ldpred/ldpred2_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# Polygenic Risk Score Analysis on Height GWAS data\n",
    "\n",
    "Here we show an example of our [LDpred2 pipeline](https://github.com/cumc/bioworkflows/blob/master/ldpred/ldpred.ipynb) for height PRS on [an example public data-set](https://drive.google.com/file/d/1x_G0Gxk9jFMY-PMqwtg6-vdEyUPp5p5u/view) from github user [@choishingwan](https://github.com/choishingwan).\n",
    "\n",
    "Analysis in this tutorial is performed by running our pipeline sequentially on a single computer (a desktop, laptop, or a single interactive node on a cluster). The pipeline iteself, implemented in the SoS workflow language, can be configured to run in parallel on a high performance computing cluster environment. Please read the [SoS documentation](https://vatlab.github.io/sos-docs/doc/user_guide/host_setup.html) on how to configure the software and workflow to efficiently perform the analysis for real-world data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "## Data used"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "### Reference panel\n",
    "\n",
    "Obtained via `download_1000G()` in `bigsnpr`. \n",
    "\n",
    "We extracted unrelated European individuals (~500  samples) and ~1.7M SNPs in common with either HapMap3 or the UK Biobank. Classification of European population can be found at [IGSR](https://www.internationalgenome.org/category/population/). European individuals ID are from [IGSR data portal](https://www.internationalgenome.org/data-portal/sample).\n",
    "\n",
    "### GWAS summary statistics data\n",
    "\n",
    "`Height.QC.gz`, from public data-set provided by github user [@choishingwan](https://github.com/choishingwan), of height GWAS in European samples.\n",
    "\n",
    "### Target test data\n",
    "\n",
    "`EUR.height`, `EUR.cov`, and `EUR.eigenvec` contain phenotypes, covariates and genotype principle components of samples. `EUR.QC.*` contain the corresponding genotypes, with ~400,000 variants. We have thinned the genotype data to ~150,000 variants for speeding up the examples used in this tutorial. The resulting genotypes are in `EUR_prune.*`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "## PRS Models applied\n",
    "\n",
    "Auto model runs the algorithm for 30 different $p$ (the proportion of causal variants) values range from 10e-4 to 0.9, and heritability $h^2$ from LD score regression as initial value.\n",
    "\n",
    "Grid model tries a grid of parameters $p$, ranges from 0 to 1 and three $h^2$ which are 0.7/1/1.4 times of initial $h^2$ estimated by LD score regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "## Data preparation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "Please download the [tutorial data](http://statgen.us/files/2021/01/ldpred2.tar.gz) and [pipeline script](https://github.com/cumc/bioworkflows/blob/master/ldpred/ldpred.ipynb) to your computer. We have pre-downloaded and extracted the European genotypes from 1000 Genomes, as well as genetic map data. We have preprocessed the GWAS data as follows, to fit in our pipeline."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "**Please do not run any code from this section. The data bundle above contains all the preprocessed files for you to start the PRS analysis (next section). Code below are documented here for book-keeping and reproducibility.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "### Summary statistics formatting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "sumstats <- bigreadr::fread2(\"GWAS_data/Height.QC.gz\") \n",
    "# LDpred2 require the header to follow the exact naming\n",
    "names(sumstats) <-\n",
    "    c(\"chr\",\n",
    "    \"pos\",\n",
    "    \"rsid\",\n",
    "    \"a1\",\n",
    "    \"a0\",\n",
    "    \"n_eff\",\n",
    "    \"beta_se\",\n",
    "    \"p\",\n",
    "    \"OR\",\n",
    "    \"INFO\",\n",
    "    \"MAF\")\n",
    "# Transform the OR into log(OR)\n",
    "sumstats$beta <- log(sumstats$OR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "saveRDS(sumstats, \"GWAS_data/Height.QC.rds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "### Phenotype and covariates formatting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "options(stringsAsFactors=F)\n",
