.H4; sensitivity() shows PP.H4 stays low across the entire p12 grid.

Fix: Run coloc.susie (or eCAVIAR or PWCoCo) to allow multiple causal variants. If coloc.susie returns multiple credible sets with one pair showing PP.H4 > 0.75, this is real allelic heterogeneity not failure.

coloc.susie -- LD reference mismatch

Trigger: Z-scores from GWAS / eQTL of one ancestry, LD matrix from 1000 Genomes EUR (or any non-matched reference).

Mechanism: SuSiE assumes z-scores and the supplied LD are jointly consistent. Ancestry mismatch or sample-size mismatch produces a non-positive-definite implicit covariance; SuSiE responds by returning spurious credible sets that include LD-mismatched SNPs.

Symptom: susieR::estimate_s_rss(z, R, n) returns lambda > 0.05; susieR::kriging_rss flags off-diagonal SNPs with extreme studentized residuals; credible sets are oddly large (50+ SNPs) or include SNPs distant in LD from the lead.

Fix: Use in-sample LD when at all possible (per-cohort plink --r square). If reference must be external, match ancestry (1KG superpopulation) and superpopulation-stratify. Run estimate_s_rss and report lambda; if > 0.05, drop the locus or switch to coloc.abf.

coloc default p12 too liberal for trans-eQTL

Trigger: Applying p12 = 1e-5 (the default) to a trans-eQTL / GWAS pair.

Mechanism: The default p12 was calibrated for cis-eQTL where biological proximity makes shared causality reasonable. For trans-eQTL, prior probability of shared causality is much lower; uniform p12 over-favours H4.

Symptom: PP.H4 > 0.8 reported, but sensitivity() reveals PP.H4 falls below 0.5 for p12 < 1e-5; replication in independent data fails.

Fix: Operational definition: "trans" = >5 Mb from TSS or different chromosome. Default p12=1e-5 over-favors H4 for trans (genome-rare biology). For trans: lower p12 to 5e-6 or 1e-6 AND raise PP.H4 threshold to >= 0.8 (compensate for higher FP risk). Cross-reference Vosa 2021 Nat Genet 53:1300 (eQTLGen trans) for empirical patterns.

MHC / HLA + chr 8 inversion -- single-causal assumption breaks

Trigger: Locus within chr6:25-35 Mb (extended MHC, hg38), or chr8:8.1-11.9 Mb (chr 8 inversion, hg38).

Mechanism: The MHC contains classical HLA genes with extreme long-range LD (r2 > 0.5 over many Mb), multiple independent causal haplotypes, and structural variation. The chr 8p23.1 inversion similarly produces long-range LD across megabases of polymorphic inversion alleles. The single-causal-variant assumption is biologically wrong in both regions.

Symptom: coloc.abf almost always returns PP.H3 or fragmented PP across H1/H2/H3/H4 even when the underlying biology is well-established (e.g. HLA-DRB1 in autoimmune GWAS).

Fix (MHC): Use HLA-imputed classical alleles via SNP2HLA / HIBAG / HLA-TAPAS, then HLA-coloc (Lagou 2024 medRxiv) -- NOT coloc on SNPs in MHC. OR exclude MHC from genome-wide coloc and report HLA association at the haplotype/allele level. Fix (chr 8 inversion): Exclude chr8:8.1-11.9 Mb or pre-condition on inversion genotype before coloc. Never report a single coloc PP.H4 in either region without this caveat.

Lead-SNP swap and window bias

Trigger: The two traits have different lead SNPs at the same locus; analyst centres each window on the trait-specific lead.

Mechanism: coloc PP is sensitive to the SNPs in the window; centring on different leads gives different per-SNP overlap and biases toward H3.

Symptom: Re-centring the window on the GWAS lead vs the eQTL lead produces qualitatively different PP.H4.

Fix: Use a SINGLE window (typically +/- 500 kb or 1 Mb) centred on the joint top-variant (the SNP with the lowest min-p across both traits), or on the GWAS lead consistently. Report PP under multiple centring choices; flag the locus if PP swings > 0.2 across centrings.

Underpowered eQTL (N < 200)

Trigger: Small eQTL discovery (e.g. tissue-specific bulk study, N < 200; per-cell-type sc-eQTL).

