notebooks/Pairwise analyses of simulated data.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pairwise analyses of simulated data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we explore our hypothesis that differences in tumour-specific alteration rates affect the validity of co-occurrence and mutual exclusivity tests that assume independent and identically distributed (i.i.d.) events. To this end, we first generate simulated alteration data that resemble clinical tumours, but do not contain any dependencies between alterations. Next, we add simulated co-occurrences and mutual exclusivities to these data.\n",
    "\n",
    "Based on these simulated data sets, we assess the sensitivity and specificity of two i.i.d. tests&mdash;the Binomial test and Fisher's exact test&mdash;and our DISCOVER test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"../lib\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "import pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import nbsupport.plots\n",
    "import nbsupport.simulations\n",
    "import nbsupport.util"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nbsupport.util.set_random_seed()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from discover.util import disableStackLimit\n",
    "disableStackLimit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Independent alterations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We generate a simulated alteration matrix that resembles the copy number data of the TCGA breast cancer tumours. The code below requires that the TCGA data have already been downloaded (see the notebook [Download PanCan12 data](Download PanCan12 data.ipynb))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dataFile = \"../data/tcga/tcga-pancan12.h5\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cn = pandas.read_hdf(dataFile, \"/data/BRCA/cn\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "geneMarginals = (cn == 2).sum(1)\n",
    "sampleMarginals = (cn == 2).sum(0)\n",
    "events = pandas.DataFrame(nbsupport.simulations.generate_independent_alterations(geneMarginals, sampleMarginals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plot shows that the alteration frequencies per gene (top plot) and per tumour (bottom plot) in the simulated data resemble those of the breast cancer tumours."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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xdOlSFi9ezC9/+UuuuOIKGhoaWLJkCR0dHTz44INs2LCB2bNns2zZMhYtWsTM\nmTNxbJt1VekI5izgWUk/BP4TeBg4PiKa0vkLgTOBk4DmiGiPiCLwAnAskAcWldU9o8J+mPWrRx55\nhFGjRjFhwgTOP/98xo8fz+rVqykUCgCMGzeOxx57jJUrV5LP56mqqqK6upqRI0eCY9usi6oKl/sA\nyahlPPBRkiRTnqxKQDWQA1rLyl8HarqVd9Y1G3C/+c1v+OUvf8nDDz/Mz3/+c84//3w6Ojq2zs/l\nchSLRUqlEjU1NVvLhw0bBo5tsy4qTTAbgecioh14XtLbwEfK