    "fam = read.table(\"GWAS_data/EUR_prune.fam\", header=F)\n",
    "colnames(fam) = c(\"FID\", \"IID\", \"PID\", \"MID\", \"S\", \"D\")\n",
    "pheno = read.table(\"GWAS_data/EUR.height\", header=T)\n",
    "covar = read.table(\"GWAS_data/EUR.cov\", header=T)\n",
    "pcs = read.table(\"GWAS_data/EUR.eigenvec\", header=F)\n",
    "colnames(pcs) = c(\"FID\", \"IID\", \"PC1\", \"PC2\", \"PC3\", \"PC4\", \"PC5\", \"PC6\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "require(dplyr)\n",
    "pheno_out = left_join(fam, pheno, by = c(\"FID\", \"IID\"))\n",
    "pheno_out = left_join(pheno_out, covar, by = c(\"FID\", \"IID\"))\n",
    "pheno_out = left_join(pheno_out, pcs, by = c(\"FID\", \"IID\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "write.table(pheno_out[, \"Height\"], \"GWAS_data/EUR.height.matched.txt\", col.names=\"Height\",row.names=F)\n",
    "write.table(pheno_out[, c(\"Sex\",'PC1', 'PC2', 'PC3', 'PC4', 'PC5', 'PC6')], \"GWAS_data/EUR.cov.matched.txt\", col.names=T,row.names=F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "The directory should have the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[01;34m.\u001b[00m\n",
      "├── \u001b[01;34m1000G.EUR\u001b[00m\n",
      "│   ├── 1000G.EUR.bed\n",
      "│   ├── 1000G.EUR.bim\n",
      "│   └── 1000G.EUR.fam\n",
      "├── \u001b[01;34mGWAS_data\u001b[00m\n",
      "│   ├── EUR.cov\n",
      "│   ├── EUR.cov.matched.txt\n",
      "│   ├── EUR.eigenvec\n",
      "│   ├── EUR.height\n",
      "│   ├── EUR.height.matched.txt\n",
      "│   ├── EUR_prune.bed\n",
      "│   ├── EUR_prune.bim\n",
      "│   ├── EUR_prune.fam\n",
      "│   ├── EUR_prune.log\n",
      "│   ├── \u001b[01;31mHeight.QC.gz\u001b[00m\n",
      "│   └── Height.QC.rds\n",
      "├── \u001b[01;34mheight_results\u001b[00m\n",
      "│   ├── chr10.OMNI.interpolated_genetic_map\n",
      "│   ├── chr11.OMNI.interpolated_genetic_map\n",
      "│   ├── chr12.OMNI.interpolated_genetic_map\n",
      "│   ├── chr13.OMNI.interpolated_genetic_map\n",
      "│   ├── chr14.OMNI.interpolated_genetic_map\n",
      "│   ├── chr15.OMNI.interpolated_genetic_map\n",
      "│   ├── chr16.OMNI.interpolated_genetic_map\n",
      "│   ├── chr17.OMNI.interpolated_genetic_map\n",
      "│   ├── chr18.OMNI.interpolated_genetic_map\n",
      "│   ├── chr19.OMNI.interpolated_genetic_map\n",
      "│   ├── chr1.OMNI.interpolated_genetic_map\n",
      "│   ├── chr20.OMNI.interpolated_genetic_map\n",
      "│   ├── chr21.OMNI.interpolated_genetic_map\n",
      "│   ├── chr22.OMNI.interpolated_genetic_map\n",
      "│   ├── chr2.OMNI.interpolated_genetic_map\n",
      "│   ├── chr3.OMNI.interpolated_genetic_map\n",
      "│   ├── chr4.OMNI.interpolated_genetic_map\n",
      "│   ├── chr5.OMNI.interpolated_genetic_map\n",
      "│   ├── chr6.OMNI.interpolated_genetic_map\n",
      "│   ├── chr7.OMNI.interpolated_genetic_map\n",
      "│   ├── chr8.OMNI.interpolated_genetic_map\n",
      "│   └── chr9.OMNI.interpolated_genetic_map\n",
      "├── ldpred2_example.ipynb\n",
      "└── ldpred.ipynb\n",
      "\n",
      "3 directories, 38 files\n"
     ]
    }
   ],
   "source": [
    "tree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "## Analysis of height GWAS data\n",
    "\n",
    "We set the work directory to `height_results` folder (to be created by the workflow). This will also be used as part of the filenames in the outputs to identify this analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [],
   "source": [
    "work_dir=\"height_results\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "### Step 1: QC on reference panel\n",
    "\n",
    "Here we assume the GWAS genotype data `EUR.*` has already been QC-ed. We perform here QC for reference panel,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: Running \u001b[32mbasic QC filters\u001b[0m: Filter SNPs and select individuals\n",
      "INFO: \u001b[32mbasic QC filters\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mbasic QC filters\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/1000G.EUR.height_results.bed\u001b[0m\n",
      "INFO: Workflow snp_qc (ID=015cfd3cc381496b) is executed successfully with 1 completed step.\n"
     ]
    }
   ],
   "source": [
    "sos run ldpred.ipynb snp_qc \\\n",