Mechanism: With low N, varbeta is large; the eQTL's per-SNP Bayes factors are flat; the joint likelihood concentrates on H0 or H1 (GWAS-only).

Symptom: PP.H0 or PP.H1 dominates; the eQTL panel shows visible signal but coloc cannot resolve causal vs noise.

Fix: Use eQTLGen (N ~ 31k whole-blood) or GTEx v8 (N ~ 70-700 per tissue) where possible. For rare cell types, accept the limitation and report the locus as underpowered rather than claim absence of colocalization.

eQTL N	Coloc viability	Notes
< 200	Underpowered	PP.H1 dominant; flag
200-500	Cis only, modest	Single-tissue cis
500-1000	Good for cis	Most GTEx v8 tissues
>= 1000	Well-powered	Trans accessible
>= 10000	Meta (eQTLGen)	Cross-tissue / sc

Reference QTL panel choice

GTEx v8 (838 donors, 49 tissues, 2020) is the current PredictDB-supported standard. GTEx v10 (released 2024) has limited harmonisation and is not yet PredictDB-default. eQTLGen blood meta-eQTL (N ~ 31k) wins on sample size for blood cis-eQTL discovery, beating any single tissue on power. Always pin version in methods (e.g. "GTEx v8 MASHR-EUR, PredictDB release 2022-01").

PP.H4 Threshold Framework

Threshold	Use case	Source
0.5 - 0.7	Suggestive / pilot / hypothesis-generating	Giambartolomei 2014 original
>= 0.7	Triangulation tier for TWAS / cis-MR / effector-gene cross-evidence	Open Targets Genetics common practice; cross-reference downstream skills
>= 0.75	Open Targets Platform / eQTL Catalogue / FinnGen default screening threshold	Open Targets Genetics docs; Mountjoy 2021 Nat Genet 53:1527
>= 0.80	Most published colocalizations / standard publication tier	Wallace 2020 PLoS Genet 16:e1008720
>= 0.90	Stringent clinical / therapeutic-target prioritization	Reserved for high-confidence claims
>= 0.95	Industry / regulatory drug-target submission grade	Internal pharma default
PP.H3 >= 0.80	Confident distinct causal variants (negative coloc result)	Standard
PP.H4 / (PP.H3 + PP.H4) >= 0.9	Conditional probability framing (some pipelines)	Foley 2021

Operational rule: Three operational tiers map onto the most common downstream uses: (a) >= 0.7 when PP.H4 is one of several lines of triangulating evidence (TWAS + coloc, cis-MR + coloc, effector-gene multi-evidence) -- this is the threshold downstream skills (causal-genomics/transcriptome-wide-association, causal-genomics/mendelian-randomization cis-MR, causal-genomics/effector-gene-prioritization, causal-genomics/proteome-mr-drug-target) require; (b) >= 0.8 for standard peer-reviewed publication as a stand-alone coloc claim (Wallace 2020); (c) >= 0.95 for industry / clinical drug-target submission. Open Targets and FinnGen pipelines screen at >= 0.75 but downstream publication-grade coloc claims should clear >= 0.8 and triangulation claims >= 0.7. ALWAYS report PP.H3 alongside PP.H4 -- a locus with PP.H4 = 0.6, PP.H3 = 0.3 is qualitatively different from PP.H4 = 0.6, PP.H3 = 0.05 (the former is real ambiguity over single vs distinct causal; the latter is underpowered evidence). Run coloc::sensitivity() and report the p12 range over which PP.H4 stays above the threshold.

Default Priors and the p12 Sensitivity Question

Prior	Default	Interpretation	When to change
p1	1e-4	Prob a random SNP is associated with trait 1	Rarely changed
p2	1e-4	Prob a random SNP is associated with trait 2	Rarely changed
p12	1e-5	Prob a random SNP is associated with both traits	Lower (5e-6 or 1e-6) for trans-eQTL or unrelated trait pairs; raise (5e-5) only with strong prior, e.g. molecular QTL in the same tissue as causal cell type

The p12/p1 ratio (= 0.1 under defaults) is the prior odds of colocalization given a trait-1 association. Wallace 2020 (PLoS Genet 16:e1008720) showed default p12 = 1e-5 is too liberal for many real-world settings and recommended sensitivity analysis as standard practice. Wallace 2025 (PLoS Genet 21:e1011697) extended this with variant-specific priors weighted by functional annotation.

