XMAP_example_LDL.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3fd49012",
   "metadata": {},
   "source": [
    "# Tutorial\n",
    "In this document, we show the complete pipeline of using XMAP to identify causal SNPs by leveraging cross population GWAS data. As an example, we use LDL GWASs from AFR and EUR.\n",
    "The files involced in the analysis are:\n",
    "1. __GWAS summary statistics__ from different populations\n",
    "2. __LD scores__ estimated with samples from the analyzed populations\n",
    "3. __LD matrices__ of the target locus estimated with samples from the analyzed populations\n",
    "\n",
    "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.\n",
    "\n",
    "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ebdfaa22",
   "metadata": {},
   "outputs": [],
   "source": [
    "library(susieR)\n",
    "library(data.table)\n",
    "library(Matrix)\n",
    "library(XMAP)\n",
    "library(RhpcBLASctl)\n",
    "set.seed(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8182b4f",
   "metadata": {},
   "source": [
    "## 1. Estimate polygenic parameters and inflation constants\n",
    "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8c1904b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# read GWAS summary statistics\n",
    "sumstat_EUR <- fread(\"/home/share/sumstats/format/LDL_allSNPs_UKBNealLab_summary_format.txt\")\n",
    "sumstat_AFR <- fread(\"/home/share/sumstats/format/LDL_AFR_GLGC_summary_format.txt\")\n",
    "\n",
    "# read LD scores\n",
    "ldscore <- data.frame()\n",
    "for (chr in 1:22) {\n",
    "  ldscore_chr <- fread(paste0(\"/home/share/mingxuan/UKB_geno_finemap/LDscore_eas_brit_afr_chr\", chr, \".txt\"))\n",
    "  ldscore <- rbind(ldscore, ldscore_chr)\n",
    "  cat(\"CHR\", chr, \"\\n\")\n",
    "}\n",
    "\n",
    "# pre-process: remove ambiguous SNPs\n",
    "idx_amb <- which(ldscore$allele1 == comple(ldscore$allele2))\n",
    "ldscore <- ldscore[-idx_amb,]\n",
    "\n",
    "\n",
    "# pre-process: overlap SNPs\n",
    "snps <- Reduce(intersect, list(ldscore$rsid, sumstat_AFR$SNP, sumstat_EUR$SNP))\n",
    "sumstat_AFR_ldsc <- sumstat_AFR[match(snps, sumstat_AFR$SNP),]\n",
    "sumstat_EUR_ldsc <- sumstat_EUR[match(snps, sumstat_EUR$SNP),]\n",
    "ldscore <- ldscore[match(snps, ldscore$rsid),]\n",
    "\n",
    "\n",
    "# pre-process: flip alleles\n",
    "z_afr <- sumstat_AFR_ldsc$beta / sumstat_AFR_ldsc$se\n",
    "z_eur <- sumstat_EUR_ldsc$Z\n",
    "\n",
    "idx_flip <- which(sumstat_AFR_ldsc$A1 != ldscore$allele1 & sumstat_AFR_ldsc$A1 != comple(ldscore$allele1))\n",
    "z_afr[idx_flip] <- -z_afr[idx_flip]\n",
    "\n",
    "idx_flip <- which(sumstat_EUR_ldsc$A1 != ldscore$allele1 & sumstat_EUR_ldsc$A1 != comple(ldscore$allele1))\n",
    "z_eur[idx_flip] <- -z_eur[idx_flip]\n",
    "\n",
    "\n",
    "idx1 <- which(z_afr^2 < 30 & z_eur^2 < 30)\n",
    "ld_afr_w <- 1 / sapply(ldscore$AFR, function(x) max(x, 1))\n",
    "ld_eur_w <- 1 / sapply(ldscore$EUR, function(x) max(x, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a09cefac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# bi-variate LDSC: AFR-EUR\n",
    "# step 1: estimate intercepts\n",
    "fit_step1 <- estimate_gc(data.frame(Z = z_afr[idx1], N = sumstat_AFR_ldsc$N[idx1]), data.frame(Z = z_eur[idx1], N = sumstat_EUR_ldsc$N[idx1]),\n",
    "                         ldscore$AFR[idx1], ldscore$EUR[idx1], ldscore$AFR_EUR[idx1],\n",
    "                         reg_w1 = ld_afr_w[idx1], reg_w2 = ld_eur_w[idx1], reg_wx = sqrt(ld_afr_w[idx1] * ld_eur_w[idx1]),\n",
    "                         constrain_intercept = F)\n",
    "# step 1: estimate slopes\n",
    "fit_step2 <- estimate_gc(data.frame(Z = z_afr, N = sumstat_AFR_ldsc$N), data.frame(Z = z_eur, N = sumstat_EUR_ldsc$N),\n",
    "                         ldscore$AFR, ldscore$EUR, ldscore$AFR_EUR,\n",
    "                         reg_w1 = ld_afr_w, reg_w2 = ld_eur_w, reg_wx = sqrt(ld_afr_w * ld_eur_w),\n",
    "                         constrain_intercept = T, fit_step1$tau1[1], fit_step1$tau2[1], fit_step1$theta[1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8753c5bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assign LDSC estimates to covariance of polygenic effects\n",
    "OmegaHat <- diag(c(fit_step2$tau1[2], fit_step2$tau2[2])) # AFR EUR\n",
    "OmegaHat[1, 2] <- fit_step2$theta[2] # co-heritability\n",
    "OmegaHat[lower.tri(OmegaHat)] <- OmegaHat[upper.tri(OmegaHat)]\n",
