Illumina_450k_Analysis_Pipeline.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Illumina 450k Analysis Pipeline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "DNA methylation is a process in which a methyl group (CH<sub>3</sub>) is added to the C-5 position of the cytosine ring of DNA by DNA methyltransferase. CpG islands are stretches of DNA, at least 200 bp long, with a GC content greater than 50% and an observed-to-expected CpG ratio greater than 60%. When methylation occurs inside CpG islands of promoters it causes silencing of gene expression and is, therefore, a very important epigenetic modification. It can be measured as a mean of the methylation status (non-methylated, hemimethylated or methylated) of a population of DNA molecules using methylation arrays.\n",
    "\n",
    "Infinium HumanMethylation450 BeadChip is a slide composed of 12 arrays that can altogether accomodate 12 samples. With 485 512 probes it covers 99% of RefSeq genes. For each probe sequence, a median of 14 beads, each containing hundreds of thousands of oligonucleotides, is randomly distributed on the array.\n",
    "\n",
    "Sample preparation includes bisulfite conversion which transforms the unmethylated cytosine to uracil while leaving the methylated cytosine intact. PCR amplification then substitutes uracil with thymine reducing the differentiation between methylated and unmethylated cytosine to a differentiation between cytosine and thymine. Samples are subsequently hybridized to the array and fluorescently labeled nucleotides are added for a single-base extension. The emission of red light indicates the incorporation of A or T, while the emission of green light indicates the incorporation of C or G.\n",
    "\n",
    "Illumina 450k combines two different assay chemistry technologies. Infinium I uses two types of probes (one for the methylated allele and one for the unmethylated allele) but both signals are measured in the same color (red or green). Infinium II uses a single probe type for both alleles but methylated and unmethylated signals are measured in green and red, respectively.\n",
    "\n",
    "This report describes a pipeline for the analysis of Illumina 450k DNA methylation data in R using the Bioconductor package [minfi](http://bioconductor.org/packages/release/bioc/html/minfi.html). It includes the following sections:\n",
    "1. Importing raw data files\n",
    "2. Quality checks\n",
    "3. Background correction and normalization\n",
    "4. Batch effects\n",
    "5. Differential methylation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dependencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "suppressWarnings(suppressMessages(library(minfi)))\n",
    "suppressWarnings(suppressMessages(library(gap)))\n",
    "suppressWarnings(suppressMessages(library(gplots)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These dependencies can be installed from Bioconductor and from a specified CRAN mirror."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "source(\"https://bioconductor.org/biocLite.R\")\n",
    "biocLite(\"minfi\") \n",
    "\n",
    "repos <- 'http://cran.mirror.garr.it/mirrors/CRAN/'\n",
    "install.packages(\"gap\",repos)\n",
    "install.packages(\"gplots\",repos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Importing raw data files"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we set the base directory and read the Illumina methylation sample sheet that specifies the layout of the experiment. We then read the .idat files which contain the unprocessed intensity values generated by the Illumina iScan. The raw data is loaded into an RGChannelSet object which stores red and green intensities for each address (probe)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[read.metharray.sheet] Found the following CSV files:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"./SampleSheet_report.csv\"\n"
     ]
    }
   ],
   "source": [
    "baseDir <- (\".\")\n",
    "targets <- read.metharray.sheet(baseDir)\n",
    "RGset <- read.metharray.exp(targets = targets,extend=T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The red and green fluorescences are transformed into two data frames for further analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Red <- data.frame(getRed(RGset))\n",