    "    --cwd $work_dir \\\n",
    "    --genoFiles 1000G.EUR/1000G.EUR.bed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "The output of a command in our pipeline is highlighted in the green text above, in this case, ` /home/jovyan/work/height_results/1000G.EUR.height_results.bed`. These are typically intermediate files generated and kept by the pipeline program. In this tutorial we will show contents from these outputs only when they are relevant to the final results, although in practice users are always encouraged to check these immediate files to ensure of no obvious sign of problems in each analysis step."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "### Step 2: Intersect SNPs among summary stats, reference panel and target data\n",
    "\n",
    "SNPs shared between summary statistics, reference panels and target genotype data (for which PRS will be computed) are extracted. Genetic distances will be computed for each variant using interpolated genetic map. **This step can take a bit of time to execute**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: Running \u001b[32msnp_intersect_1\u001b[0m: SNP intersect of summary stats and genotype data\n",
      "INFO: \u001b[32msnp_intersect_1\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32msnp_intersect_1\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/Height.QC.intersect.rds /home/jovyan/work/height_results/Height.QC.intersect.snplist\u001b[0m\n",
      "INFO: Running \u001b[32msnp_intersect_2\u001b[0m: \n",
      "INFO: \u001b[32msnp_intersect_2\u001b[0m is \u001b[32mcompleted\u001b[0m (pending nested workflow).\n",
      "INFO: Running \u001b[32mpreprocess_1\u001b[0m: Filter SNPs and select individuals\n",
      "INFO: \u001b[32mpreprocess_1\u001b[0m (index=1) is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mpreprocess_1\u001b[0m (index=0) is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mpreprocess_1\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/1000G.EUR.height_results.snp_intersect.extracted.bed /home/jovyan/work/height_results/EUR_prune.snp_intersect.extracted.bed in 2 groups\u001b[0m\n",
      "INFO: Running \u001b[32mconvert PLINK to bigsnpr format with missing data mean imputed\u001b[0m: \n",
      "INFO: \u001b[32mconvert PLINK to bigsnpr format with missing data mean imputed\u001b[0m (index=0) is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mconvert PLINK to bigsnpr format with missing data mean imputed\u001b[0m (index=1) is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mconvert PLINK to bigsnpr format with missing data mean imputed\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/1000G.EUR.height_results.snp_intersect.extracted.bk /home/jovyan/work/height_results/1000G.EUR.height_results.snp_intersect.extracted.rds... (4 items in 2 groups)\u001b[0m\n",
      "INFO: \u001b[32msnp_intersect_2\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/1000G.EUR.height_results.snp_intersect.extracted.bed /home/jovyan/work/height_results/1000G.EUR.height_results.snp_intersect.extracted.rds... (4 items)\u001b[0m\n",
      "INFO: Workflow snp_intersect (ID=f5859b94a542bf56) is executed successfully with 4 completed steps and 6 completed substeps.\n"
     ]
    }
   ],
   "source": [
    "sos run ldpred.ipynb snp_intersect \\\n",
    "    --cwd $work_dir \\\n",
    "    --ss GWAS_data/Height.QC.rds \\\n",
    "    --genoFiles $work_dir/1000G.EUR.$work_dir.bed GWAS_data/EUR_prune.bed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"There are 109963 shared SNPs.\"\n"
     ]
    }
   ],
   "source": [
    "cat $work_dir/Height.QC.intersect.stdout"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "### Step 3: Harmonize alleles for shared SNPs\n",
    "\n",
    "To handle major/minor allele, strand flips and consequently possible flips in sign for summary statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: Running \u001b[32msnp_match\u001b[0m: \n",
      "INFO: \u001b[32msnp_match\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32msnp_match\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/Height.QC.snp_matched.rds /home/jovyan/work/height_results/Height.QC.snp_matched.snplist\u001b[0m\n",
      "INFO: Workflow snp_match (ID=aa8f5f3cb5665126) is executed successfully with 1 completed step.\n"