    "\n",
    "c1 <- fit_step2$tau1[1] # AFR\n",
    "c2 <- fit_step2$tau2[1] # EUR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb50b7f3",
   "metadata": {},
   "source": [
    "## 2. Compute posterior inclusion probability and obtain credible sets\n",
    "Given the estimated polygenic parameters and inflation constants, we use variational inference to combine cross-population GWASs and evaluate PIP for SNP in the target locus. We need LD matrices and GWAS Z-scores from AFR and EUR as input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "09c36693",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in asMethod(object):\n",
      "“sparse->dense coercion: allocating vector of size 1.6 GiB”\n",
      "Warning message in asMethod(object):\n",
      "“sparse->dense coercion: allocating vector of size 1.6 GiB”\n"
     ]
    }
   ],
   "source": [
    "# read loci information\n",
    "info <- fread(\"/home/share/mingxuan/UKB_geno_finemap/chr8_20000001_23000001.info\")\n",
    "\n",
    "# detect allele ambiguous SNPs\n",
    "idx_amb <- which(info$allele1 == comple(info$allele2))\n",
    "\n",
    "\n",
    "# overlap SNPs\n",
    "snps <- Reduce(intersect, list(info$rsid[-idx_amb], sumstat_AFR$SNP, sumstat_EUR$SNP))\n",
    "sumstat_AFR_i <- sumstat_AFR[match(snps, sumstat_AFR$SNP),]\n",
    "sumstat_EUR_i <- sumstat_EUR[match(snps, sumstat_EUR$SNP),]\n",
    "\n",
    "# read LD matrix of AFR\n",
    "R_afr <- readMM(\"/home/share/mingxuan/UKB_geno_finemap/chr8_20000001_23000001_afr.mtx.gz\")\n",
    "R_afr <- as.matrix(R_afr + t(R_afr))\n",
    "idx_afr <- match(snps, info$rsid)\n",
    "R_afr <- R_afr[idx_afr, idx_afr]\n",
    "\n",
    "# read LD matrix of EUR\n",
    "R_brit <- readMM(\"/home/share/mingxuan/UKB_geno_finemap/chr8_20000001_23000001_brit.mtx.gz\")\n",
    "R_brit <- as.matrix(R_brit + t(R_brit))\n",
    "idx_brit <- match(snps, info$rsid)\n",
    "R_brit <- R_brit[idx_brit, idx_brit]\n",
    "\n",
    "info <- info[match(snps, info$rsid),]\n",
    "\n",
    "# remove SNPs with small GWAS sample size\n",
    "idx_outlier_EUR <- which(sumstat_EUR_i$N < 0.7 * median(sumstat_EUR_i$N))\n",
    "idx_outlier_AFR <- which(sumstat_AFR_i$N < 0.7 * median(sumstat_AFR_i$N))\n",
    "\n",
    "idx_outlier <- unique(c(idx_outlier_EUR, idx_outlier_AFR))\n",
    "\n",
    "snps <- snps[-idx_outlier]\n",
    "sumstat_AFR_i <- sumstat_AFR_i[-idx_outlier,]\n",
    "sumstat_EUR_i <- sumstat_EUR_i[-idx_outlier,]\n",
    "info <- info[-idx_outlier,]\n",
    "R_afr <- R_afr[-idx_outlier, -idx_outlier]\n",
    "R_brit <- R_brit[-idx_outlier, -idx_outlier]\n",
    "\n",
    "\n",
    "# flip alleles\n",
    "z_afr <- sumstat_AFR_i$beta / sumstat_AFR_i$se\n",
    "z_eur <- sumstat_EUR_i$Z\n",
    "\n",
    "idx_flip <- which(sumstat_AFR_i$A1 != info$allele1 & sumstat_AFR_i$A1 != comple(info$allele1))\n",
    "z_afr[idx_flip] <- -z_afr[idx_flip]\n",
    "\n",
    "idx_flip <- which(sumstat_EUR_i$A1 != info$allele1 & sumstat_EUR_i$A1 != comple(info$allele1))\n",
    "z_eur[idx_flip] <- -z_eur[idx_flip]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6b007a9a",
   "metadata": {},
   "outputs": [
    {
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6+oq3DAfonHerc8yQvsYOdlzckTeXl5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",
      "text/plain": [
       "Plot with title “XMAP”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Main XMAP analysis\n",
    "blas_set_num_threads(30)\n",
    "xmap <- XMAP(simplify2array(list(R_brit, R_afr)), cbind(z_eur, z_afr), c(median(sumstat_EUR_i$N), median(sumstat_AFR_i$N)),\n",
    "             K = 10, Omega = OmegaHat, Sig_E = c(c1, c2), tol = 1e-6,\n",
    "             maxIter = 200, estimate_residual_variance = F, estimate_prior_variance = T,\n",
    "             estimate_background_variance = F)\n",
    "cs1 <- get_CS(xmap, Xcorr = R_afr, coverage = 0.9, min_abs_corr = 0.1)\n",
    "cs2 <- get_CS(xmap, Xcorr = R_brit, coverage = 0.9, min_abs_corr = 0.1)\n",
    "cs_xmap <- cs1$cs[intersect(names(cs1$cs), names(cs2$cs))]\n",
    "pip_xmap <- get_pip(xmap$gamma)\n",
    "plot_CS(pip_xmap, cs_xmap, main = \"XMAP\",b = (info$rsid == \"rs900776\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "89c2f666",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.991621802747886"
      ],
      "text/latex": [
       "0.991621802747886"
      ],
      "text/markdown": [
       "0.991621802747886"
      ],