    "Green <- data.frame(getGreen(RGset))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now look at the red and green fluorescences for a specific address, for example **18744490**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Red</th><th scope=col>Green</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X9376538140_R01C02</th><td> 479 </td><td>  289</td></tr>\n",
       "\t<tr><th scope=row>X9376538140_R03C01</th><td> 598 </td><td>  476</td></tr>\n",
       "\t<tr><th scope=row>X9376538140_R03C02</th><td> 520 </td><td>  513</td></tr>\n",
       "\t<tr><th scope=row>X9376538140_R06C01</th><td>3925 </td><td>11471</td></tr>\n",
       "\t<tr><th scope=row>X9403904089_R03C01</th><td>3667 </td><td>12224</td></tr>\n",
       "\t<tr><th scope=row>X9403904089_R04C02</th><td>4262 </td><td>11662</td></tr>\n",
       "\t<tr><th scope=row>X9403904089_R05C01</th><td> 645 </td><td>  542</td></tr>\n",
       "\t<tr><th scope=row>X9403904089_R06C01</th><td> 505 </td><td>  493</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       "  & Red & Green\\\\\n",
       "\\hline\n",
       "\tX9376538140\\_R01C02 &  479  &   289\\\\\n",
       "\tX9376538140\\_R03C01 &  598  &   476\\\\\n",
       "\tX9376538140\\_R03C02 &  520  &   513\\\\\n",
       "\tX9376538140\\_R06C01 & 3925  & 11471\\\\\n",
       "\tX9403904089\\_R03C01 & 3667  & 12224\\\\\n",
       "\tX9403904089\\_R04C02 & 4262  & 11662\\\\\n",
       "\tX9403904089\\_R05C01 &  645  &   542\\\\\n",
       "\tX9403904089\\_R06C01 &  505  &   493\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Red | Green | \n",
       "|---|---|---|---|---|---|---|---|\n",
       "| X9376538140_R01C02 |  479  |   289 | \n",
       "| X9376538140_R03C01 |  598  |   476 | \n",
       "| X9376538140_R03C02 |  520  |   513 | \n",
       "| X9376538140_R06C01 | 3925  | 11471 | \n",
       "| X9403904089_R03C01 | 3667  | 12224 | \n",
       "| X9403904089_R04C02 | 4262  | 11662 | \n",
       "| X9403904089_R05C01 |  645  |   542 | \n",
       "| X9403904089_R06C01 |  505  |   493 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "                   Red  Green\n",
       "X9376538140_R01C02  479   289\n",
       "X9376538140_R03C01  598   476\n",
       "X9376538140_R03C02  520   513\n",
       "X9376538140_R06C01 3925 11471\n",
       "X9403904089_R03C01 3667 12224\n",
       "X9403904089_R04C02 4262 11662\n",
       "X9403904089_R05C01  645   542\n",
       "X9403904089_R06C01  505   493"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "address <- \"18744490\"\n",
    "fluorescence <- cbind(t(Red[address,]),t(Green[address,]))\n",
    "colnames(fluorescence) <- c(\"Red\",\"Green\")\n",
    "fluorescence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we create a MethylSet object by converting the red/green channel into methylation signal, without using any normalization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: IlluminaHumanMethylation450kmanifest\n"
     ]
    }
   ],
   "source": [
    "MSet.raw <- preprocessRaw(RGset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Quality checks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1. QC plot\n",
    "Sample-specific quality control information is extracted from the MethylSet object and the log median intensity of the methylated channels is plotted agains that of unmethylated channels. Good samples usually cluster together, while failed samples tend to separate and have lower median intensities. Therefore, the plot below does not show any outlier samples that may be of poor quality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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32szKTQdut1/RhuCJKvrme2R+rt/9rV0NHyvrtmkyD17xS3Dxy6f3cdfEjS9QNt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\n0SUuAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qc <- getQC(MSet.raw)\n",
    "plotQC(qc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2. Negative controls\n",
    "Illumina 450k contains both sample-independent (not based on the hybridization) and sample-dependent (based on the hybridization) control probes. We plot the negative control probes, which are randomly permutated bisulphite-converted sequences that should not hybridize to DNA. Since these controls are sample-dependent, a dramatic increase in the signal intensity may indicate poor DNA template quality, but this is not our case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/NBORpEsgSP54NyNIhkCR7PB+VoEMkSPJ4PytEgkiV4PB+Uo0EkS/B4PihHg0iW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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "controlStripPlot(RGset, controls=\"NEGATIVE\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3. Detection p-value\n",