5ueATUCRrjtYDngtLc91q7sNSWNJ\nTsEBHNpbPbP+ctBBB1FbW0tVVRVHHHEEQ4cO5Ve/+tXW+aVSieHDh1NdXU2xWOxSjmPbrItKT5E1\nk1xTQdKHgQOAx9NrMwDjgCZgFZCXNFhSDXAU8CywFDgnrXtOWncbEbE4ImZFxCxgHd4JLWP5fJ5F\ni5IzXC+//DJvvPEGn/zkJ1myZAkACxcupFAoUFdXR3NzM21tbbS2ttLS0gKObbMuKhrBRMR8SQVJ\nKwGRXNhcB3wzvdD5HHB/RISkO0gSkkhuAmiTNAe4W1ITsBm4sB+2xazPzj33XJqamjjppJOICObM\nmcOhhx7KJZdcwpYtW6itrWXSpElIYvr06eTzeSKChoYGJkyY4Ng2K6OIGOg+7BRJiwEiYmwly9fU\nHB3F4poe5+VytaxY8QNqa2sr7p8ZyUHUe1+oj7Et3RpweQ9zlnPkkTNoaVleyWrNOlUU1+AHLc3M\nLCNOMGZmlgknGDMzy4QTjJmZZcIJxszMMuEEY2ZmmXCCMTOzTDjBpAqFM5HU47+DDz50oLtnVpEX\nX/xZr3Ht2LasVfousr3Oxo2/Bnp+6HTDhoqfMzIbUO+8U6K3uAbHtmXLIxgzM8uEE4yZmWXCCcbM\nzDLhBGNmZplwgjEzs0w4wZiZWSacYMzMLBNOMGZmlgknGDMzy4QTjJmZZcIJxszMMtGnBCPpQ5J+\nKekISR+T1CRpiaQ7y+pMkbRK0lJJ56ZlQyXdL6lR0sOSDurrhpj1p1deeYU/+IM/4Pnnn2ft2rUU\nCgXGjBnDtGnTttaZO3cudXV11NfXM3/+fMCxbVau4gQjqQr4J+DNtOgW4OqIGAMMkvRpSSOAy4BT\ngbOBGyXtB0wFnomI0cA9wLV92AazftXe3s6ll17K/vvvD8AVV1xBQ0MDS5YsoaOjgwcffJANGzYw\ne/Zsli1gbXx5AAALwElEQVRbxqJFi5g5cyaObbOu+jKCuRmYA7wMCDg+IprSeQuBM4GTgOaIaI+I\nIvACcCyQBxaV1T2jD/0w61dXXnklU6dO5cMf/jARwerVqykUCgCMGzeOxx57jJUrV5LP56mqqqK6\nupqRI0eCY9usi4oSjKQ/A16JiMdIkkv3dZWAaiAHtJaVvw7UdCvvrGs24P7t3/6ND33oQ5x55plE\nJK+57+jo2Do/l8tRLBYplUrU1NRsLR82bBg4ts26qPT7YP4c6JB0JslR27eBD5bNzwGbgCJdd7Ac\n8FpanutWdxuSxgJj08lDe6tn1l/uuusuBg0axGOPPcbTTz/NxRdfzKuvvrp1fqlUYvjw4VRXV1Ms\nFruU49g266KiEUxEjImI0yLiNOCnwEXAQkmj0yrjgCZgFZCXNFhSDXAU8CywFDgnrXtOWrendhZH\nxKyImAWswzuhZWzJkiU8+eSTPPnkk3z84x/nnnvuYdy4cTQ2NgKwcOFCCoUCdXV1NDc309bWRmtr\nKy0tLeDYNuuiP7/R8kpgbnqh8zng/ogISXcAzSSn0q6OiDZJc4C7JTUBm4EL+7EfZv3q5ptvZsqU\nKWzZsoXa2lomTZqEJKZPn04+nyciaGhoYMKECY5tszLqPM+8u5O0GCAixlayfE3N0VEsrulxXi5X\nS6nUQu9fLSv2lN+TDaiKvn+4r7Et3RpweQ9zlpPcwLm92HVs2w5V/L3aftDSzMwy4QRjZmaZcIIx\nM7NMOMGYmVkmnGDMzCwTTjBmZpYJJxgzM8uEE4yZmWXCCcbMzDLhBGNmZplwgjEzs0w4wZiZWSac\nYMzMLBNOMGZmlgknGDMzy4QTjJmZZcIJxszMMuEEY2ZmmXCCMTOzTDjBmJlZJipKMJKqJH1bUqOk\n5ZLOk/QxSU2Slki6s6zuFEmrJC2VdG5aNlTS/enyD0s6qL82yKwv2tvbufjiixk9ejSnnHIKDz30\nEGvXrqVQKDBmzBimTZu2te7cuXOpq6ujvr6e+fPnA45ts3KVjmD+FPhNRIwGzgb+EbgFuDoixgCD\nJH1a0gjgMuDUtN6NkvYDpgLPpMvfA1zbx+0w6xf33nsvH/jAB2hsbGTRokX89V//NVdccQUNDQ0s\nWbKEjo4OHnzwQTZs2MDs2bNZtmwZixYtYubMmTi2zbqqqnC5fwe+n35+H9AOHB8RTWnZQuBTQAfQ\nHBHtQFHSC8CxQB74Rlld74S2W/jsZz/LZz7zGQDeeecdqqqqWL16NYVCAYBx48bx6KOPMmjQIPL5\nPFVVVVRXVzNy5EjWrFnj2DYrU9EIJiLejIg3JOVIEs2XAZVVKQHVQA5oLSt/HajpVt5Z12zA7b//\n/hxwwAGUSiU+85nP8LWvfY2I2Do/l8tRLBYplUrU1NRsLR82bBg4ts26qPgiv6TfB54A7o6I75GM\nVjrlgE1Aka47WA54LS3PdavbUxtjJc2SNAs4FBheaX/Ndtb69es5/fTTmTx5Mp///OcZNOjd3aRU\nKjF8+HCqq6spFotdynFsm3VR6UX+EcAjwN9ExN1p8VOSRqefxwFNwCogL2mwpBrgKOBZYClwTlr3\nnLTuNiJicUTMiohZwDp62VnN+suGDRs466yz+Pu//3smT54MwHHHHUdjYyMACxcupFAoUFdXR3Nz\nM21tbbS2ttLS0gKObbMuKr0GM5PkiOtaSdcBAXwRmJ1e6HwOuD8iQtIdQDPJKbSrI6JN0hzgbklN\nwGbgwr5uiFl/uPHGG9m0aRM33HAD119