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In this example, we show the complete pipeline of using XMAP to identify causal SNPs by using real GWAS data. As an example, we use LDL GWASs from AFR and EUR.

Step 0: Data preparation

XMAP requires three types of data as input:

  1. GWAS summary statistics from different populations
  2. LD scores estimated with samples from the analyzed populations
  3. LD matrices of the target locus estimated with samples from the analyzed populations

The GWAS summary statistics are available at Neal Lab or GLGC. Here, we use LD matrices contructed from UK Biobank genotypes as it is the in-sample genotype data for the EUR summary statistics and has a large sample size. The EUR LD matrices resources are available at Prof Alkes Price’s group or AWS site: s3://broad-alkesgroup-ukbb-ld/UKBB_LD/. We constrcutes the AFR LD matrices from the UK Biobank genotypes by ourselves. If you wish to construct LD matrices from your own plink files or public dataset (e.g., 1000 Genomes), please refer to the example with 1000 Genomes Reference Panel.

The XMAP analysis involves two steps. We first estimate the polygenic parameters and inflation constants using GWAS summary data from the whole genome. Then we fix these parameters and use variational inference to evaluate the posteriror inclusion probability of SNPs in the target locus. In this example, we focus on the SNP rs900776 that was previously reported to be related with LDL. This SNP is located at the locus defined by base pair 20000001-23000001 in Chromosome 8. We provide the AFR and EUR LD matrices of this locus estimated from UK Biobank genotypes with the link given in the XMAP GitHub page.

library(XMAP)
library(susieR)
library(data.table)
library(Matrix)
set.seed(1)

Step 1: Estimate polygenic parameters and inflation constants

We first apply bi-variate LDCS to estimate the inflation constants and parameters of polygenic effects. We need GWASs Z-scores of the whole genome from AFR and EUR, and their LD scores as input.

We first read GWAS summary statistics and LD scores.

# read GWAS summary statistics
sumstat_EUR <- fread("/Users/cmx/Documents/Research/Project/Fine_Mapping/sumstats/LDL_allSNPs_UKBNealLab_summary_format.txt")
sumstat_AFR <- fread("/Users/cmx/Documents/Research/Project/Fine_Mapping/sumstats/LDL_AFR_GLGC_summary_format.txt")

# read LD scores
ldscore <- data.frame()
for (chr in 1:22) {
  ldscore_chr <- fread(paste0("/Users/cmx/Documents/Research/Project/Fine_Mapping/LD_ref/LD_score/LDscore_eas_brit_afr_chr", chr, ".txt"))
  ldscore <- rbind(ldscore, ldscore_chr)
  cat("CHR", chr, "\n")
}

# pre-process: remove ambiguous SNPs
idx_amb <- which(ldscore$allele1 == comple(ldscore$allele2))
ldscore <- ldscore[-idx_amb,]


# pre-process: overlap SNPs
snps <- Reduce(intersect, list(ldscore$rsid, sumstat_AFR$SNP, sumstat_EUR$SNP))
sumstat_AFR_ldsc <- sumstat_AFR[match(snps, sumstat_AFR$SNP),]
sumstat_EUR_ldsc <- sumstat_EUR[match(snps, sumstat_EUR$SNP),]
ldscore <- ldscore[match(snps, ldscore$rsid),]


# pre-process: flip alleles
z_afr <- sumstat_AFR_ldsc$beta / sumstat_AFR_ldsc$se
z_eur <- sumstat_EUR_ldsc$Z

idx_flip <- which(sumstat_AFR_ldsc$A1 != ldscore$allele1 & sumstat_AFR_ldsc$A1 != comple(ldscore$allele1))
z_afr[idx_flip] <- -z_afr[idx_flip]

idx_flip <- which(sumstat_EUR_ldsc$A1 != ldscore$allele1 & sumstat_EUR_ldsc$A1 != comple(ldscore$allele1))
z_eur[idx_flip] <- -z_eur[idx_flip]


idx1 <- which(z_afr^2 < 30 & z_eur^2 < 30)
ld_afr_w <- 1 / sapply(ldscore$AFR, function(x) max(x, 1))
ld_eur_w <- 1 / sapply(ldscore$EUR, function(x) max(x, 1))

Then we apply bi-variate LDSC to estimate polygenic and confounding parameters. The two-stage LDSC is used here.