p12 Sensitivity Grid

p12 grid point	Use case	Reporting rule
1e-4	Suggestive only / EUR cis-eQTL relaxed	PP.H4 here cannot support a publication claim
1e-5	Default for most cis-eQTL <-> GWAS pairs	Standard
5e-6	Conservative cis; default for trans-eQTL coloc	Recommended publication baseline
1e-6	Very conservative; trans coloc with weak prior	Required for cross-trait genome-rare coloc

Operational rule: Require PP.H4 to remain above threshold across at least 3 adjacent grid points; report the lowest p12 at which PP.H4 >= 0.75. Use coloc::sensitivity(result, rule = 'H4 > 0.75') for the diagnostic plot.

Required reporting: PP.H4 at default priors + p12 range over which PP.H4 stays above threshold.

eCAVIAR CLPP Threshold Framework

CLPP (Colocalization Posterior Probability) is the per-SNP product of the two per-trait fine-mapping posteriors. Threshold conventions:

• Hormozdiari 2016 AJHG 99:1245 used CLPP >= 0.01 (validated against null simulations).
• 2024 GTEx / Open Targets pipelines use CLPP >= 0.05.
• High-confidence claims require CLPP >= 0.1.
• Report both sum-CLPP across the credible set AND max-CLPP at any single SNP -- the two answer different questions (locus-level vs lead-SNP-level confidence).
• LaPierre 2021 Bioinformatics (CAVIARBF) extends CLPP to conditional analysis.

eCAVIAR -l ld_gwas.ld -l ld_eqtl.ld \
        -z gwas.z -z eqtl.z \
        -o coloc_out -c 2     # -c = max independent causal variants per trait
# Output: per-SNP CLPP in coloc_out_col file; report sum and max

LD Matrix Construction for coloc.susie

Requirements:

• Signed Pearson r (not r2). coloc.susie expects directional LD; squared LD silently inverts effect-direction inference.
• Ancestry-matched to GWAS / eQTL ancestry. EUR LD on AFR z-scores produces spurious credible sets.
• SNP-order-aligned to the beta vector and named to match (row/column names = SNP IDs).
• Positive semi-definite. Numerical-noise negative eigenvalues must be repaired.
• Effective N sample-size-matched to the trait being fine-mapped (provide via runsusie(..., n = N)).

# plink2 phased r (signed Pearson); square matrix output
plink2 --pfile 1KG_EUR \
    --extract snps.txt --chr 6 --from-bp X --to-bp Y \
    --r-phased square spaces --out locus_ld

# Alternative: in-sample LD from BED via bigsnpr
R <- bigsnpr::snp_cor(snp_obj$genotypes, ind.col = locus_snps)
# PSD repair if negative eigenvalues from numerical noise
R <- as.matrix(Matrix::nearPD(R)$mat)
dimnames(R) <- list(snp_ids, snp_ids)

Critical: Row and column order of R MUST match SNP order in the beta vector -- silent failure otherwise. The SuSiE objective stays finite under mis-ordering and returns nonsense credible sets. Verify with stopifnot(rownames(R) == names(beta)) before runsusie. Cross-reference causal-genomics/fine-mapping for the full LD diagnostic block (estimate_s_rss lambda < 0.05, kriging_rss outlier inspection).

SMR vs coloc Reconciliation

SMR (Zhu 2016) and coloc test related but non-identical questions:

• SMR tests pleiotropy vs linkage: does the top eQTL SNP show a GWAS effect explainable by its eQTL effect (pleiotropic / causal) or does the GWAS effect come from a different SNP in LD (linkage)?
• coloc tests shared vs distinct causal variants over an entire window of SNPs.
• HEIDI is SMR's heterogeneity test; null hypothesis is single shared causal SNP. Zhu 2016 Nat Genet 48:481 specifies HEIDI p > 0.05 (NOT 0.01) as non-rejection of single shared causal. HEIDI p > 0.05 does NOT prove shared causality -- only that data cannot reject it; pair with SMR p Bonferroni-corrected across probes. When LD between causal SNPs > 0.7, HEIDI loses power same as coloc.

When LD between two true causal SNPs is high (r2 > 0.7), both SMR/HEIDI and coloc.abf lose discriminatory power: SMR cannot pick which of the LD-tied SNPs is causal, and coloc.abf cannot reject H4 even if biology is two-distinct-causal. coloc.susie + ancestry-matched LD is the modern resolution.