/PZK4/fbbueyyy9iyZQu1tbVMmjQJSUyfPp18Pk9E0NDQ\nwIQJExzbZmVUfn55dyZpMUBEjK1k+Zqao6NYXNPjvFyullKphSRP9tg6e8rvyQaUdlylh4X6GNvS\nrQGX9zBnOckNnNuLXce27VBFcQ1+0NLMzDLiBGNmZplwgjEzs0w4wZiZWSacYMzMLBNOMGb7tCFI\n6vHfwQcfOtCdsz2cE8xO8U5oe6vNJLcxb/tvw4aXBrJjtheo9EHLfUznTritDRsqvkXczGyv5hGM\nmZllwgnGzMwy4QRjZmaZcIIxM7NMOMGYmVkmnGAydvDBh/oWZ9vrbC+uHdvWybcpZyx5lsC3ONve\nZXtxncx3bJtHMGZmlhGPYPosecrfzMy68gimz3p/1cb2v0lwYOzo3Pn73neAz6vbPsfXSrPhEcw+\nZkfnzjs61Ot8n1ff1/RldN77siNGHMJ///e6inuVBV8rzYZHMGbWi+2Nzitfds97iaZfdlupAUsw\nSsyRtFTSE5I+OlB9GTjZBO72hvuWPcf27mdHp4a3b29KlrvWQI5gJgBDIqIemAncMoB9GSCVB+72\ndph3h/v9fU3IR3I7ybE9ACrfJ/qyX/S+T3i/GNhrMHlgEUBErJB04gD2ZTe0M+e/e9sxshqp+GsL\ndpJje7t6j+1Bg/ano+PNXpfc0fzdaZ8A7xcDmWCqgday6XZJgyKiI4vG3nprHdXV5/Uyb30WTfbR\n9gM3ux2mUttPiNv7w7C9ebvjBeGdsEtje+jQbzJ48BPblL/zzmu88UYWLfZV77G9vZtMdjx/d9sn\noNJk2pdEuzvtMwOZYIpArmx6mx1Q0lhgbDo5FPhVpY21tZX6EH3b+0O/o+F1pcvuaet9ewfr3afs\n0th+663/MwCxvafF50Ctd9/eLxQxMM9qSPojYHxEfEHSKcC1EXHugHTGrB85ts0SA5lgBPxv4Ji0\n6M8j4vkB6YxZP3JsmyUGLMGYmdnezQ9amplZJpxgzMwsE04wZmaWCScYMzPLhBOMmZllYp94Xb+k\n24CPD3Q/bK/304iYsSsbdGzbLlBxXO9LI5jh+2Db3uZd6yMD1O6++Lv2Nu86lcd1ROwT/4BZ+1rb\n3uZ9o+19rV1v857T7r40gjEzs13ICcbMzDKxLyWYxftg2wPV7kC2PVDtDmTb+1q7A9n2QLU7kG1X\n3K7fRWZmZpnYl0YwZma2CznBmJlZJvb6BKPEHElLJT0h6aO7oM2fpG09IelfJX1MUpOkJZLuzKC9\nkyU9mX7usS1JUyStSn8P/fLlV93a/bikX5Vt92eyaFdSlaRvS2qUtFzSebtim3tpd5ds83b6tEtj\ne1fHddqmY3tPju2Buqd7F97DPRH4Vvr5ZOCHGbc3BPhJt7IHgUL6eQ7w6X5s70vAM8DS3toCRqR1\nqki+L/4ZYL9+bvcvgMu71cmi3T8Dbkk/Dwde2hXb3K3dA9N2v7Artnl3iO1dHdeO7b0jtvf6EQyQ\nBxYBRMQK4MSM2zsWOEDSI5J+JOlk4PiIaErnLwTO6Mf2XiT5Q9PphG5tnQmcBDRHRHtEFIEXePfb\nFvutXeDc9EhrrqRhGbX778C16ef3Ae1s+/vNYpvL2x0EbCHZ5vG7YJt7sytje1fHNTi29/jY3hcS\nTDXQWjbdLinL7X4TuCkizgKmAt8BVDa/BNT0V2MR8QBJIHbq3lY1kKPr7+D1vvahh3ZXAF+KiDHA\nz4GvsO3vvj/afTMi3pCUA74PfJldsM09tHsNsBK4Mutt3o5dGdu7NK7Bsc1eENv7QoIpkvyHdBoU\nER0Ztvc8yc5HRLwAbCQZWnbKAZsybL982zrbKpIER5Z9+GFEPNX5meQFjK1ZtCvp94EngLsj4nvs\nom3uod1dts292JWxPdBxDY7tPS6294UE82PgHABJpwBrMm7vC8A/pO19mOQ/5FFJY9L544CmXpbt\nD6slje7W1iogL2mwpBrgKODZfm73EUmdp2g+Cfwki3YljQAeAf4mIu5Oi5/Kept7aXeXbPN27MrY\nHui4Bsf2nhfbfbkotSf8IxliziHZGX8MHJFxe/sB96aBsITk4uvhJE/D/hj4JukDrv3Y5iG8e0Fy\nZE9tkVyoXJkGyYQM2j0OaCY5CpoHDMuiXeA24OW0nSfTn0dnvc29tHvqrtjm3SG2ByKuHdt7fmz7\nSX4zM8vEvnCKzMzMBoATjJmZZcIJxszMMuEEY2ZmmXCCMTOzTDjBmJlZJpxgzMwsE04wZmaWif8P\neK1dz5sEqBQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f806ade1b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f805890f910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    bins = numpy.linspace(0, max(events.sum(1).max(), (cn == 2).sum(1).max()), 20)\n",
    "    plt.suptitle(\"Gene marginals\")\n",
    "    plt.subplot(121)\n",
    "    plt.title(\"Simulated\")\n",
    "    plt.hist(events.sum(1), bins)\n",
    "    plt.subplot(122, sharex=plt.gca(), sharey=plt.gca())\n",
