Bio Causal Genomics Colocalization Analysis

Five hypotheses tested by coloc:

• H0: No association with either trait
• H1: Association with trait 1 only
• H2: Association with trait 2 only
• H3: Both associated, different causal variants
• H4: Both associated, shared causal variant

coloc.abf Analysis

Goal: Test whether two traits share a causal variant at a GWAS locus using Bayesian colocalization.

Approach: Format summary statistics for each trait as named lists, run coloc.abf to compute posterior probabilities for five hypotheses (H0-H4), and interpret PP.H4 as evidence for a shared causal variant.

library(coloc)

# --- Input format: named list with GWAS summary stats ---
# Required fields: beta, varbeta, snp, position, type, N
# type = 'quant' (continuous) or 'cc' (case-control)

gwas_data <- list(
  beta = gwas_df$BETA,
  varbeta = gwas_df$SE^2,
  snp = gwas_df$SNP,
  position = gwas_df$POS,
  type = 'cc',           # Case-control study
  s = 0.3,               # Proportion of cases (required for cc)
  N = 50000              # Total sample size
)

eqtl_data <- list(
  beta = eqtl_df$BETA,
  varbeta = eqtl_df$SE^2,
  snp = eqtl_df$SNP,
  position = eqtl_df$POS,
  type = 'quant',        # Quantitative trait (expression)
  N = 500,               # eQTL sample size
  sdY = 1                # SD of trait (1 if already normalized)
)

# --- Run colocalization ---
result <- coloc.abf(dataset1 = gwas_data, dataset2 = eqtl_data)

# Posterior probabilities
# PP.H4 > 0.8: Strong evidence for colocalization (shared variant)
# PP.H3 > 0.8: Distinct causal variants at the locus
# PP.H4 between 0.5-0.8: Suggestive but inconclusive
print(result$summary)

Prior Sensitivity

# Default priors: p1 = 1e-4, p2 = 1e-4, p12 = 1e-5
# p1: Prior probability a SNP is associated with trait 1
# p2: Prior probability a SNP is associated with trait 2
# p12: Prior probability a SNP is associated with both traits
#
# Ratio p12/p1 represents prior belief in colocalization
# Default: p12/p1 = 0.1 (10% of trait 1 SNPs also affect trait 2)

result_sensitive <- coloc.abf(
  dataset1 = gwas_data,
  dataset2 = eqtl_data,
  p1 = 1e-4,
  p2 = 1e-4,
  p12 = 5e-6    # More conservative prior for shared association
)

# Sensitivity analysis across prior values
sensitivity(result, 'H4 > 0.8')

Using P-values (No Beta/SE)

# When only p-values are available, use MAF to approximate
gwas_pval <- list(
  pvalues = gwas_df$P,
  MAF = gwas_df$MAF,
  snp = gwas_df$SNP,
  position = gwas_df$POS,
  type = 'cc',
  s = 0.3,
  N = 50000
)

result <- coloc.abf(dataset1 = gwas_pval, dataset2 = eqtl_data)

SuSiE-Coloc (Multiple Causal Variants)

Goal: Test colocalization at loci with multiple independent causal signals.

Approach: Run SuSiE fine-mapping on each dataset to identify credible sets, then test colocalization between all pairs of credible sets using coloc.susie.

library(coloc)
library(susieR)

# coloc.abf assumes a single causal variant per locus
# SuSiE-coloc handles multiple causal variants

# LD matrix required (correlation matrix from reference panel)
ld_matrix <- as.matrix(read.table('ld_matrix.txt'))

# Run SuSiE on each dataset
susie_gwas <- 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       # Max number of causal variants to search for
)

susie_eqtl <- runsusie(
  list(beta = eqtl_df$BETA, varbeta = eqtl_df$SE^2,
       snp = eqtl_df$SNP, position = eqtl_df$POS,
       type = 'quant', N = 500, sdY = 1, LD = ld_matrix),
  L = 10
)

# Coloc using SuSiE credible sets
result_susie <- coloc.susie(susie_gwas, susie_eqtl)
print(result_susie$summary)
# Each row tests colocalization between a pair of credible sets
# hit1, hit2: Credible set indices from dataset 1 and 2

HyPrColoc (Multi-Trait)

Goal: Test colocalization across three or more traits simultaneously to identify shared causal variant clusters.