    "Detection p-value indicates the chance that the target sequence signal is distinguishable from the negative controls and is an objective measure of overall probe performance. We compute the detection p-value and obtain the positions with nonsignificant p-values (for example above **0.05**). A summary of these positions is provided below. Since they are only few (up to 500 per sample) and, as such, will not affect normalization procedures, we do not filter them out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Sample</th><th scope=col>Number of probes (detP&gt;0.05)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>9376538140_R01C02</td><td>TRUE :502        </td></tr>\n",
       "\t<tr><td>9376538140_R03C01</td><td>TRUE :412        </td></tr>\n",
       "\t<tr><td>9376538140_R03C02</td><td>TRUE :393        </td></tr>\n",
       "\t<tr><td>9376538140_R06C01</td><td>TRUE :98         </td></tr>\n",
       "\t<tr><td>9403904089_R03C01</td><td>TRUE :121        </td></tr>\n",
       "\t<tr><td>9403904089_R04C02</td><td>TRUE :119        </td></tr>\n",
       "\t<tr><td>9403904089_R05C01</td><td>TRUE :357        </td></tr>\n",
       "\t<tr><td>9403904089_R06C01</td><td>TRUE :441        </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " Sample & Number of probes (detP>0.05)\\\\\n",
       "\\hline\n",
       "\t 9376538140\\_R01C02 & TRUE :502          \\\\\n",
       "\t 9376538140\\_R03C01 & TRUE :412          \\\\\n",
       "\t 9376538140\\_R03C02 & TRUE :393          \\\\\n",
       "\t 9376538140\\_R06C01 & TRUE :98           \\\\\n",
       "\t 9403904089\\_R03C01 & TRUE :121          \\\\\n",
       "\t 9403904089\\_R04C02 & TRUE :119          \\\\\n",
       "\t 9403904089\\_R05C01 & TRUE :357          \\\\\n",
       "\t 9403904089\\_R06C01 & TRUE :441          \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Sample | Number of probes (detP>0.05) | \n",
       "|---|---|---|---|---|---|---|---|\n",
       "| 9376538140_R01C02 | TRUE :502         | \n",
       "| 9376538140_R03C01 | TRUE :412         | \n",
       "| 9376538140_R03C02 | TRUE :393         | \n",
       "| 9376538140_R06C01 | TRUE :98          | \n",
       "| 9403904089_R03C01 | TRUE :121         | \n",
       "| 9403904089_R04C02 | TRUE :119         | \n",
       "| 9403904089_R05C01 | TRUE :357         | \n",
       "| 9403904089_R06C01 | TRUE :441         | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Sample            Number of probes (detP>0.05)\n",
       "1 9376538140_R01C02 TRUE :502                   \n",
       "2 9376538140_R03C01 TRUE :412                   \n",
       "3 9376538140_R03C02 TRUE :393                   \n",
       "4 9376538140_R06C01 TRUE :98                    \n",
       "5 9403904089_R03C01 TRUE :121                   \n",
       "6 9403904089_R04C02 TRUE :119                   \n",
       "7 9403904089_R05C01 TRUE :357                   \n",
       "8 9403904089_R06C01 TRUE :441                   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "detP <- detectionP(RGset)\n",
    "threshold <- 0.05\n",
    "failed <- summary(detP>threshold)\n",
    "failed <- data.frame(failed)\n",
    "failed <- failed[seq(3,nrow(failed),3),2:3]\n",
    "rownames(failed) <- c()\n",
    "colnames(failed) <- c(\"Sample\",paste(\"Number of probes (detP>\",threshold,\")\",sep=''))\n",
    "failed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Background correction and normalization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1. Raw data\n",
    "First, we extract raw beta and M values from the MethylSet object using the appropriate accessor functions. Beta values are the percentage of methylation at a given CpG site ($\\beta = \\frac{M}{M+U}$), while M values are the log ratio between methylated and unmethylated signals ($M = log_2\\frac{M}{U}$). They are both continuous variables, but beta values can vary between 0 (absent methylation) and 1 (completely methylated), while M values can in principle take on any real value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "beta <- getBeta(MSet.raw)\n",