     ]
    }
   ],
   "source": [
    "sos run ldpred.ipynb snp_match \\\n",
    "    --cwd $work_dir \\\n",
    "    --reference_geno $work_dir/1000G.EUR.$work_dir.snp_intersect.extracted.rds \\\n",
    "    --ss GWAS_data/Height.QC.rds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "### Step 4: Summary statistics quality control (optional)\n",
    "\n",
    "Please refer to documentation in the pipeline notebook [`ldpred.ipynb`](https://github.com/cumc/bioworkflows/blob/master/ldpred/ldpred.ipynb) for an explanation of summary statistics QC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: Running \u001b[32msumstats_qc\u001b[0m: \n",
      "INFO: \u001b[32msumstats_qc\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32msumstats_qc\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/Height.QC.snp_matched.qc.png /home/jovyan/work/height_results/Height.QC.snp_matched.qc.snplist... (3 items)\u001b[0m\n",
      "INFO: Workflow sumstats_qc (ID=dbbf3e7458e2f8a0) is executed successfully with 1 completed step.\n"
     ]
    }
   ],
   "source": [
    "sos run ldpred.ipynb sumstats_qc \\\n",
    "    --cwd $work_dir \\\n",
    "    --reference_geno $work_dir/1000G.EUR.$work_dir.snp_intersect.extracted.rds \\\n",
    "    --ss $work_dir/Height.QC.snp_matched.rds \\\n",
    "    --sdy 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "kernel": "SoS"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"sos_hint\">> height_results/Height.QC.snp_matched.qc.png (63.9 KiB):</div>"
      ],
      "text/plain": [
       "\n",
       "> height_results/Height.QC.snp_matched.qc.png (63.9 KiB):"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "image/png": {}
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%preview height_results/Height.QC.snp_matched.qc.png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "From the results, we observe only a few outliers significantly deviating from the majority of the variants. We suspect that quality control recommanded in [LDpred2 manuscript](https://academic.oup.com/bioinformatics/article/36/22-23/5424/6039173) may be too stringent and should not be needed for this data-set. Notice that as the manuscript pointed out, the quality control procedure is not suitable for meta-analyzed GWAS summary statistics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "### Step 5: Calculate LD matrix and fit LDSC model\n",
    "\n",
    "As an illustration, hereafter all analysis are performed on both summary statistics before QC in Step 4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: Running \u001b[32mldsc\u001b[0m: \n",
      "INFO: \u001b[32mldsc\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mldsc\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/Height.QC.snp_matched.ld.rds\u001b[0m\n",
      "INFO: Workflow ldsc (ID=e9a3f5af1a3a1a9c) is executed successfully with 1 completed step.\n"
     ]
    }
   ],
   "source": [
    "sos run ldpred.ipynb ldsc \\\n",
    "    --cwd $work_dir \\\n",
    "    --ss $work_dir/Height.QC.snp_matched.rds \\\n",
    "    --reference-geno $work_dir/1000G.EUR.$work_dir.snp_intersect.extracted.rds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "and after QC in Step 4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: Running \u001b[32mldsc\u001b[0m: \n",
      "INFO: \u001b[32mldsc\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mldsc\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/Height.QC.snp_matched.qc.ld.rds\u001b[0m\n",
      "INFO: Workflow ldsc (ID=bacc9e382c830fa4) is executed successfully with 1 completed step.\n"
     ]
    }
   ],
   "source": [
    "sos run ldpred.ipynb ldsc \\\n",
    "    --cwd $work_dir \\\n",
    "    --ss $work_dir/Height.QC.snp_matched.qc.rds \\\n",
    "    --reference-geno $work_dir/1000G.EUR.$work_dir.snp_intersect.extracted.rds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "### Step 6: Estimate posterior effect sizes and PRS\n",
    "\n",
    "For QC-ed data, we perform 3 PRS models implemented in `ldpred2`. We demonstrate the infinitesimal model here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: Running \u001b[32minf_prs\u001b[0m: \n",
      "INFO: \u001b[32minf_prs\u001b[0m is \u001b[32mcompleted\u001b[0m (pending nested workflow).\n",
