bio-causal-genomics-fine-mapping

SkillAI & models

Resolves GWAS associations to candidate causal variants and credible sets via SuSiE, susie_rss, FINEMAP, CAVIAR, DAP-G, PAINTOR, PolyFun, SuSiEx, MultiSuSiE, and FOCUS. Use when narrowing a GWAS lead SNP to a 95 percent credible set, choosing between in-sample and reference LD, calibrating non-sparse loci with SuSiE-inf or FINEMAP-inf, integrating functional priors via PolyFun, fine-mapping across ancestries with SuSiEx, diagnosing LD mismatch via estimate_s_rss and kriging_rss, handling HLA or long-range LD, or feeding credible sets into coloc.susie for colocalization.

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Then ask your AI: use the bio-causal-genomics-fine-mapping skill

What this skill tells your AI

The instructions your AI receives, as published by pku-yuangroup/openai4s in skills/bioskills/bio-causal-genomics-fine-mapping/SKILL.md and read by ahel’s review.

Version Compatibility

Reference examples tested with: susieR 0.12.27+, coloc 5.2.3+, FINEMAP 1.4.2+, PolyFun (head of omerwe/polyfun 2024), PAINTOR V3.0, SuSiEx (head of getian107/SuSiEx), DAP-G (head of xqwen/dap), pyfocus 0.8+, R 4.3+, PLINK 1.9 / 2.0.

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

  • R: packageVersion('susieR') then ?susie_rss to confirm argument names (e.g., prior_weights vs prior_variance semantics)
  • CLI: finemap --help, SuSiEx --help, PAINTOR --help, dap-g --help to confirm flags
  • Python: polyfun.py --help

If a call throws an error about an argument that no longer exists, introspect the installed function and adapt rather than retrying.

Fine-Mapping

"Narrow my GWAS locus to the variants likely to be causal" -> Fit a sparse Bayesian regression that propagates LD into posterior inclusion probabilities (PIPs) and credible sets, then validate that credible sets correspond to physically reasonable haplotypes given the LD reference.

  • R (summary statistics + LD): susieR::susie_rss(z, R, n, L=10) + estimate_s_rss LD diagnostic
  • R (individual-level genotypes): susieR::susie(X, y, L=10)
  • CLI (shotgun stochastic search): finemap --sss --in-files master.z --n-causal-snps 5 --prob-tol 0.001
  • CLI (cross-ancestry joint): SuSiEx --sst_file=eur.sst,eas.sst --n_gwas=N1,N2 --ref_file=eur.bim,eas.bim --ld_file=eur_ld,eas_ld --chr_col=1,1 --snp_col=2,2 --bp_col=3,3 --a1_col=4,4 --a2_col=5,5 --eff_col=6,6 --se_col=7,7 --pval_col=8,8 --chr=<chr> --bp=<start,end> --out_dir=<dir> --out_name=<name> (column-number flags and --ld_file are required; populations are assigned by the ORDER of the comma-separated --sst_file/--n_gwas/--ref_file/--ld_file lists, not a --pop flag; see SuSiEx --help)
  • Python (functional priors): polyfun.py --compute-h2-L2 -> per-SNP priors -> susie_rss with prior_weights=
  • Python (TWAS fine-mapping): focus finemap on gene-level Z-scores

Fine-mapping is a Bayesian model selection problem; LD is not noise but structured prior information. Most failure modes trace back to one of three issues: (a) LD reference mismatched to the GWAS sample; (b) the sparse-effects prior being wrong for the locus (polygenic background); or (c) too small an L cap. The estimate_s_rss() lambda and kriging_rss() per-SNP diagnostic catch (a) before downstream credible sets are reported.