    "M <- getM(MSet.raw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We calculate mean beta and mean M values with their respective densities in order to plot them. The mean beta density plot shows two clearly separated peaks corresponding to unmethylated and methylated signals, respectively, while in the mean M density plot the two peaks are not that well separated and are closer together. Boxplots of beta and M values are also generated and show the same pattern of median values between samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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EZAJIfiUpIZiMppqgxqhOFriDTDRGnS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",
      "text/plain": [
       "Plot with title \"Density of mean M values\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"Boxplot of M values\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_of_beta <- apply(beta,1,mean)\n",
    "mean_of_M <- apply(M,1,mean)\n",
    "d_mean_of_beta <- density(mean_of_beta,na.rm=T)\n",
    "d_mean_of_M <- density(mean_of_M,na.rm=T)\n",
    "\n",
    "par(mfrow=c(1,2))\n",
    "plot(d_mean_of_beta,main=\"Density of mean beta values\")\n",
    "plot(d_mean_of_M,main=\"Density of mean M values\")\n",
    "\n",
    "options(warn=-1) #turns off the warnings\n",
    "par(mfrow=c(1,2))\n",
    "boxplot(beta,las=2,cex.axis=0.4,main=\"Boxplot of beta values\")\n",
    "boxplot(M,las=2,cex.axis=0.4,main=\"Boxplot of M values\")\n",
    "options(warn=0) #turns the warnings back on"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2. Functional normalization (Funnorm)\n",
    "Next, normalization is performed on the RGChannelSet object in order to remove technical variation. Functional normalization (Funnorm) is a between-array normalization method that removes unwanted variation by regressing out variability explained by the control probes present on the array. It includes background and dye bias correction, mapping to genome, quantile extraction and normalization. Normalized beta and M values are extracted as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[preprocessFunnorm] Background and dye bias correction with noob\n",
      "Loading required package: IlluminaHumanMethylation450kanno.ilmn12.hg19\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[preprocessNoob] Applying R/G ratio flip to fix dye bias...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[preprocessFunnorm] Mapping to genome\n",
      "[preprocessFunnorm] Quantile extraction\n",
      "[preprocessFunnorm] Normalization\n"
     ]
    }
   ],
   "source": [
    "preprocessFunnorm_results <- preprocessFunnorm(RGset)\n",
    "\n",
    "beta_preprocessFunnorm <- getBeta(preprocessFunnorm_results)\n",
    "M_preprocessFunnorm <- getM(preprocessFunnorm_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We calculate the mean and the standard deviation of the normalized beta and M values, plotting them against each other to check for homo/heteroscedasticity (constant/non constant variance). Normalized beta values in the low (&lt;0.2) and high (>0.8) methylation range are significanty heteroscedastic, while normalized M values are slightly less so."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qtfcY90/fPz8z0m97jDhgdIl+zrwUOXUhXPQcROSnU1v6cDkjmFA0lKtEGQwlrW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\nDYqsx2kRDzsAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Mean vs stdev of M values\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta_preprocessFunnorm_mean <- apply(beta_preprocessFunnorm, 1, mean)\n",
    "beta_preprocessFunnorm_stdev <- apply(beta_preprocessFunnorm, 1, sd)\n",
    "M_preprocessFunnorm_mean <- apply(M_preprocessFunnorm,1, mean)\n",
    "M_preprocessFunnorm_stdev <- apply(M_preprocessFunnorm,1, sd)\n",
    "\n",
    "M_preprocessFunnorm_mean <- M_preprocessFunnorm_mean[!M_preprocessFunnorm_mean==\"-Inf\"] #removes -Inf values for the mean of M\n",
    "M_preprocessFunnorm_stdev <- M_preprocessFunnorm_stdev[!is.na(M_preprocessFunnorm_stdev)] #removes missing values for the standard deviation of M\n",
    "\n",
    "par(mfrow=c(1,2))\n",
    "smoothScatter(beta_preprocessFunnorm_mean, beta_preprocessFunnorm_stdev, main=\"Mean vs stdev of Beta values\")\n",