      "INFO: Running \u001b[32mprs_core\u001b[0m: \n",
      "INFO: \u001b[32mprs_core\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mprs_core\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/Height.QC.snp_matched.qc.inf_prs.rds\u001b[0m\n",
      "INFO: \u001b[32minf_prs\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/Height.QC.snp_matched.qc.inf_prs.rds\u001b[0m\n",
      "INFO: Workflow inf_prs (ID=1219f13000c52cc3) is executed successfully with 2 completed steps.\n"
     ]
    }
   ],
   "source": [
    "sos run ldpred.ipynb inf_prs \\\n",
    "    --cwd $work_dir \\\n",
    "    --ss $work_dir/Height.QC.snp_matched.qc.rds \\\n",
    "    --target-geno $work_dir/EUR_prune.snp_intersect.extracted.rds \\\n",
    "    --ldsc $work_dir/Height.QC.snp_matched.qc.ld.rds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "Here we examine the PRS generated from this command,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"104564 SNPs are used for PRS calculations\"\n"
     ]
    }
   ],
   "source": [
    "cat $work_dir/Height.QC.snp_matched.qc.inf_prs.stdout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'beta'</li>\n",
       "\t<li>'prs'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'beta'\n",
       "\\item 'prs'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'beta'\n",
       "2. 'prs'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"beta\" \"prs\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dat = readRDS('height_results/Height.QC.snp_matched.qc.inf_prs.rds')\n",
    "names(dat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6IscEgL0uu6ljpWp5p8BhKSjJBiJ3BII+bnl+eM8hlISDJCip3AIaVX5Jcv9blS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\nzNuHAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “PRS distribution”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(dat$prs, breaks=20, main=\"PRS distribution\", xlab=\"PRS\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "Commands below will execute the \"auto\" model and \"grid\" model implemented in `LDpred2`. They are typically more powerful but also computationally intensive. We document them here without executing:\n",
    "\n",
    "```\n",
    "sos run ldpred.ipynb auto_prs \\\n",
    "    --cwd $work_dir \\\n",
    "    --ss $work_dir/Height.QC.snp_matched.qc.rds \\\n",
    "    --target-geno $work_dir/EUR_prune.snp_intersect.extracted.rds \\\n",
    "    --ldsc $work_dir/Height.QC.snp_matched.qc.ld.rds\n",
    "```\n",
    "\n",
    "```\n",
    "sos run ldpred.ipynb grid_prs \\\n",
    "    --cwd $work_dir \\\n",
    "    --ss $work_dir/Height.QC.snp_matched.qc.rds \\\n",
    "    --target-geno $work_dir/EUR_prune.snp_intersect.extracted.rds \\\n",
    "    --ldsc $work_dir/Height.QC.snp_matched.qc.ld.rds \\\n",
    "    --phenoFile GWAS_data/EUR.height.matched.txt \\\n",
    "    --covFile GWAS_data/EUR.cov.matched.txt \\\n",
    "    --response continuous\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "We then run the infinitesimal model for original data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: Running \u001b[32minf_prs\u001b[0m: \n",
      "INFO: \u001b[32minf_prs\u001b[0m is \u001b[32mcompleted\u001b[0m (pending nested workflow).\n",
      "INFO: Running \u001b[32mprs_core\u001b[0m: \n",
      "INFO: \u001b[32mprs_core\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mprs_core\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/Height.QC.snp_matched.inf_prs.rds\u001b[0m\n",
      "INFO: \u001b[32minf_prs\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/Height.QC.snp_matched.inf_prs.rds\u001b[0m\n",
      "INFO: Workflow inf_prs (ID=f266994e074ae431) is executed successfully with 2 completed steps.\n"
     ]
    }
   ],
   "source": [
    "sos run ldpred.ipynb inf_prs \\\n",
    "    --cwd $work_dir \\\n",
    "    --ss $work_dir/Height.QC.snp_matched.rds \\\n",
    "    --target-geno $work_dir/EUR_prune.snp_intersect.extracted.rds \\\n",
    "    --ldsc $work_dir/Height.QC.snp_matched.ld.rds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"109963 SNPs are used for PRS calculations\"\n"
     ]
    }
   ],
   "source": [
    "cat $work_dir/Height.QC.snp_matched.inf_prs.stdout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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O9n53vKPjfq7h8eaP+kqre89x8n//LF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",