Algorithmic Taxonomy

ToolModelInputStrengthFails when
SuSiE / susie_rss (Wang 2020 JRSSB 82:1273; Zou 2022 PLoS Genet)Iterative Bayesian sum-of-single-effects (IBSS), variationalIndividual-level (X, y) or (z, R, n)Fast; native PIP + credible sets; pluggable priors; default in modern pipelinesReference LD mismatched to GWAS sample; locus dominated by polygenic background; >L true effects
SuSiE-inf / FINEMAP-inf (Cui 2024 Nat Genet 56:162)SuSiE + infinitesimal random-effect component(z, R, n)Calibrated credible sets when locus is non-sparse (polygenic shoulder around a sparse causal); recommended for biobank-scale GWASVery small loci with truly sparse architecture (over-conservative); slower convergence
FINEMAP (Benner 2016 Bioinformatics 32:1493)Shotgun stochastic search over causal configurations.z + .ld + .master filesExact Bayes factors at small k; widely citedSlow at L > 5; binary install only (christianbenner.com); same LD-mismatch fragility as SuSiE
CAVIAR (Hormozdiari 2014 Genetics 198:497)Exhaustive enumeration up to k causals(z, R)Exact posterior at small kCombinatorial explosion beyond k=6; legacy method largely superseded by SuSiE
DAP-G (Wen 2016 AJHG 98:1114)Deterministic posterior approximation with adaptive scanSBAMS format; TORUS for enrichment priorsFast at QTL scale (whole-transcriptome); pairs with TORUS hierarchical priorsSBAMS format is awkward; less ubiquitous tooling
PAINTOR (Kichaev 2014 PLoS Genet 10:e1004722)EM with binary functional annotations(z, R, A) per locusLocus-level functional priors; multi-trait variantSingle-trait mode often matched by PolyFun + SuSiE; slower than SuSiE
PolyFun + SuSiE/FINEMAP (Weissbrod 2020 Nat Genet 52:1355)Stratified LDSC genome-wide -> per-SNP prior_weightsGWAS sumstats + pre-baked baseline-LFMost powerful single-trait functional prior; >20% more high-PIP (PIP>0.95) variants in simulations, >32% in real UK Biobank traits (Weissbrod 2020)Requires matched-ancestry baseline-LF; runs in two stages
SuSiEx (Yuan 2024 Nat Genet 56:1841)Joint cross-ancestry SuSiE; shared causal, population-specific LDPer-pop sumstats + per-pop LD referenceSmaller credible sets than per-ancestry meta or marginal fine-mapping; principled when causal variants are sharedTrans-ethnic heterogeneity violated (population-specific causals); ancestry must be cleanly assigned
MultiSuSiE (Rossen 2025 Nat Genet)Cross-ancestry SuSiE variant; flexible heterogeneityPer-pop sumstats + per-pop LDSimilar to SuSiEx; alternative implementationSame as SuSiEx; newer, less battle-tested
FOCUS / MA-FOCUS (Mancuso 2019 Nat Genet 51:675)Probabilistic TWAS fine-mapping over gene modelsTWAS Z-scores + gene LD (predicted expression)Identifies likely causal gene among co-regulated TWAS hits; cross-ancestry MA-FOCUS variantRequires pre-computed expression weights (e.g., FUSION/PrediXcan); gene-level rather than variant-level inference

Methodology evolves; verify the latest susieR vignette and the SuSiE-inf paper before locking on a single method. Wang Lab maintains susieR; the IBSS algorithm is stable but argument semantics (e.g., prior_weights vs prior_variance) have changed across versions.

Decision Tree by Experimental Scenario

ScenarioRecommended workflowWhy
Individual-level genotypes available (UKB, in-house cohort)susie(X, y, L=10)In-sample LD is exact; no mismatch fragility
Summary statistics only, ancestry matches reference panelsusie_rss(z, R, n, L=10) + estimate_s_rss diagnosticStandard external-LD pattern; verify lambda < 0.05
Single-locus EUR GWAS, sparse architecturesusie_rss with L=10, baseline functional priors optionalMost-common setting; SuSiE default works
Locus with strong polygenic shoulder (biobank scale)SuSiE-inf (Cui 2024)Adds infinitesimal component; calibrates non-sparse PIPs
Multi-ancestry GWAS (EUR + EAS + AFR)SuSiEx with per-pop sumstats and LDJoint inference shrinks credible sets; per-ancestry meta loses LD information
Locus with > 5 expected independent signals (HLA, lipid loci)susie_rss with L=20-30Default L=10 caps signal count; HLA needs extension
TWAS hits with co-regulated genesFOCUS / MA-FOCUSVariant-level fine-mapping cannot distinguish co-regulated gene candidates
Want functional priors (coding, conserved, regulatory)PolyFun -> susie_rss with prior_weightsGenome-wide SLDSC priors sharpen PIPs more than locus-level annotations
QTL fine-mapping (eQTL, sQTL, caQTL) at transcriptome scaleDAP-G + TORUS OR susie_rss per geneDAP-G is built for QTL throughput; SuSiE works per gene
Low-N QTL (GTEx tissue panel, N < 1000)susie_rss with coverage = 0.9 (or 0.8); document choiceDefault 0.95 returns very wide credible sets at low power; report the relaxed coverage explicitly in methods
HLA region (chr6:28-34 Mb) or chr8 inversionSpecialized workflow: stratify haplotypes; consider HLA-specific imputation; or excludeLD structure is too complex; standard methods unreliable
Cross-feed into colocalizationsusie_rss -> coloc.susie()Modern coloc operates on credible sets, not single SNPs