Operational rule: SMR + HEIDI is appropriate when the question is "does this eQTL gene mediate the GWAS effect at all?" coloc is appropriate when the question is "do the two traits share a causal variant in this window?" Run both; agreement (significant SMR + non-rejected HEIDI + PP.H4 >= 0.75) is high-confidence; disagreement requires inspection (often the multi-causal / LD scenario above).

moloc Multi-Omic Framework (3-5 Traits)

For k traits, moloc tests 2^k - 1 hypotheses. 3 traits -> 15 hypotheses (H_a, H_b, H_c, H_ab, H_ac, H_bc, H_abc, plus "none of the above"); 4 traits -> 31; 5 traits -> 63. The hypothesis H_{all-share} (all k share a single causal variant) is the multi-omic analog of PP.H4.

# moloc 3-trait example; install via remotes::install_github('clagiamba/moloc')
library(moloc)
# Input: list of k dataframes with PVAL/N/F (frequency) per SNP and shared SNP IDs
result_moloc <- moloc_test(listData=list(gwas=gwas_df, eqtl=eqtl_df, sqtl=sqtl_df),
                            prior_var=c(0.01, 0.1, 0.5), priors=c(1e-4, 1e-6, 1e-7))
# PPA: posterior over all 15 hypotheses (3-trait case)
# Key column: PPA.abc (all-three-share)

moloc is computationally tractable up to k = 5 but explodes beyond; use HyPrColoc for k >= 6.

HyPrColoc Cluster-Based Coloc (Many Traits)

HyPrColoc (Foley 2021) extends single-causal coloc to many traits by clustering traits that share a causal variant. Output: per-cluster posterior + per-trait cluster assignment.

library(hyprcoloc)
# Inputs: SNPs-by-traits matrices of betas and standard errors
# Rows = SNPs (must be shared across all traits); Columns = traits
res <- hyprcoloc(effect.est=betas, effect.se=ses,
                  trait.names=colnames(betas), snp.id=rownames(betas),
                  reg.thresh=0.7,     # regional probability of coloc threshold
                  align.thresh=0.7)   # alignment threshold for traits within a cluster
res$results  # cluster assignment per trait + posterior

HyPrColoc inherits the single-causal-per-cluster assumption from coloc.abf; clusters can fragment if the true biology is allelic heterogeneity.

PWCoCo (Conditional Pairwise Coloc)

PWCoCo (Robinson 2022) wraps GCTA-COJO conditional analysis around coloc.abf. For a locus with k1 independent trait-1 signals and k2 independent trait-2 signals, PWCoCo runs k1 * k2 pairwise coloc.abf tests after conditioning each summary statistic on the other independent signals.

When to use: When GCTA-COJO has identified >= 2 independent signals in at least one trait and individual-level reference genotypes are available. Particularly suited to bulk eQTL with secondary cis signals.

Inputs: Per-trait summary stats (SNP, A1, A2, freq, beta, se, p, N) + plink bfile reference. Output: One coloc.abf result per (conditional signal 1, conditional signal 2) pair. Interpret each row as an independent single-signal coloc.

Caveats: PWCoCo requires individual-level reference (plink bfile); cannot run on summary stats alone. Collinearity threshold in COJO (default --cojo-collinear 0.9) controls how aggressively independent signals are split; lower values fragment, higher values merge. Worked CLI recipe in usage-guide.md.

Standard coloc.abf Pipeline

Goal: Test whether a single GWAS lead variant shares a causal variant with an eQTL gene's top signal at a defined locus.

Approach: Extract a 1 Mb window centred on the GWAS lead; harmonise alleles between datasets; format coloc input lists with type ('quant' or 'cc'), sample size N, and either sdY (quant) or s (cc); run coloc.abf; run sensitivity() over the p12 grid.

library(coloc)

