class14_partialcorr_R.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CS446/546 - Class Session 14 - Network inference using partial correlations\n",
    "\n",
    "In this class session we will continue with analyzing the tumor gene expression dataset from the NIH human bladder cancer cohort (*M*=414 tumors), building on what we learned in Class Session 19 (Correlation Network).  In order to keep the analysis simple&ast;, in this notebook will restrict our analysis to a set of *N*=164 genes that are very highly expressed in bladder cancer. Using the 164 x 414 matrix of transcript abundance measurements, we will construct a network based on gene-gene partial correlation coefficients. We will also compare the distribution of partial correlation coefficients to the distribution of Pearson correlation coefficients. Do you think they will be different?  In what way would you expect them to be different?\n",
    "\n",
    "&ast; Here, \"simple\" means that the covariance matrix will be nonsingular, so that we can obtain the partial correlation matrix by inversion."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by loading the two R packages that we will need for this exercise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(corpcor)  ## we will use this library for computing partial correl.\n",
    "\n",
    "suppressPackageStartupMessages(   \n",
    "library(igraph)   ## we will use this library for plotting the network\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read the tab-deliminted text file of gene expression measurements (rows correspond to genes, columns correspond to bladder tumor samples; the first row of the file contains the \"names\" of the tumor samples). As usual, you will use `read.table` with `row.names=1`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "gene_matrix_for_network <- read.table(\"shared/bladder_cancer_genes_tcga.txt\",\n",
    "                                     sep=\"\\t\",\n",
    "                                     header=TRUE,\n",
    "                                     row.names=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As always, you should check using `dim` to verify that the file that you loaded has the expected dimensions (in this case, 4,473 x 414)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4473</li>\n",
       "\t<li>414</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4473\n",
       "\\item 414\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4473\n",
       "2. 414\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4473  414"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(gene_matrix_for_network)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Filter the matrix `gene_matrix_for_network` to include only rows for which the row median expression level is > 12 (a reasonbly high transcript tag count since these measurements are in log2 scale); matrix should now be 164 x 414; this is not strictly necessary but will help prevent us from over-burderning the EC2 instance and it will enable us to easily compute the partial correlation matrix using the inverse of the covariance matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, compute the row-wise median expression levels, using `apply` with `MARGIN=1`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "gene_median_express <- apply(gene_matrix_for_network, 1, median)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, use array indexing `[` to make a matrix `gene_matrix_filt` that contains only the rows for which `gene_median_express > 12`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "gene_matrix_filt <- gene_matrix_for_network[gene_median_express > 12, ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use `nrow` to verify that this matrix has 164 rows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "164"
      ],
      "text/latex": [
       "164"
      ],
      "text/markdown": [
       "164"
      ],
      "text/plain": [
       "[1] 164"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N <- nrow(gene_matrix_filt)\n",
    "N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the `cor` function (our friend from last class session), compute the 164 x 164 matrix of gene-gene Pearson correlation coefficients. Don't forget that `cor` computes correlations between *columns* of its matrix argument, so you will have to transpose the data matrix using the `t` function before passing it to `cor`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "matrix_cor <- cor(t(gene_matrix_filt))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use `dim` to verify that your matrix is now *N* x *N*, where *N* = 164.  (If you get 414 x 414 instead, you forgot to transpose.) This illustrates why it is good to always be checking matrix and data frame dimensions as you go through your analysis!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>164</li>\n",
       "\t<li>164</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 164\n",
       "\\item 164\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 164\n",