Critical LD Diagnostic Block (susie_rss)

Goal: Detect LD reference mismatch before reporting credible sets.

Approach: estimate_s_rss() quantifies the global Z-score / LD inconsistency as a scalar; kriging_rss() identifies individual SNPs whose Z-scores are inconsistent with the LD reference (typically genotyping errors, strand flips, or wrong reference panel).

library(susieR)
s_hat <- estimate_s_rss(z = z_scores, R = ld_matrix, n = N)
# s_hat is the inferred scale of LD inconsistency.
# Source: susieR vignette "Diagnostic for summary statistic"; Zou 2022 PLoS Genet.
# Rule of thumb: s_hat < 0.05 acceptable; 0.05-0.10 marginal; > 0.10 refit or change LD reference.

cond_z <- kriging_rss(z = z_scores, R = ld_matrix, n = N)
# cond_z$conditional_dist returns per-SNP expected vs observed z; flag |z_obs - z_exp| > 3
# Common cause: strand flip, allele coding mismatch, or single-SNP imputation error.

# If diagnostic fails: refit with explicit scale parameter to absorb LD mismatch
fit <- susie_rss(z = z_scores, R = ld_matrix, n = N, L = 10, estimate_residual_variance = TRUE)

Skipping this block is the dominant cause of irreproducible fine-mapping. Always run before reporting credible sets.

Per-Tool Failure Modes

LD reference mismatch (most common)

Trigger: External LD matrix from 1000 Genomes / UK Biobank reference used for a GWAS conducted on a different cohort or ancestry mix.

Mechanism: Z-scores reflect the GWAS sample's LD; the reference R does not. The susie_rss likelihood depends on z' R^{-1} z being consistent with the modeled effects, and inconsistency manifests as spurious credible sets containing tag SNPs from the reference but not from the discovery cohort.

Symptom: estimate_s_rss() lambda > 0.05; kriging_rss() flags many SNPs with |z_obs - z_exp| > 3; credible sets contain physically distant SNPs (anti-correlated in LD with the lead) or include all SNPs at the locus.

Fix: Use in-sample LD whenever the cohort genotypes are accessible (compute with plink --r2 square on the GWAS samples themselves). When only summary statistics are available, ancestry-stratify the LD reference exactly (e.g., 1000G EUR FIN+CEU+GBR+IBS+TSI for a Northern European GWAS, not full EUR). For mixed-ancestry GWAS, fine-map per ancestry then meta-analyze, or move to SuSiEx.

Non-sparse architecture (biobank scale)

Trigger: Locus with one strong signal plus hundreds of weakly associated SNPs (polygenic shoulder); typical at biobank scale.

Mechanism: Vanilla SuSiE assumes a sparse sum-of-single-effects prior. With polygenic background, the model misallocates effects, producing inflated credible sets or many small spurious ones. Cui 2024 (Nat Genet 56:162) showed PIPs from SuSiE in this regime are systematically miscalibrated.

Symptom: Many small credible sets (5-15 per locus); replication in independent cohorts fails for non-lead credible sets; PIP distribution has a heavy tail.

Fix: Use SuSiE-inf or FINEMAP-inf (Cui 2024). These augment the sum-of-single-effects with an infinitesimal random-effect component that absorbs polygenic background. Source: github.com/FinucaneLab/fine-mapping-inf.

L too small

Trigger: Locus with > 5 independent signals (HLA region, APOC1/APOE, LPA, IL6R region for some traits).

Mechanism: SuSiE assumes at most L independent effects. When the true number exceeds L, some signals are absorbed into existing components, distorting PIPs and credible sets for the captured signals.