      "text/plain": [
       "[1] 0.9916218"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pip_xmap[info$rsid == \"rs900776\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73ac3447",
   "metadata": {},
   "source": [
    "The PIP of SNP rs900776 is 0.99 as computed by XMAP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e8da05a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[4m\u001b[35mHINT:\u001b[39m\u001b[24m\u001b[22m If the in-sample LD matrix is available, we recommend calling susie_rss with the in-sample LD matrix, and setting estimate_residual_variance = TRUE\n",
      "\n",
      "\u001b[1m\u001b[4m\u001b[31mWARNING:\u001b[39m\u001b[24m\u001b[22m Providing the sample size (n), or even a rough estimate of n, is highly recommended. Without n, the implicit assumption is n is large (Inf) and the effect sizes are small (close to zero).\n",
      "\n",
      "\u001b[1m\u001b[4m\u001b[35mHINT:\u001b[39m\u001b[24m\u001b[22m For large R or large XtX, consider installing theRfast package for better performance.\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"objective:-0.615669456822658\"\n",
      "[1] \"objective:-0.615669456822658\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "0.887278410529523"
      ],
      "text/latex": [
       "0.887278410529523"
      ],
      "text/markdown": [
       "0.887278410529523"
      ],
      "text/plain": [
       "[1] 0.8872784"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[4m\u001b[35mHINT:\u001b[39m\u001b[24m\u001b[22m If the in-sample LD matrix is available, we recommend calling susie_rss with the in-sample LD matrix, and setting estimate_residual_variance = TRUE\n",
      "\n",
      "\u001b[1m\u001b[4m\u001b[31mWARNING:\u001b[39m\u001b[24m\u001b[22m Providing the sample size (n), or even a rough estimate of n, is highly recommended. Without n, the implicit assumption is n is large (Inf) and the effect sizes are small (close to zero).\n",
      "\n",
      "\u001b[1m\u001b[4m\u001b[35mHINT:\u001b[39m\u001b[24m\u001b[22m For large R or large XtX, consider installing theRfast package for better performance.\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"objective:4.3924172297648\"\n",
      "[1] \"objective:4.44086919972531\"\n",
      "[1] \"objective:4.44101973386259\"\n"
     ]
    },
    {
     "data": {
      "image/png": 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QEChAQIEBIgQEiAACEBAoQECBASIEBI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\n+a90ptvNz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      "text/plain": [
       "Plot with title “GWAS-GLGC_AFR”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.0137694428431469"
      ],
      "text/latex": [
       "0.0137694428431469"
      ],
      "text/markdown": [
       "0.0137694428431469"
      ],
      "text/plain": [
       "[1] 0.01376944"
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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AACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAACIewAAAIh7AAAAiHsAAAC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\nwQ4AAEARBDsAAABF/A/dRUE5onS5bwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “GWAS-UKB_EUR”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "susie_afr <- susie_rss(z_afr, R_afr,\n",
    "                       L = 10,\n",
    "                       verbose = TRUE,\n",
    "                       coverage = 0.9,\n",
    "                       min_abs_corr = 0.1,\n",
    "                       check_prior = F)\n",
    "susie_plot(susie_afr, y = \"PIP\", b = (info$rsid == \"rs900776\"), main = \"GWAS-GLGC_AFR\")\n",
    "susie_afr$pip[info$rsid == \"rs900776\"]\n",
    "\n",
    "susie_eur <- susie_rss(z_eur, R_brit,\n",
    "                       L = 10,\n",
    "                       verbose = TRUE,\n",
    "                       coverage = 0.9,\n",
    "                       min_abs_corr = 0.1,\n",
    "                       check_prior = F)\n",
    "susie_plot(susie_eur, y = \"PIP\", b = (info$rsid == \"rs900776\"), main = \"GWAS-UKB_EUR\")\n",
    "susie_eur$pip[info$rsid == \"rs900776\"]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1d1db0e",
   "metadata": {},
   "source": [
    "Without leveraging the cross-population GWASs, the PIP of rs900776 is 0.89 with AFR GWAS and only 0.014 with EUR GWAS."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.1.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}