# Inputs: harmonised gwas_df and eqtl_df with SNP, BETA, SE, MAF, N, POS columns
# Both must share the same SNP set and allele coding (verify with harmonise step)

gwas_input <- list(
    beta=gwas_df$BETA, varbeta=gwas_df$SE^2,
    snp=gwas_df$SNP, position=gwas_df$POS,
    type='cc',           # case-control GWAS
    s=0.30,              # case fraction
    N=50000)

eqtl_input <- list(
    beta=eqtl_df$BETA, varbeta=eqtl_df$SE^2,
    snp=eqtl_df$SNP, position=eqtl_df$POS,
    type='quant',        # quantitative eQTL
    sdY=1,               # SD(expression); 1 if standardised, else estimate from MAF+varbeta
    N=500)

res <- coloc.abf(dataset1=gwas_input, dataset2=eqtl_input,
                  p1=1e-4, p2=1e-4, p12=5e-6)   # conservative p12

print(res$summary)
sens <- coloc::sensitivity(res, rule='H4 > 0.75')   # generates plot + table

sdY semantics: when omitted, coloc estimates from MAF and varbeta; supplying sdY=1 ASSUMES the trait is already standardised (eQTL with inverse-normal-transformed expression). Mismatch produces silently wrong Bayes factors -- the most common silent failure.

• For quantitative trait: leave sdY=NULL to estimate via coloc:::sdY.est(varbeta, MAF, N). If CV of estimated sdY across SNPs > 0.5, varbeta/MAF are inconsistent -- coloc will silently miscalibrate Bayes factors.
• For inverse-normal-transformed expression: use sdY = 1 (already standardized).
• Mismatch produces silently wrong PP -- most common silent failure.

s parameter for case-control (type='cc'):

• s = N_cases / N_total (NOT cases-per-control; NOT 0.5 default).
• For population-cohort case-control: s ~ disease prevalence in the cohort (~0.005 for rare disease).
• Wrong s does not error -- silently biases PP at extreme MAF.

coloc.susie Multi-Causal Pipeline

Goal: Test colocalization at a locus with multiple independent signals (allelic heterogeneity).

Approach: Run SuSiE on each trait's summary statistics with ancestry-matched LD; verify LD-z-score consistency; coloc-test each pair of credible sets.

library(coloc); library(susieR)

# Diagnostic: z-score vs LD consistency MUST be checked
z_gwas <- gwas_df$BETA / gwas_df$SE
lam_gwas <- susieR::estimate_s_rss(z=z_gwas, R=ld_matrix, n=gwas_n)
if (lam_gwas > 0.05) stop('LD reference mismatched to z-scores; lambda=', lam_gwas)

s1 <- runsusie(list(beta=gwas_df$BETA, varbeta=gwas_df$SE^2,
                    snp=gwas_df$SNP, position=gwas_df$POS,
                    type='cc', s=0.3, N=50000, LD=ld_matrix), L=10)
s2 <- runsusie(list(beta=eqtl_df$BETA, varbeta=eqtl_df$SE^2,
                    snp=eqtl_df$SNP, position=eqtl_df$POS,
                    type='quant', sdY=1, N=500, LD=ld_matrix), L=10)

res_susie <- coloc.susie(s1, s2)   # NULL if no overlapping CS
# res_susie$summary rows: each (hit1, hit2) pair of credible sets

LD matrix MUST be in the same SNP order as the beta vector; mis-ordering silently produces nonsense.

SMR + HEIDI Pipeline

# SMR is a command-line tool. Pre-format GWAS into .ma (SNP A1 A2 freq beta se p N).
# eQTL data as BESD (binary eQTL summary data); pre-built BESD available from eQTLGen / GTEx.

smr --bfile 1KG_EUR_chr6 \
    --gwas-summary gwas.ma \
    --beqtl-summary eqtl_chr6.besd \
    --out smr_result \
    --thread-num 4 \
    --peqtl-smr 5e-8 \
    --heidi-mtd 1
# Output smr_result.smr: probe (gene) | top SNP | p_SMR | p_HEIDI | nsnp_HEIDI

Interpretation: significant p_SMR (Bonferroni-corrected across probes tested, typically < 5e-8 / N_probes) AND non-rejection by HEIDI (p_HEIDI > 0.05, per Zhu 2016) indicates pleiotropy / shared causal; p_HEIDI <= 0.05 rejects shared-causal -> linkage. HEIDI p > 0.05 does NOT prove shared causality, only that data cannot reject it. Require nsnp_HEIDI >= 10 for HEIDI reliability.