# bi-variate LDSC: AFR-EUR
# stage 1 of LDSC: estimate intercepts
fit_step1 <- estimate_gc(data.frame(Z = z_afr[idx1], N = sumstat_AFR_ldsc$N[idx1]), data.frame(Z = z_eur[idx1], N = sumstat_EUR_ldsc$N[idx1]),
                         ldscore$AFR[idx1], ldscore$EUR[idx1], ldscore$AFR_EUR[idx1],
                         reg_w1 = ld_afr_w[idx1], reg_w2 = ld_eur_w[idx1], reg_wx = sqrt(ld_afr_w[idx1] * ld_eur_w[idx1]),
                         constrain_intercept = F)
# stage 2 of LDSC: fix intercepts and estimate slopes
fit_step2 <- estimate_gc(data.frame(Z = z_afr, N = sumstat_AFR_ldsc$N), data.frame(Z = z_eur, N = sumstat_EUR_ldsc$N),
                         ldscore$AFR, ldscore$EUR, ldscore$AFR_EUR,
                         reg_w1 = ld_afr_w, reg_w2 = ld_eur_w, reg_wx = sqrt(ld_afr_w * ld_eur_w),
                         constrain_intercept = T, fit_step1$tau1$coefs[1], fit_step1$tau2$coefs[1], fit_step1$theta$coefs[1])

We now extract the LDSC output and construct \(\hat{\Omega}\) and \(c_1\), \(c_2\) for XMAP analysis

# Assign LDSC estimates to covariance of polygenic effects
OmegaHat <- diag(c(fit_step2$tau1$coefs[2], fit_step2$tau2$coefs[2])) # AFR EUR
OmegaHat[1, 2] <- fit_step2$theta$coefs[2] # co-heritability
OmegaHat[lower.tri(OmegaHat)] <- OmegaHat[upper.tri(OmegaHat)]

c1 <- fit_step2$tau1$coefs[1] # AFR
c2 <- fit_step2$tau2$coefs[1] # EUR

Step 2: Compute posterior inclusion probability and obtain credible sets

Given the estimated polygenic parameters and inflation constants, we use variational inference to combine cross-population GWASs and evaluate PIP for SNP in the target locus. We need LD matrices and GWAS Z-scores from AFR and EUR as input.

First, we load the reference LD matrices of EUR and AFR populations estimated from UKBB samples, extract overlapped SNPs, conduct quality control, and align the effect alleles.

# read loci information
info <- fread("/Users/cmx/Documents/Research/Project/Fine_Mapping/LD_ref/LD_mat/chr8_20000001_23000001.info")

# detect allele ambiguous SNPs
idx_amb <- which(info$allele1 == comple(info$allele2))


# overlap SNPs
snps <- Reduce(intersect, list(info$rsid[-idx_amb], sumstat_AFR$SNP, sumstat_EUR$SNP))
sumstat_AFR_i <- sumstat_AFR[match(snps, sumstat_AFR$SNP),]
sumstat_EUR_i <- sumstat_EUR[match(snps, sumstat_EUR$SNP),]

# read LD matrix of AFR
R_afr <- readMM("/Users/cmx/Documents/Research/Project/Fine_Mapping/LD_ref/LD_mat/chr8_20000001_23000001_afr.mtx.gz")
R_afr <- as.matrix(R_afr + t(R_afr))
idx_afr <- match(snps, info$rsid)
R_afr <- R_afr[idx_afr, idx_afr]

# read LD matrix of EUR
R_brit <- readMM("/Users/cmx/Documents/Research/Project/Fine_Mapping/LD_ref/LD_mat/chr8_20000001_23000001_brit.mtx.gz")
R_brit <- as.matrix(R_brit + t(R_brit))
idx_brit <- match(snps, info$rsid)
R_brit <- R_brit[idx_brit, idx_brit]

info <- info[match(snps, info$rsid),]