      "text/plain": [
       "Plot with title “PRS distribution (without summary statistics QC)”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dat = readRDS('height_results/Height.QC.snp_matched.inf_prs.rds')\n",
    "hist(dat$prs, breaks=20, main=\"PRS distribution (without summary statistics QC)\", xlab=\"PRS\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "Again, here are commands for \"auto\" and \"grid\" models:\n",
    "\n",
    "```\n",
    "sos run ldpred.ipynb auto_prs \\\n",
    "    --cwd $work_dir \\\n",
    "    --ss $work_dir/Height.QC.snp_matched.rds \\\n",
    "    --target-geno $work_dir/EUR_prune.snp_intersect.extracted.rds \\\n",
    "    --ldsc $work_dir/Height.QC.snp_matched.ld.rds\n",
    "```\n",
    "\n",
    "```\n",
    "sos run ldpred.ipynb grid_prs \\\n",
    "    --cwd $work_dir \\\n",
    "    --ss $work_dir/Height.QC.snp_matched.rds \\\n",
    "    --target-geno $work_dir/EUR_prune.snp_intersect.extracted.rds \\\n",
    "    --ldsc $work_dir/Height.QC.snp_matched.ld.rds \\\n",
    "    --phenoFile GWAS_data/EUR.height.matched.txt \\\n",
    "    --covFile GWAS_data/EUR.cov.matched.txt \\\n",
    "    --response continuous\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "**For `grid` model, in practice we should use another subset of individuals to train the model, independent from the subset to make PRS predictions. Here we use the same target genotype data only to illustrate the workflow.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "### Step 7: predict phenotypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "Baseline model: Trait ~ Sex + PCs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: Running \u001b[32mpred_eval\u001b[0m: \n",
      "INFO: \u001b[32mpred_eval\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mpred_eval\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/EUR.height.matched.baseline.rds\u001b[0m\n",
      "INFO: Workflow pred_eval (ID=bd7c33f977855a7a) is executed successfully with 1 completed step.\n"
     ]
    }
   ],
   "source": [
    "sos run ldpred.ipynb pred_eval \\\n",
    "    --cwd $work_dir \\\n",
    "    --phenoFile GWAS_data/EUR.height.matched.txt \\\n",
    "    --covFile GWAS_data/EUR.cov.matched.txt \\\n",
    "    --response continuous"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = ., data = dat[train.ind, ])\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-1.88058 -0.57445 -0.02782  0.51809  2.60256 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error  t value Pr(>|t|)    \n",
       "(Intercept) 168.78869    0.13623 1238.982   <2e-16 ***\n",
       "Sex           0.89443    0.08528   10.488   <2e-16 ***\n",
       "PC1          -0.99439    0.90011   -1.105   0.2700    \n",
       "PC2          -2.36803    0.94434   -2.508   0.0126 *  \n",
       "PC3          -0.67896    0.95222   -0.713   0.4763    \n",
       "PC4           0.11199    1.72585    0.065   0.9483    \n",
       "PC5           0.44029    0.95044    0.463   0.6435    \n",
       "PC6           0.22226    0.91901    0.242   0.8090    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.82 on 367 degrees of freedom\n",
       "  (11 observations deleted due to missingness)\n",
       "Multiple R-squared:  0.244,\tAdjusted R-squared:  0.2296 \n",
       "F-statistic: 16.92 on 7 and 367 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 1 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>model</th><th scope=col>R2</th><th scope=col>MSE</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>model</td><td>0.22956</td><td>0.81868</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 1 × 3\n",
       "\\begin{tabular}{lll}\n",
       " model & R2 & MSE\\\\\n",
       " <chr> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t model & 0.22956 & 0.81868\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 1 × 3\n",
       "\n",
       "| model &lt;chr&gt; | R2 &lt;dbl&gt; | MSE &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| model | 0.22956 | 0.81868 |\n",
       "\n"
      ],
      "text/plain": [
       "  model R2      MSE    \n",
       "1 model 0.22956 0.81868"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res = readRDS(\"height_results/EUR.height.matched.baseline.rds\")\n",