Symptom: length(fit$sets$cs) equals L (all L slots used); credible set purity for higher-indexed sets is low (fit$sets$purity[,'min.abs.corr'] < 0.5); fits with larger L change top-PIP variants.

Fix: Increase L iteratively (L=10 -> 20 -> 30) until length(fit$sets$cs) < L (susieR auto-prunes unsupported effects so the returned CS count is the effective L). For HLA, start at L=30. The cost is mostly computational, not statistical: SuSiE prunes unused slots, so L=30 is safe when L=10 was right.

prior_weights vs prior_variance confusion (PolyFun integration)

Trigger: Passing PolyFun output to susie_rss with prior_variance=polyfun_priors (wrong argument).

Mechanism: prior_variance in susie_rss is a single scalar (or vector of length L) for the per-effect variance, NOT a per-SNP probability. prior_weights is the per-SNP causal probability vector (sums to ~1). Passing PolyFun's per-SNP prior to prior_variance is silently accepted but applies a numerically nonsensical per-effect variance.

Symptom: PIPs nearly identical to the uniform-prior fit; functional annotations appear to have no effect.

Fix: Use prior_weights = polyfun_priors$SNPVAR (the PolyFun output column is uppercase SNPVAR; R is case-sensitive). Verify with ?susie_rss in the installed version. Reference: github.com/omerwe/polyfun README, Weissbrod 2020 supplementary methods.

Credible-set misinterpretation

Trigger: Reporting per-variant PIP without distinguishing "in credible set" from "high PIP".

Mechanism: The 95 percent credible-set guarantee is P(causal variant in set) >= 0.95. Per-variant PIPs within a set do not necessarily sum to 1 across all variants, and PIPs across overlapping sets can double-count posterior mass.

Symptom: Reporting "the top PIP variant" when the credible set is wide (size > 50); claiming a single variant is causal when the set contains 30 high-LD SNPs.

Fix: Always report (a) number of credible sets, (b) size of each set, (c) purity (fit$sets$purity[,'min.abs.corr']), (d) the top PIP variant within the set as the candidate lead. The credible set is the unit of inference; the top PIP variant is a candidate, not a conclusion.

Cross-ancestry with single-ancestry LD

Trigger: Multi-ancestry meta-analyzed GWAS, then susie_rss with EUR LD.

Mechanism: Meta-analysis z-scores reflect a weighted mix of population LD structures; no single-population LD matrix matches.

Fix: Move to SuSiEx (joint cross-ancestry SuSiE; Yuan 2024). Per-ancestry fine-mapping followed by manual merging loses the shared-causal-variant information that SuSiEx exploits.

Case-control GWAS passing Ntotal instead of Neff

Trigger: Passing n = N_total to susie_rss() for case-control GWAS derived from logistic regression.

Mechanism: susie_rss expects the effective sample size that determined the standard errors. For case-control logistic regression, Neff = 4 / (1/Ncase + 1/Ncontrol); when cases are rare, total N can exceed Neff by 25x or more. Passing Ntotal rescales z-scores into a regime SuSiE never sees and makes the implied prior variance wrong.

Symptom: PIPs systematically biased; credible sets either too narrow (PIPs collapse to a single SNP that is not robust) or too wide (PIPs flatten); replication poor; sometimes z-score scale warnings from susieR.

Fix: Neff = 4 / (1/Ncase + 1/Ncontrol). Example: Ncase=5000, Ncontrol=495000 -> Neff ~= 19,800 (NOT 500,000). For quantitative traits from linear regression, n = N_total is correct. Reference: Privé F et al 2022 HGG Adv 3:100136 (bigsnpr documents Neff handling); Willer 2010 Bioinformatics (METAL Neff convention).

Allele Harmonization with the LD Reference

Trigger: Effect allele in GWAS sumstats differs from the coding/A1 allele in the LD reference panel; or palindromic SNPs (A/T, C/G) carried without strand resolution.

Mechanism: susie_rss treats z and R as defined on the same allele coding. If the effect allele is swapped relative to the LD-reference A1, the sign of z is wrong and the LD row/column for that SNP is implicitly flipped. SNPs matching by rsID can silently swap alleles between sumstats and reference, breaking the z' R z consistency the model relies on.