# remove SNPs with small GWAS sample size
idx_outlier_EUR <- which(sumstat_EUR_i$N < 0.7 * median(sumstat_EUR_i$N))
idx_outlier_AFR <- which(sumstat_AFR_i$N < 0.7 * median(sumstat_AFR_i$N))

idx_outlier <- unique(c(idx_outlier_EUR, idx_outlier_AFR))

snps <- snps[-idx_outlier]
sumstat_AFR_i <- sumstat_AFR_i[-idx_outlier,]
sumstat_EUR_i <- sumstat_EUR_i[-idx_outlier,]
info <- info[-idx_outlier,]
R_afr <- R_afr[-idx_outlier, -idx_outlier]
R_brit <- R_brit[-idx_outlier, -idx_outlier]


# flip alleles
z_afr <- sumstat_AFR_i$beta / sumstat_AFR_i$se
z_eur <- sumstat_EUR_i$Z

idx_flip <- which(sumstat_AFR_i$A1 != info$allele1 & sumstat_AFR_i$A1 != comple(info$allele1))
z_afr[idx_flip] <- -z_afr[idx_flip]

idx_flip <- which(sumstat_EUR_i$A1 != info$allele1 & sumstat_EUR_i$A1 != comple(info$allele1))
z_eur[idx_flip] <- -z_eur[idx_flip]

Then, we run XMAP to obtain the PIP and credible sets

# Main XMAP analysis
xmap <- XMAP(simplify2array(list(R_brit, R_afr)), cbind(z_eur, z_afr), n=c(median(sumstat_EUR_i$N), median(sumstat_AFR_i$N)),
             K = 10, Omega = OmegaHat, Sig_E = c(c1, c2), tol = 1e-6,
             maxIter = 200, estimate_residual_variance = F, estimate_prior_variance = T,
             estimate_background_variance = F)

To visualize the results, we plot the PIP and credible sets obtained by XMAP

cs1 <- get_CS(xmap, Xcorr = R_afr, coverage = 0.9, min_abs_corr = 0.1)
cs2 <- get_CS(xmap, Xcorr = R_brit, coverage = 0.9, min_abs_corr = 0.1)
cs_xmap <- cs1$cs[intersect(names(cs1$cs), names(cs2$cs))]
pip_xmap <- get_pip(xmap$gamma)
plot_CS(pip_xmap, cs_xmap, main = "XMAP",b = (info$rsid == "rs900776"))

Version Author Date
64b7578 mxcai 2024-04-29

The PIP of SNP rs900776 is 0.99 as computed by XMAP.


sessionInfo()
R version 4.1.2 (2021-11-01)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS 13.6.3

Matrix products: default
BLAS:   /opt/homebrew/Cellar/openblas/0.3.19/lib/libopenblasp-r0.3.19.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1-arm64/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] Matrix_1.5-4.1    data.table_1.14.2 susieR_0.12.35    XMAP_1.0         

loaded via a namespace (and not attached):
 [1] tidyselect_1.2.0   xfun_0.32          bslib_0.4.0        lattice_0.20-45   
 [5] colorspace_2.0-2   vctrs_0.6.3        generics_0.1.1     htmltools_0.5.4   
 [9] yaml_2.3.5         utf8_1.2.2         rlang_1.1.1        mixsqp_0.3-43     
[13] jquerylib_0.1.4    later_1.3.0        pillar_1.9.0       glue_1.6.2        
[17] matrixStats_0.61.0 lifecycle_1.0.3    plyr_1.8.6         stringr_1.4.1     
[21] munsell_0.5.0      gtable_0.3.0       workflowr_1.7.0    evaluate_0.16     
[25] knitr_1.40         fastmap_1.1.0      httpuv_1.6.5       irlba_2.3.5       
[29] fansi_0.5.0        highr_0.9          Rcpp_1.0.10        promises_1.2.0.1  
[33] scales_1.1.1       cachem_1.0.6       jsonlite_1.8.0     fs_1.5.2          
[37] ggplot2_3.3.5      digest_0.6.29      stringi_1.7.8      dplyr_1.1.2       
[41] rprojroot_2.0.2    grid_4.1.2         cli_3.6.1          tools_4.1.2       
[45] magrittr_2.0.3     sass_0.4.2         tibble_3.2.1       crayon_1.5.1      
[49] whisker_0.4        pkgconfig_2.0.3    rmarkdown_2.16     reshape_0.8.8     
[53] rstudioapi_0.13    R6_2.5.1           git2r_0.31.0       compiler_4.1.2