    "summary(res$fitted)\n",
    "res$summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "Infinitesimal model: Trait ~ Sex + PCs + PRS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO: Running \u001b[32mpred_eval\u001b[0m: \n",
      "INFO: \u001b[32mpred_eval\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mpred_eval\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/EUR.height.matched.Height.QC.snp_matched.qc.inf_prs.rds\u001b[0m\n",
      "INFO: Workflow pred_eval (ID=d4028a7c469c4955) is executed successfully with 1 completed step.\n",
      "INFO: Running \u001b[32mpred_eval\u001b[0m: \n",
      "INFO: \u001b[32mpred_eval\u001b[0m is \u001b[32mcompleted\u001b[0m.\n",
      "INFO: \u001b[32mpred_eval\u001b[0m output:   \u001b[32m/home/jovyan/work/height_results/EUR.height.matched.Height.QC.snp_matched.inf_prs.rds\u001b[0m\n",
      "INFO: Workflow pred_eval (ID=4a11957219f352cc) is executed successfully with 1 completed step.\n"
     ]
    }
   ],
   "source": [
    "sos run ldpred.ipynb pred_eval \\\n",
    "    --cwd $work_dir \\\n",
    "    --prs $work_dir/Height.QC.snp_matched.qc.inf_prs.rds \\\n",
    "    --phenoFile GWAS_data/EUR.height.matched.txt \\\n",
    "    --covFile GWAS_data/EUR.cov.matched.txt \\\n",
    "    --response continuous\n",
    "\n",
    "sos run ldpred.ipynb pred_eval \\\n",
    "    --cwd $work_dir \\\n",
    "    --prs $work_dir/Height.QC.snp_matched.inf_prs.rds \\\n",
    "    --phenoFile GWAS_data/EUR.height.matched.txt \\\n",
    "    --covFile GWAS_data/EUR.cov.matched.txt \\\n",
    "    --response continuous"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = ., data = dat[train.ind, ])\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-1.73015 -0.52593 -0.02821  0.47019  2.40833 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error  t value Pr(>|t|)    \n",
       "(Intercept) 168.33930    0.13481 1248.673   <2e-16 ***\n",
       "Sex           0.86128    0.07794   11.050   <2e-16 ***\n",
       "PC1          -1.02292    0.82162   -1.245    0.214    \n",
       "PC2          -1.32026    0.87049   -1.517    0.130    \n",
       "PC3          -1.23730    0.87159   -1.420    0.157    \n",
       "PC4          -0.33065    1.57618   -0.210    0.834    \n",
       "PC5           0.41502    0.86756    0.478    0.633    \n",
       "PC6           0.06739    0.83906    0.080    0.936    \n",
       "PRS           0.48896    0.05666    8.630   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.7485 on 366 degrees of freedom\n",
       "  (11 observations deleted due to missingness)\n",
       "Multiple R-squared:  0.3718,\tAdjusted R-squared:  0.3581 \n",
       "F-statistic: 27.08 on 8 and 366 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 1 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>model</th><th scope=col>R2</th><th scope=col>MSE</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>model.inf_prs</td><td>0.35808</td><td>0.6695</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 1 × 3\n",
       "\\begin{tabular}{lll}\n",
       " model & R2 & MSE\\\\\n",
       " <chr> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t model.inf\\_prs & 0.35808 & 0.6695\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 1 × 3\n",
       "\n",
       "| model &lt;chr&gt; | R2 &lt;dbl&gt; | MSE &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| model.inf_prs | 0.35808 | 0.6695 |\n",
       "\n"
      ],
      "text/plain": [
       "  model         R2      MSE   \n",
       "1 model.inf_prs 0.35808 0.6695"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res = readRDS(\"height_results/EUR.height.matched.Height.QC.snp_matched.qc.inf_prs.rds\")\n",
    "summary(res$fitted)\n",
    "res$summary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = ., data = dat[train.ind, ])\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-1.76983 -0.49570 -0.03415  0.48238  2.46186 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error  t value Pr(>|t|)    \n",
       "(Intercept) 168.31863    0.13505 1246.328   <2e-16 ***\n",
       "Sex           0.85878    0.07772   11.049   <2e-16 ***\n",
       "PC1          -1.14006    0.81936   -1.391   0.1649    \n",