Allele Harmonisation (Critical Pre-Step)

Mismatched effect alleles silently invert signs of betas, collapsing PP.H4 into PP.H3. Required steps before coloc:

1. Merge GWAS and eQTL summary stats by SNP ID (rsID or chr:pos:ref:alt).
2. Mark SNP-pairs as same (A1/A2 match) or flip (A1/A2 swap); drop SNPs that match neither.
3. For flip rows, negate the second dataset's beta (and swap A1/A2).
4. Drop palindromic SNPs (A/T or C/G) at MAF > 0.42; their strand cannot be inferred from coding alone (TwoSampleMR harmonise_data standard cutoff).
5. Verify genome build alignment (hg19 vs hg38 must match; lift over if not).

Worked harmonisation code and build-mismatch pitfalls: see usage-guide.md.

Anticipated Reviewer Pushback

Pushback	Standard response
"Sensitivity to p12 prior?"	coloc::sensitivity() reported; PP.H4 robust across 1e-7 to 1e-5 grid
"Why not coloc.susie? Multi-causal possible?"	coloc.abf single-causal assumption stated; if PP.H3 dominant or GCTA-COJO identifies >= 2 independent signals, coloc.susie / SuSiE-based run; reported
"LD reference matched?"	In-sample preferred; if reference panel used, estimate_s_rss(z, R, N) lambda < 0.05; kriging_rss diagnostic clean
"PP.H4 = 0.6 is colocalization?"	No -- bands stated: 0.5-0.7 suggestive; >= 0.7 triangulation tier; >= 0.8 standard publication; >= 0.95 industry/clinical
"MHC region included?"	chr6:25-35 Mb excluded; HLA-coloc (Lagou 2024) for classical-allele-level coloc
"Ancestry mismatch?"	LD reference ancestry-matched to GWAS; for cross-ancestry use SharePro_coloc or coloc.susiex
"Sentinel SNP swap?"	Re-centered window on each trait's lead, joint top, eQTL top; PP.H4 stable within 0.1

Common Errors

Error / symptom	Cause	Solution
Error in coloc.abf: dataset must have N	Forgot N in list, or type not set	Supply both; case-control also needs s; quant also needs sdY
PP.H3 dominant despite obvious visual overlap	2+ causal in moderate LD breaks single-causal assumption	Run coloc.susie or eCAVIAR
estimate_s_rss lambda > 0.05	LD reference does not match z-scores (ancestry / sample / build)	Use in-sample LD or ancestry-matched reference; do not proceed
PP.H4 unstable across p12 sensitivity grid	Borderline evidence; default priors not justified	Report the p12 range; lower priors for trans-eQTL; do not over-claim
coloc.susie returns NULL summary	No overlapping credible sets between traits	Genuine result (no shared signal) or both traits underpowered
Per-SNP betas have opposite signs but same magnitude across traits	Effect-allele mismatch	Run harmonisation; flip betas where A1/A2 swap; drop palindromic at high MAF
SMR significant + HEIDI p <= 0.05	Linkage, not shared causal	Report as linkage; do not call colocalization
moloc all-share PPA collapses to ~0	Different sample sizes / power across omics	Inspect per-omic effect sizes; consider HyPrColoc for cluster output
HyPrColoc trait cluster fragments	Underlying biology is multi-causal	Switch to coloc.susie at each suspected cluster centre
MHC PP.H4 close to 0 with strong visual signal	Long-range LD breaks single-causal	Use HLA-coloc or exclude MHC; never report standard coloc PP at MHC

Tool Install Notes

• coloc: CRAN. install.packages('coloc'). Bundles susieR dependency for >= 5.1.
• susieR: CRAN. install.packages('susieR'). >= 0.12.35 for estimate_s_rss and kriging_rss.
• HyPrColoc: GitHub only (never CRAN). remotes::install_github('jrs95/hyprcoloc'). Requires R >= 3.5.
• SMR: Pre-compiled binary from cnsgenomics.com/software/smr. Linux/Mac/Windows binaries; no R package.
• eCAVIAR: Compile from GitHub fhormoz/caviar; C++ source. CLI eCAVIAR. PAINTOR is the related multi-trait fine-mapping toolkit.
• PWCoCo: GitHub jwr-git/pwcoco. Compiled C++ CLI; can also be invoked from R via wrapper scripts.
• SharePro_coloc: Python pip install sharepro-coloc or GitHub zhwm/SharePro_coloc.
• moloc: GitHub clagiamba/moloc. R package; minimally updated since 2019, no CRAN release. R >= 3.5.