Approach: Provide beta and SE matrices (SNPs x traits) to hyprcoloc, which clusters traits sharing a causal variant using a branch-and-bound algorithm.

# install.packages('remotes')
# remotes::install_github('jrs95/hyprcoloc')
library(hyprcoloc)

# Test colocalization across multiple traits simultaneously
# Input: matrices of betas and SEs (rows = SNPs, columns = traits)
betas <- cbind(gwas_df$BETA, eqtl1_df$BETA, eqtl2_df$BETA)
ses <- cbind(gwas_df$SE, eqtl1_df$SE, eqtl2_df$SE)
colnames(betas) <- colnames(ses) <- c('GWAS', 'eQTL_gene1', 'eQTL_gene2')
rownames(betas) <- rownames(ses) <- gwas_df$SNP

result_hypr <- hyprcoloc(
  effect.est = betas,
  effect.se = ses,
  trait.names = colnames(betas),
  snp.id = rownames(betas)
)

# Output: clusters of traits sharing a causal variant
print(result_hypr$results)

Input Preparation

# --- Extract a locus (1 Mb window around lead SNP) ---
extract_locus <- function(sumstats, lead_snp_pos, chr, window = 500000) {
  locus <- sumstats[sumstats$CHR == chr &
                    sumstats$POS >= (lead_snp_pos - window) &
                    sumstats$POS <= (lead_snp_pos + window), ]
  locus[order(locus$POS), ]
}

# --- Generate LD matrix from plink ---
# plink --bfile ref_panel --chr 6 --from-bp 30000000 --to-bp 31000000 \
#   --r square --out ld_matrix
# Read into R:
ld <- as.matrix(read.table('ld_matrix.ld'))

Visualization

library(ggplot2)

plot_coloc_locus <- function(gwas_df, eqtl_df, result) {
  pp4 <- round(result$summary['PP.H4.abf'], 3)

  p1 <- ggplot(gwas_df, aes(x = POS / 1e6, y = -log10(P))) +
    geom_point(alpha = 0.6) +
    labs(x = 'Position (Mb)', y = '-log10(P)', title = paste('GWAS | PP.H4 =', pp4)) +
    theme_minimal()

  p2 <- ggplot(eqtl_df, aes(x = POS / 1e6, y = -log10(P))) +
    geom_point(alpha = 0.6, color = 'steelblue') +
    labs(x = 'Position (Mb)', y = '-log10(P)', title = 'eQTL') +
    theme_minimal()

  library(patchwork)
  p1 / p2
}

LocusCompare Plot

# LocusCompare: scatter of -log10(P) for GWAS vs eQTL at shared SNPs
plot_locuscompare <- function(gwas_df, eqtl_df) {
  merged <- merge(
    gwas_df[, c('SNP', 'P')],
    eqtl_df[, c('SNP', 'P')],
    by = 'SNP', suffixes = c('.gwas', '.eqtl')
  )

  ggplot(merged, aes(x = -log10(P.gwas), y = -log10(P.eqtl))) +
    geom_point(alpha = 0.5) +
    geom_smooth(method = 'lm', se = FALSE, linetype = 'dashed', color = 'grey50') +
    labs(x = '-log10(P) GWAS', y = '-log10(P) eQTL', title = 'LocusCompare') +
    theme_minimal()
}

Decision Framework

PP.H4 > 0.8:  Strong colocalization -- traits share a causal variant
PP.H3 > 0.8:  Distinct causal variants -- LD-driven overlap, not shared causality
PP.H4 0.5-0.8: Suggestive -- increase sample size, try SuSiE-coloc
PP.H0/H1/H2 dominant: Insufficient signal at this locus

Common pitfalls:

• Small eQTL sample sizes reduce power (N < 200 is problematic)
• LD can inflate PP.H3 when two nearby causal variants exist -- use SuSiE-coloc
• Always check that both traits have significant signals at the locus before running coloc

Related Skills

• mendelian-randomization - Test causal effects using genetic instruments
• fine-mapping - Identify causal variants and credible sets
• population-genetics/linkage-disequilibrium - LD reference panels for SuSiE-coloc
• differential-expression/deseq2-basics - Generate eQTL data for colocalization