    "lines(lowess(beta_preprocessFunnorm_mean, beta_preprocessFunnorm_stdev), col=\"red\")\n",
    "smoothScatter(M_preprocessFunnorm_mean, M_preprocessFunnorm_stdev, main=\"Mean vs stdev of M values\")\n",
    "lines(lowess(M_preprocessFunnorm_mean, M_preprocessFunnorm_stdev), col=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3. Subset-quantile Within Array Normalization (SWAN)\n",
    "Normalization is also performed using, for example, the **preprocessSWAN** function. Subset-quantile Within Array Normalization (SWAN) is a within array normalization method which allows Infinium I and II type probes on a single array to be normalized together. After the normalization, beta and M values are extracted once again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "preprocessSWAN_results <- preprocessSWAN(RGset)\n",
    "\n",
    "beta_preprocessSWAN <- getBeta(preprocessSWAN_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For annotation purposes, [Illumina 450k manifest](http://support.illumina.com/array/array_kits/infinium_humanmethylation450_beadchip_kit/downloads.html) is downloaded in the spreadsheet format (486428 rows and 33 columns). Probes that do not map to a chromosome are removed and the remaining probes are divided by design type into Infinium I and Infinium II probes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "Illumina450Manifest <- read.table(\"Illumina450Manifest.txt\",sep=\"\\t\",header=T)\n",
    "notMappedToCHR <- Illumina450Manifest[Illumina450Manifest$CHR==\"\",]\n",
    "notMappedToCHR <- droplevels(notMappedToCHR)\n",
    "Illumina450Manifest_clean <- Illumina450Manifest[!Illumina450Manifest$IlmnID %in% notMappedToCHR$IlmnID,]\n",
    "Illumina450Manifest_clean <- droplevels(Illumina450Manifest_clean)\n",
    "\n",
    "dfI <- Illumina450Manifest_clean[Illumina450Manifest_clean$Infinium_Design_Type==\"I\",]\n",
    "dfI <- droplevels(dfI)\n",
    "dfII <- Illumina450Manifest_clean[Illumina450Manifest_clean$Infinium_Design_Type==\"II\",]\n",
    "dfII <- droplevels(dfII)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We extract beta I and beta II values from both raw and normalized data. Then, we calculate the means and the standard deviations with the respective densities. Three plots are generated in order to compare raw data with normalized data: density of means of beta values, density of standard deviations of beta values and boxplot of beta values. \n",
    "\n",
    "For both raw and normalized data we observe that: the density of means of beta values for Infinium II probes is shifted towards the centre with respect to Infinium I probes (Infinium II assay is less sensitive for the detection of extreme methylation values than the Infinium I assay) and the standard deviation of beta values for Infinium II probes is higher with respect to Infinium I probes (beta values obtained from Infinium II probes are less accurate and reproducible than those obtained from Infinium I probes).\n",
    "\n",
    "If we compare the raw and the normalized data it becomes evident that the shift of Infinium II probes towards the centre is much smaller for the normalized data and the standard deviation of Infinium II probes is also closer to that of Infinium I probes. In addition, for the normalized data the boxes are slightly longer in the upper part of the boxplot and the medians are generally higher."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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BaJXUhW1iCxSO3XukKk84lU1c9rXV8f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\nxIiUopBZH6pwXyJZVbq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      "text/plain": [
       "Plot with title \"Boxplot of beta values\n",
       "for preprocessSWAN data\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta_I <- beta[rownames(beta) %in% dfI$IlmnID,]\n",
    "beta_II <- beta[rownames(beta) %in% dfII$IlmnID,]\n",
    "\n",
    "mean_of_beta_I <- apply(beta_I,1,mean)\n",
    "mean_of_beta_II <- apply(beta_II,1,mean)\n",
    "d_mean_of_beta_I <- density(mean_of_beta_I,na.rm=T)\n",
    "d_mean_of_beta_II <- density(mean_of_beta_II,na.rm=T)\n",
    "\n",
    "sd_of_beta_I <- apply(beta_I,1,sd)\n",
    "sd_of_beta_II <- apply(beta_II,1,sd)\n",
    "d_sd_of_beta_I <- density(sd_of_beta_I,na.rm=T)\n",
    "d_sd_of_beta_II <- density(sd_of_beta_II,na.rm=T)\n",
    "\n",