Reviewer-Grade Reporting Template

For each colocalization claim, the report should include:

1. Method and version (e.g. coloc 5.2.3 coloc.abf, or coloc.susie with SuSiE L=10).
2. Window definition (e.g. +/- 500 kb around the GWAS lead rs12345 at chr6:30450000, hg38), and lead-SNP-swap sensitivity (PP.H4 at GWAS lead vs eQTL lead vs joint top).
3. Priors p1, p2, p12 used; sensitivity plot from coloc::sensitivity() and the p12 range over which PP.H4 stays above threshold.
4. All five posteriors PP.H0 through PP.H4 (not PP.H4 alone).
5. Threshold band the result clears (>= 0.7 triangulation tier, >= 0.75 Open Targets screening, >= 0.80 published, >= 0.90 stringent, >= 0.95 clinical).
6. LD reference ancestry, source (1000G phase 3 EUR / in-sample / UKBB), and lambda from estimate_s_rss if coloc.susie.
7. Reference QTL panel version (e.g. GTEx v8 MASHR-EUR, PredictDB release 2022-01; eQTLGen 2019).
8. Conditional analysis GCTA-COJO results if multi-causal; per-credible-set PP if coloc.susie.
9. Failure-mode caveats explicitly addressed: MHC excluded, chr 8 inversion excluded, ancestry-matched LD, sdY/s correctly specified, palindromic SNPs handled.
10. Methods-section H0-H4 prose describing what each hypothesis means (see usage-guide.md).

References

• Giambartolomei C et al 2014 PLoS Genet 10:e1004383 (coloc.abf)
• Wallace C 2020 PLoS Genet 16:e1008720 (default-prior sensitivity; variant-specific priors)
• Wallace C 2025 PLoS Genet 21:e1011697 (further p12 prior refinements)
• Wallace C 2021 PLoS Genet 17:e1009440 (coloc.susie; multiple causal variants)
• Zhu Z et al 2016 Nat Genet 48:481 (SMR + HEIDI)
• Hormozdiari F et al 2016 AJHG 99:1245 (eCAVIAR / CLPP)
• Giambartolomei C et al 2018 Bioinformatics 34:2538 (moloc)
• Foley CN et al 2021 Nat Commun 12:764 (HyPrColoc)
• Robinson JW et al 2022 bioRxiv 2022.08.08.503158 (PWCoCo)
• Wang W et al 2024 Bioinformatics 40:btae295 (SharePro_coloc)
• Lagou V et al 2024 medRxiv (HLA-coloc)
• Mountjoy E et al 2021 Nat Genet 53:1527 (Open Targets Genetics colocalization pipeline)
• Vosa U et al 2021 Nat Genet 53:1300 (eQTLGen, N ~ 31,684 whole blood)
• GTEx Consortium 2020 Science 369:1318 (GTEx v8 multi-tissue eQTL)

Related Skills

• causal-genomics/mendelian-randomization - Causal effect estimation from coloc-validated SNPs
• causal-genomics/fine-mapping - SuSiE / FINEMAP / CAVIAR credible sets feeding coloc.susie; LD construction protocol cross-ref
• causal-genomics/mediation-analysis - Downstream causal mediation given coloc shared causal variants
• causal-genomics/pleiotropy-detection - Distinguishing horizontal pleiotropy from shared causality
• causal-genomics/transcriptome-wide-association - TWAS / PrediXcan / FOCUS gene-level prioritization complementary to coloc
• causal-genomics/proteome-mr-drug-target - pQTL coloc + MR for drug-target prioritization
• causal-genomics/effector-gene-prioritization - Locus-to-gene with coloc, ABC, V2G integration
• population-genetics/association-testing - GWAS summary statistic generation and locus extraction
• population-genetics/linkage-disequilibrium - LD reference panels for coloc.susie and PWCoCo
• variant-calling/variant-annotation - Functional annotation for variant-specific priors
• variant-calling/filtering-best-practices - Pre-coloc QC for summary stats
• differential-expression/deseq2-basics - Generating eQTL / molecular QTL counts
• single-cell/scatac-analysis - Per-cell-type chromatin context for coloc interpretation
• workflows/gwas-pipeline - Upstream GWAS analysis producing coloc input
• data-visualization/ggplot2-fundamentals - Regional and LocusCompare plot construction