Symptom: estimate_s_rss lambda inflated despite ancestry-matched panel; kriging_rss flags many SNPs with |z_obs - z_exp| > 3 clustered at SNPs where reference A1 != GWAS effect allele; credible sets pick up tag-only SNPs anti-correlated with the lead.

Fix: Harmonize before fitting:

harmonize_z_to_ref <- function(z, gwas_a1, gwas_a2, ref_a1, ref_a2) {
    palindromic <- (gwas_a1 == 'A' & gwas_a2 == 'T') | (gwas_a1 == 'T' & gwas_a2 == 'A') |
                   (gwas_a1 == 'C' & gwas_a2 == 'G') | (gwas_a1 == 'G' & gwas_a2 == 'C')
    flip <- (gwas_a1 == ref_a2) & (gwas_a2 == ref_a1)
    z[flip] <- -z[flip]
    drop <- palindromic | !((gwas_a1 == ref_a1 & gwas_a2 == ref_a2) | flip)
    list(z = z, keep = !drop)
}

Drop palindromic SNPs at MAF > 0.42 (ambiguous strand); or resolve via external strand info (TopMed, 1000G strand files). TwoSampleMR::harmonise_data() offers an alternative implementation. See causal-genomics/colocalization-analysis for an equivalent harmonize helper used downstream.

Reconciliation: When Methods Disagree

PatternLikely causeAction
SuSiE finds 3 credible sets, FINEMAP finds 1FINEMAP's stochastic search did not converge OR SuSiE absorbed background into spurious setsIncrease FINEMAP --n-iterations; check SuSiE purity (sets with purity < 0.5 are spurious)
SuSiE PIPs much sharper than FINEMAPsusie_rss assumes single residual variance; FINEMAP marginalizes over noiseBoth can be correct; report the intersection of high-PIP variants from both as primary candidates
PolyFun + SuSiE collapses 10-variant credible set to 1Functional priors are doing real work (coding variant in set)Verify with prior_weights plot; if priors are coding-specific the result is interpretable
SuSiEx credible set excludes the EUR top-PIP variantEUR signal is tag, true causal shared across ancestries lies elsewhereTrust SuSiEx if both populations have well-powered GWAS; verify with conditional analysis
HLA gives 50-variant credible set in every methodHLA LD structure cannot be fine-mapped by linear methodsUse HLA-specific imputation (HIBAG, SNP2HLA) and haplotype-level analysis

Operational rule: For high-confidence reporting, require that (a) estimate_s_rss() lambda < 0.05; (b) at least one credible set has purity > 0.5 (min_abs_corr >= 0.5, equivalent to r2 >= 0.25); (c) the lead PIP variant within that set is reproduced by an independent method (FINEMAP, SuSiEx, or in-sample SuSiE if reference-LD was used). Anything failing these three is exploratory.

Quantitative Thresholds

QuantityThresholdSource / Rationale
Credible set coverage (well-powered GWAS)0.95 (default)Wang 2020 JRSSB; standard convention
Credible set coverage (low-N eQTL, GTEx tissue)0.9 or 0.8At N < 1000, default 0.95 returns very wide CS; document choice in methods
Credible set purity (rare-variant fine-mapping)min_abs_corr >= 0.1LD genuinely sparse; relax to retain signal
Credible set purity (default common-variant)min_abs_corr >= 0.5 (r2 >= 0.25)susieR default; below this the set is LD-confounded
Credible set purity (publication-strict)min_abs_corr >= 0.7Stringent claim; rare in practice
PIP suggestive> 0.5Convention; "more likely than not causal among set"
PIP strong> 0.9Convention; high-confidence single candidate
PIP very strong> 0.95Convention; near-certain candidate within credible set
L (default cap)10susieR default; sufficient for most non-HLA loci
L (HLA / complex loci)20-30Empirical; HLA hosts > 10 independent signals for many traits
n for case-control susie_rssNeff = 4/(1/Ncase + 1/Ncontrol), NOT NtotalPrivé F et al 2022 HGG Adv 3:100136; matches the SE scale of logistic-regression sumstats
estimate_s_rss lambda acceptable< 0.05susieR vignette; > 0.10 indicates serious LD mismatch
kriging_rss per-SNP flagz_obs - z_exp
Locus window (default)+/- 500 kb from sentinelConventional; covers most LD blocks
Locus window (conditional-p floor)Extend until conditional -log10(p) < 4Avoids truncating a secondary signal whose conditional evidence leaks into the window edge
Locus window (long-range LD)5+ Mb or stratifyHLA chr6:25-35Mb, chr8 inversion chr8:8.1-11.9Mb hg38, chr17 H1/H2 inversion
FINEMAP --n-causal-snps5Default; raise for HLA
FINEMAP --prob-tol0.001Convergence tolerance; rarely needs change

Functional Priors with PolyFun

Goal: Use genome-wide stratified LDSC heritability to weight per-SNP causal priors, sharpening PIPs at coding, conserved, and regulatory variants.