    "beta_preprocessSWAN_I <- beta_preprocessSWAN[rownames(beta_preprocessSWAN) %in% dfI$IlmnID,]\n",
    "beta_preprocessSWAN_II <- beta_preprocessSWAN[rownames(beta_preprocessSWAN) %in% dfII$IlmnID,]\n",
    "\n",
    "mean_of_beta_preprocessSWAN_I <- apply(beta_preprocessSWAN_I,1,mean)\n",
    "mean_of_beta_preprocessSWAN_II <- apply(beta_preprocessSWAN_II,1,mean)\n",
    "d_mean_of_beta_preprocessSWAN_I <- density(mean_of_beta_preprocessSWAN_I,na.rm=T)\n",
    "d_mean_of_beta_preprocessSWAN_II <- density(mean_of_beta_preprocessSWAN_II,na.rm=T)\n",
    "\n",
    "sd_of_beta_preprocessSWAN_I <- apply(beta_preprocessSWAN_I,1,sd)\n",
    "sd_of_beta_preprocessSWAN_II <- apply(beta_preprocessSWAN_II,1,sd)\n",
    "d_sd_of_beta_preprocessSWAN_I <- density(sd_of_beta_preprocessSWAN_I,na.rm=T)\n",
    "d_sd_of_beta_preprocessSWAN_II <- density(sd_of_beta_preprocessSWAN_II,na.rm=T)\n",
    "\n",
    "par(mfrow=c(2,3))\n",
    "plot(d_mean_of_beta_I,col=\"blue\",main=\"Density of means\\nof beta values for\\nraw data\")\n",
    "lines(d_mean_of_beta_II,col=\"red\")\n",
    "plot(d_sd_of_beta_I,col=\"blue\",main=\"Density of standard deviations\\nof beta values for\\nraw data\")\n",
    "lines(d_sd_of_beta_II,col=\"red\")\n",
    "boxplot(beta,las=2,cex.axis=0.5,main=\"Boxplot of beta values\\nfor raw data\")\n",
    "plot(d_mean_of_beta_preprocessSWAN_I,col=\"blue\",main=\"Density of means\\nof beta values for\\npreprocessSWAN data\")\n",
    "lines(d_mean_of_beta_preprocessSWAN_II,col=\"red\")\n",
    "plot(d_sd_of_beta_preprocessSWAN_I,col=\"blue\",main=\"Density of standard deviations\\nof beta values for\\npreprocessSWAN data\")\n",
    "lines(d_sd_of_beta_preprocessSWAN_II,col=\"red\")\n",
    "boxplot(beta_preprocessSWAN,las=2,cex.axis=0.5,main=\"Boxplot of beta values\\nfor preprocessSWAN data\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Batch effects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Principal component analysis (PCA) is a dimension-reduction technique that minimizes dimensions while preserving covariance of the data. We perform the PCA on the functionally normalized beta values in order to check for batch effects (technical sources of variation that have been added to the samples due to experimental conditions and are unrelated to the biological variables in the study). The plot shows no clear separation between samples of the same slide or of the same array so no evident batch effects are observed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5x05uJm0qiciMTDSevxboIy7+fdugvfNiGl5am2Hy5up5iI0204PV5Mms27CSr4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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"PCA on beta_preprocessFunnorm\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca <- prcomp(t(beta_preprocessFunnorm),scale=T)\n",
    "\n",
    "plot(pca$x[,1], pca$x[,2], xlim=c(-1000,1000),cex=2, main=\"PCA on beta_preprocessFunnorm\")\n",
    "text(pca$x[,1], pca$x[,2],labels=rownames(pca$x),cex=0.5,pos=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Differential methylation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1. ANOVA test correcting for body mass index (BMI)\n",
    "In order to identify differentially methylated probes between group A and group B, a statistical test, for example, **ANOVA test correcting for body mass index (BMI)**, is performed. First, we load the sample sheet that contains phenotypical information. Next, an ad hoc function is implemented which performs the ANOVA test using BMI as a covariate and returns the p-value from the summary of the ANOVA test. We apply the function to the normalized SWAN beta values and obtain the p-values. A data frame is created from the SWAN normalized beta values and the calculated p-values which is then sorted based on the latter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "pheno <- read.csv(\"SampleSheet_report.csv\",sep=\",\")\n",
    "\n",
    "MYanovaFunction <- function(x) {\n",
    "\tanova_test <- aov(x ~ pheno$Group+pheno$BMI)\n",
    "\treturn(summary(anova_test)[[1]][[5]][1])\n",
    "}\n",
    "\n",
    "pValuesAnova <- apply(beta_preprocessSWAN,1,MYanovaFunction)\n",
    "final_Anova <- data.frame(beta_preprocessSWAN,pValuesAnova)\n",
    "final_Anova <- final_Anova[order(final_Anova$pValuesAnova),]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2. Multiple test correction\n",