       "PC2          -1.43282    0.86602   -1.654   0.0989 .  \n",
       "PC3          -1.25347    0.86909   -1.442   0.1501    \n",
       "PC4          -0.30386    1.57142   -0.193   0.8468    \n",
       "PC5           0.44159    0.86500    0.511   0.6100    \n",
       "PC6           0.13108    0.83646    0.157   0.8756    \n",
       "PRS           0.47990    0.05466    8.780   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 0.7463 on 366 degrees of freedom\n",
       "  (11 observations deleted due to missingness)\n",
       "Multiple R-squared:  0.3755,\tAdjusted R-squared:  0.3619 \n",
       "F-statistic: 27.51 on 8 and 366 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 1 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>model</th><th scope=col>R2</th><th scope=col>MSE</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>model.inf_prs</td><td>0.36185</td><td>0.69409</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 1 × 3\n",
       "\\begin{tabular}{lll}\n",
       " model & R2 & MSE\\\\\n",
       " <chr> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t model.inf\\_prs & 0.36185 & 0.69409\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 1 × 3\n",
       "\n",
       "| model &lt;chr&gt; | R2 &lt;dbl&gt; | MSE &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| model.inf_prs | 0.36185 | 0.69409 |\n",
       "\n"
      ],
      "text/plain": [
       "  model         R2      MSE    \n",
       "1 model.inf_prs 0.36185 0.69409"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res = readRDS(\"height_results/EUR.height.matched.Height.QC.snp_matched.inf_prs.rds\")\n",
    "summary(res$fitted)\n",
    "res$summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "Here are commands for running prediction with \"auto\" and \"grid\" models:\n",
    "\n",
    "```\n",
    "sos run ldpred.ipynb pred_eval \\\n",
    "    --cwd $work_dir \\\n",
    "    --prs $work_dir/Height.QC.snp_matched.qc.auto_prs.rds \\\n",
    "    --phenoFile GWAS_data/EUR.height.matched.txt \\\n",
    "    --covFile GWAS_data/EUR.cov.matched.txt \\\n",
    "    --response continuous\n",
    "\n",
    "sos run ldpred.ipynb pred_eval \\\n",
    "    --cwd $work_dir \\\n",
    "    --prs $work_dir/Height.QC.snp_matched.auto_prs.rds \\\n",
    "    --phenoFile GWAS_data/EUR.height.matched.txt \\\n",
    "    --covFile GWAS_data/EUR.cov.matched.txt \\\n",
    "    --response continuous\n",
    "\n",
    "sos run ldpred.ipynb pred_eval \\\n",
    "    --cwd $work_dir \\\n",
    "    --prs $work_dir/Height.QC.snp_matched.qc.grid_prs.rds \\\n",
    "    --phenoFile GWAS_data/EUR.height.matched.txt \\\n",
    "    --covFile GWAS_data/EUR.cov.matched.txt \\\n",
    "    --response continuous\n",
    "\n",
    "sos run ldpred.ipynb pred_eval \\\n",
    "    --cwd $work_dir \\\n",
    "    --prs $work_dir/Height.QC.snp_matched.grid_prs.rds \\\n",
    "    --phenoFile GWAS_data/EUR.height.matched.txt \\\n",
    "    --covFile GWAS_data/EUR.cov.matched.txt \\\n",
    "    --response continuous\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "## Results summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "Following table shows adjusted R squared of height prediction models. \"QC\" refers to quality control in Step 4.\n",
    "\n",
    "Compared to baseline model, higher R squared with PRS included implies PRS explains part of the variation of height in the target data-set. Higher R squared is observed without performing quality control for the summary statistics, as we already expected and discussed after seeing the results in Step 4. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "| QC? |   # of SNPs  |   Baseline R2 |   Inf R2  |   Grid R2 |   Auto R2 |\n",
    "|:---:|:------------:|:-------:|:-------:|:-------:|:-------:|\n",
    "| Yes | 104,564 | 0.2296 | 0.3581 | -  | - |\n",
    "|  No | 109,963 | 0.2296 | 0.3619 |    -  |    -   |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "## Homework\n",
    "\n",
    "Please complete the runs with `grid` and `auto` model and complete the table above. **Computation with these models are intensive and long-running; it is suggested that the analysis be performed in a powerful computing environment**."
   ]
  }
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