Approach: Run PolyFun once genome-wide to estimate per-SNP h2 from the baseline-LF annotation set; extract per-SNP causal prior; pass to susie_rss as prior_weights.

# Parametric route: L2-regularized S-LDSC writes per-SNP priors directly (--no-partitions)
polyfun.py --compute-h2-L2 --no-partitions \
    --output-prefix polyfun_h2 \
    --sumstats gwas_munged.sumstats \
    --ref-ld-chr UKB_baseline_LF/baselineLF2.2.UKB. \
    --w-ld-chr UKB_baseline_LF/weights.UKB.
# Per-SNP priors written to polyfun_h2.<CHR>.snpvar_ridge_constrained.gz

# Non-parametric route (finer, optional): drop --no-partitions above, then add an
# intermediate LD-score step before re-estimating binned per-SNP h2:
#   polyfun.py --compute-ldscores --output-prefix polyfun_h2 ...
#   polyfun.py --compute-h2-bins --output-prefix polyfun_h2 --sumstats gwas_munged.sumstats --w-ld-chr UKB_baseline_LF/weights.UKB.
library(susieR)
priors <- read.table('polyfun_h2.6.snpvar_ridge_constrained.gz', header = TRUE)
priors <- priors[match(gwas_df$SNP, priors$SNP), ]
prior_w <- priors$SNPVAR / sum(priors$SNPVAR, na.rm = TRUE)

fit <- susie_rss(z = z_scores, R = ld_matrix, n = N, L = 10,
                 prior_weights = prior_w)

UKB baseline-LF priors are pre-computed EUR-only at data.broadinstitute.org/alkesgroup/UKBB_LD/ for hg19 and hg38. For EAS, AFR, or SAS GWAS, the EUR weights are NOT valid: functional-prior fine-mapping in a non-EUR ancestry requires baseline-LF annotations matched to that ancestry. For ancestries lacking matched baseline-LF (admixed, under-represented), accept reduced power and run uniform-prior susie_rss; applying EUR weights to non-EUR sumstats produces miscalibrated PIPs that look sharper than reality.

Manual Coding-Variant Priors Without PolyFun

For postdocs without PolyFun infrastructure or with single-locus inputs, manual annotation-based priors are a reasonable approximation (Hutchinson 2020 Hum Mol Genet 29:R81). As a stated convention, coding variants get ~10x uniform weight; broadly conserved variants ~5x (binned by CADD-PHRED quantile).

build_manual_priors <- function(vep_df, cadd) {
    w <- rep(1, nrow(vep_df))
    w[vep_df$Consequence %in% c('missense_variant', 'stop_gained', 'splice_donor_variant',
                                'splice_acceptor_variant', 'frameshift_variant')] <- 10
    w[cadd >= quantile(cadd, 0.95, na.rm = TRUE)] <- pmax(w[cadd >= quantile(cadd, 0.95, na.rm = TRUE)], 5)
    w / sum(w)
}
fit <- susie_rss(z = z_scores, R = ld_matrix, n = Neff, L = 10, prior_weights = build_manual_priors(vep, cadd))

Report the prior construction explicitly; reviewers will ask whether the prior was tuned post hoc.

Cross-Ancestry Fine-Mapping with SuSiEx

Goal: Jointly fine-map a locus across multiple ancestries assuming shared causal variants but population-specific LD.

Approach: Per-ancestry summary statistics + per-ancestry LD reference; SuSiEx runs a joint SuSiE model with population-specific R matrices. SuSiEx assigns populations by the ORDER of the comma-separated --sst_file/--n_gwas/--ref_file/--ld_file lists (there is no --pop flag); keep all four lists in the same population order.

Shortened here. Read the whole file on GitHub.

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