       "2. 164\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 164 164"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(matrix_cor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read the online help page for the function `corpcor::cor2pcor`.  What is its input object type?  What is its output object type?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "?cor2pcor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the `corpcor::cor2pcor` function to compute the partial correlation matrix (note: if *N* > *M*, `cor2pcor` is not recommended; we would need to instead use `corpcor::pcor.shrink`, which uses a technique called shrinkage estimation to obtain the partial correlation matrix)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "matrix_pcor <- corpcor::cor2pcor(matrix_cor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the histograms of the correlation coefficients (upper triangle only) and the partial correlation coefficients, on the same plot using alpha blending (refer to class session 17 exercise)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Bg4ceLEK1euKOaZMGFCt27dbJMHAKyt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\nUhQ0AEiKggYASVHQACApChoAJPV/xjzvUEu4ro4AAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nbreaks <- 40\n",
    "breaks <- ((0:nbreaks)-(nbreaks/2))/(nbreaks/2)\n",
    "hist_cor <- hist(matrix_cor[upper.tri(matrix_cor)], breaks=breaks, plot=FALSE)\n",
    "hist_pcor <- hist(matrix_pcor[upper.tri(matrix_pcor)], breaks=breaks, plot=FALSE)\n",
    "plotvals <- 0.5*(breaks[1:nbreaks] + breaks[2:(nbreaks+1)])\n",
    "plot(hist_pcor, col=rgb(0,1,0,1/4), xlab=expression(C[i]), main=\"\", freq=FALSE)\n",
    "plot(hist_cor, col=rgb(0,0,1,1/4), add=TRUE, freq=FALSE)\n",
    "legend(0.3, 8, legend=c(\"cor\",\"pcor\"), fill=c(rgb(0,0,1,1/4),rgb(0,1,0,1/4)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fisher transform the partial correlation matrix, to get a matrix of z scores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "matrix_z <- 0.5*log((1+matrix_pcor)/(1-matrix_pcor))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute a p-value for each gene pair (upper triangle only), using the fact that sqrt(M-N-5) times the fisher Z sore should be approximately univariate normal (with zero mean) under the null hypothesis that a given gene pair's measurements (conditioned on the measurements for all the other 162 genes) are independent. (use `sqrt`, `upper.tri`, `abs`, and `pnorm`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "M <- ncol(gene_matrix_for_network)\n",
    "pvalues <- 2*pnorm(-abs(matrix_z[upper.tri(matrix_z)])*sqrt(M-N-5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many gene pairs have a P value less than 0.01? (use `which` and `length`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "706"
      ],
      "text/latex": [
       "706"
      ],
      "text/markdown": [
       "706"
      ],
      "text/plain": [
       "[1] 706"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(which(pvalues < 0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the sizes of the components in the undirected graph whose edges have `P < 0.01` in the statistical test that you did?  You will need to use `arrayInd`, `cbind`, `graph_from_data_frame`, and `components` (last two of those functions are old friends from `igraph`). As always, print a summary about your graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IGRAPH a6c28de UN-- 164 706 -- \n",
      "+ attr: name (v/c)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "164"
      ],
      "text/latex": [
       "164"
      ],
      "text/markdown": [
       "164"
      ],
      "text/plain": [
       "[1] 164"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "inds_tri <- which(upper.tri(matrix_z))\n",
    "inds_sig <- which(pvalues < 0.01)\n",
    "graph_edge_list <- cbind(arrayInd(inds_tri[inds_sig], \n",
    "                 .dim=c(N,N)))\n",
    "pcor_graph <- graph_from_data_frame(graph_edge_list, directed=FALSE)\n",
    "summary(pcor_graph)\n",
    "components(pcor_graph)$csize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the graph in igraph (make sure you first set the plot options using\n",
    "`igraph_options(vertex.size=1, vertex.label=NA, edge.width=0.3)`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v1+vV7nOM7j8Xi9Xqhon7tHTqVS8Xi80+nQNP0KvTzIpoPXT+QSABq4Xy6Uzuv1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kUqnRaKRpGn2JADOhq/s3Tz/ZZ4nV1VVw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\ngAYA4BQCGgCAU/8PJlvoeLDwaxkAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "igraph_options(vertex.size=1, vertex.label=NA, edge.width=0.3, margin=-5)\n",
    "plot(pcor_graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the graph degree distribution on log-log scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suppressWarnings(\n",
    "\n",
    "    plot(degree.distribution(pcor_graph), log=\"xy\", xlab=\"k\", ylab=\"Pk\")\n",
    "\n",
    ")"
   ]
  }
 ],
 "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}