    "We apply a multiple test correction procedure to adjust our statistical confidence measures based on the number of tests performed. In the case of Bonferroni correction the nominal p-values are multiplied by the number of tests (probes), while in the case of Benjamini and Hochberg (BH) correction the nominal p-values are ranked, multiplied by the number of tests (probes) and divided by the their rank. We use the significance threshold of 0.05 and obtain the number of differentially methylated probes considering the three p-values, respectively. The results are visible in the table below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>number of DMPs (p-value&lt;0.05)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>nominal p-values</th><td>54975</td></tr>\n",
       "\t<tr><th scope=row>Bonferroni corrected p-values</th><td>    4</td></tr>\n",
       "\t<tr><th scope=row>BH corrected p-values</th><td>    0</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|l}\n",
       "  & number of DMPs (p-value<0.05)\\\\\n",
       "\\hline\n",
       "\tnominal p-values & 54975\\\\\n",
       "\tBonferroni corrected p-values &     4\\\\\n",
       "\tBH corrected p-values &     0\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | number of DMPs (p-value<0.05) | \n",
       "|---|---|---|\n",
       "| nominal p-values | 54975 | \n",
       "| Bonferroni corrected p-values |     4 | \n",
       "| BH corrected p-values |     0 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "                              number of DMPs (p-value<0.05)\n",
       "nominal p-values              54975                        \n",
       "Bonferroni corrected p-values     4                        \n",
       "BH corrected p-values             0                        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "raw_pValues <- final_Anova$pValuesAnova\n",
    "corrected_pValues_Bonf <- p.adjust(raw_pValues,\"bonferroni\")\n",
    "corrected_pValues_BH <- p.adjust(raw_pValues,\"BH\")\n",
    "final_Anova_corrected <- data.frame(final_Anova,corrected_pValues_Bonf,corrected_pValues_BH)\n",
    "\n",
    "DMP <- t(data.frame(dim(final_Anova_corrected[final_Anova_corrected$pValuesAnova<=threshold,])[1],\n",
    "                    dim(final_Anova_corrected[final_Anova_corrected$corrected_pValues_BH<=threshold,])[1],\n",
    "                    dim(final_Anova_corrected[final_Anova_corrected$corrected_pValues_Bonf<=threshold,])[1]))\n",
    "colnames(DMP) <- paste(\"number of DMPs (p-value<\",threshold,\")\",sep='')\n",
    "rownames(DMP) <- c(\"nominal p-values\",\"Bonferroni corrected p-values\",\"BH corrected p-values\")\n",
    "DMP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.3. Volcano plot\n",
    "Volcano plot is a type of scatter-plot which combines a measure of statistical significance (negative logarithm of p-value) with the magnitude of the change (on the y and x axis, respectively), enabling quick visual identification of those data-points that display large magnitude changes that are also statistically significant. Using the significance threshold of 0.05 (green dashed line), we obtain hypomethylated probes depicted in blue and hypermethylated probes depicted in red."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NxlR1yaVrjr7PGjvrSegUjlcd/G5/Uy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\nAJEAUAAiAaDA/wGEVEu96ckpnwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta <- final_Anova_corrected[,1:8]\n",
    "beta_groupA <- beta[,pheno$Group==\"A\"]\n",
    "mean_beta_groupA <- apply(beta_groupA,1,mean)\n",
    "beta_groupB <- beta[,pheno$Group==\"B\"]\n",
    "mean_beta_groupB <- apply(beta_groupB,1,mean)\n",
    "delta <- mean_beta_groupB-mean_beta_groupA\n",
    "\n",
    "toVolcPlot <- data.frame(delta, -log10(final_Anova_corrected$pValuesAnova))\n",
    "plot(toVolcPlot[,1], toVolcPlot[,2],pch=16)\n",
    "toHighlight <- toVolcPlot[-toVolcPlot[,1]>0.1 & toVolcPlot[,2]>(-log10(threshold)),]\n",
    "points(toHighlight[,1], toHighlight[,2],pch=16,cex=0.7,col=\"blue\")\n",
    "toHighlight <- toVolcPlot[toVolcPlot[,1]>0.1 & toVolcPlot[,2]>(-log10(threshold)),]\n",
    "points(toHighlight[,1], toHighlight[,2],pch=16,cex=0.7,col=\"red\")\n",
    "abline(a=-log10(threshold),b=0,col=\"green\",lty=\"longdash\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4. Manhattan plot\n",
    "Manhattan plot is another type of scatter plot, usually used to display data with a large number of data-points. Chromosomes are displayed on the x axis, with a measure of statistical significance (negative logarithm of p-value) displayed on the y axis. The black horizontal line indicates the significance threshold of 0.05."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting points  1 - 23487 \n",
      "Plotting points  23488 - 41290 \n",
      "Plotting points  41291 - 53812 \n",
      "Plotting points  53813 - 64484 \n",
      "Plotting points  64485 - 76819 \n",
      "Plotting points  76820 - 95208 \n",
      "Plotting points  95209 - 110131 \n",
      "Plotting points  110132 - 120620 \n",
      "Plotting points  120621 - 125488 \n",
      "Plotting points  125489 - 137611 \n",
      "Plotting points  137612 - 151928 \n",
      "Plotting points  151929 - 164149 \n",
      "Plotting points  164150 - 170546 \n",
      "Plotting points  170547 - 177932 \n",
      "Plotting points  177933 - 185609 \n",
      "Plotting points  185610 - 196590 \n",
      "Plotting points  196591 - 210441 \n",
      "Plotting points  210442 - 213273 \n",
      "Plotting points  213274 - 225972 \n",
      "Plotting points  225973 - 231161 \n",
      "Plotting points  231162 - 233271 \n",
      "Plotting points  233272 - 237547 \n",
      "Plotting points  237548 - 243120 \n",
      "Plotting points  243121 - 243329 \n"
     ]
    },
    {
     "data": {
      "image/png": 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0RKY6f63p1PZwYKNlJkvUD2yEt52wADYprNaP6RXInJda5T96NCJOizHaJSlUil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\nIhFEA5BIBNEAJBJBNMD/AzLrIKNSzrAsAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "load('final_Anova_corrected.RData')\n",
    "final_Anova_corrected <- data.frame(rownames(final_Anova_corrected),final_Anova_corrected)\n",
    "colnames(final_Anova_corrected)[1] <- \"IlmnID\"\n",
    "final_Anova_corrected_annotated <- merge(final_Anova_corrected, Illumina450Manifest_clean,by=\"IlmnID\")\n",
    "\n",
    "db <- data.frame(final_Anova_corrected_annotated$CHR, \n",
    "                 final_Anova_corrected_annotated$MAPINFO, \n",
    "                 final_Anova_corrected_annotated$pValuesAnova)\n",
    "db$final_Anova_corrected_annotated.CHR <- factor(db$final_Anova_corrected_annotated.CHR,\n",
    "                                                 levels=c(paste(c(1:22)),'X','Y'))\n",
    "\n",
    "palette <- rep(c(\"red\",\"blue\",\"green\",\"cyan\",\"yellow\",\"gray\",\"magenta\"),4)[1:24]\n",
    "mhtplot(db,control=mht.control(colors=palette))\n",
    "axis(2,cex=0.5)\n",
    "abline(a=-log10(threshold),b=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.5. Multidimensional scaling (MDS) plot\n",
    "Multidimensional scaling (MDS) is dimension-reduction technique that minimizes dimensions while preserving distance between data points. It takes a set of dissimilarities (euclidean distances in our case) and returns a set of points such that the distances between the points are approximately equal to the dissimilarities. The MDS plot on probes selected as differentially methylated on the basis of nominal p-values (significance threshold of 0.05) clearly separates the two groups (A and B) along the x axis. However, one outlier belonging to the group A can be observed in the upper right part of the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Plot with title \"MDS plot for DMPs (p-value<0.05)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "final_Anova_corrected_annotated_sign <- final_Anova_corrected_annotated[final_Anova_corrected_annotated$pValuesAnova<threshold,]\n",
    "final_Anova_corrected_annotated_sign <- droplevels(final_Anova_corrected_annotated_sign)\n",
    "\n",
    "dist.euc=dist(t(final_Anova_corrected_annotated_sign[,2:9]))\n",
    "mds=cmdscale(dist.euc)\n",
    "\n",
    "plot(mds,type=\"n\",main=paste(\"MDS plot for DMPs (p-value<\",threshold,\")\",sep=''))\n",
    "points(mds[pheno$Group==\"A\",],col=\"red\",cex=2)\n",
    "points(mds[pheno$Group==\"B\",],col=\"blue\",cex=2)\n",
    "legend(\"topleft\",c(\"A\",\"B\"),pch=1,col=c(\"red\",\"blue\"))"
   ]
  }
 ],
 "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": "3.4.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}