    "    plt.title(\"TCGA BRCA\")\n",
    "    plt.hist((cn == 2).sum(1), bins)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "with nbsupport.plots.use_custom_style():\n",
    "    bins = numpy.linspace(0, max(events.sum(0).max(), (cn == 2).sum(0).max()), 20)\n",
    "    plt.suptitle(\"Sample marginals\")\n",
    "    plt.subplot(121)\n",
    "    plt.title(\"Simulated\")\n",
    "    plt.hist(events.sum(0), bins)\n",
    "    plt.subplot(122, sharex=plt.gca(), sharey=plt.gca())\n",
    "    plt.title(\"TCGA BRCA\")\n",
    "    plt.hist((cn == 2).sum(0), bins)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "genesMinFreq50 = numpy.where(events.sum(1) >= 50)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import discover"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model0 = discover.DiscoverMatrix(pandas.DataFrame(events))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "def estimate_binomial_background(events):\n",
    "    return numpy.repeat(events.mean(1)[:, numpy.newaxis], events.shape[1], 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "modelBinom0 = discover.DiscoverMatrix(\n",
    "    pandas.DataFrame(events),\n",
    "    pandas.DataFrame(estimate_binomial_background(events)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nullGenes1 = numpy.random.choice(genesMinFreq50, len(genesMinFreq50) / 2, False)\n",
    "nullGenes2 = numpy.setdiff1d(genesMinFreq50, nullGenes1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "group = numpy.repeat([0, 1], [len(nullGenes1), len(nullGenes2)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing for mutual exclusivities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first test for mutual exclusivity using the DISCOVER test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_mutex0_poisbinom = discover.pairwise_discover_test(model0[numpy.r_[nullGenes1, nullGenes2]], group)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8BMbZwLGR5eUkW1ZZ9yCDTw+b1ap9UQP/BZDkTcATq+pvplDjpKzaF0l2A78N/DqQKdQ2\naWv9j5wDXAi8D7gEuCTJ4mTLm6i1+gLgn4AvA18FPltVxydZ3KRV1U3A8gqrOu075yEwjgM7R5a3\nVNUjI+vOHlm3Ezg6qcKmYK2+ePT47bXATwGvmnRxE7ZWX/ws8GTgc8DbgZ9P8osTrm+S1uqLB4D7\nquqeqlpm8On79E/dm8mqfZHkx4HLgR8CFoBzk/z0xCucDZ32nfMQGLcDLwVI8nwGnwwedRj4kSRP\nGp7Iuxj428mXODFr9QXAhxmcw3jFyKGpzWrVvqiq91fVc6vqRcAfAJ+sqk9Mp8yJWOvv4l+B7xo5\n+ftCBp+yN6u1+uIYcAI4WYMD+d9gcHjq8eD0kXanfec8fPngTcCLk9w+XL4yyWsYHHK5IclbgL9m\n0CE3VNV/TqvQCVi1LxgMs68EDg5nRBTw3qr68+mUuuHW/LuYYl3TsN7/yC8Df5oEBic/90+r0AlY\nry8+DBxKchL4F+BjU6pz0goGMykZY9/pld6SpCbzcEhKkjQDDAxJUhMDQ5LUxMCQJDUxMCRJTQwM\nSVITA0OS1MTAkCQ1+T+FOy2nJx5e2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8058848590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    plt.hist(numpy.diag(result_mutex0_poisbinom.pvalues.values[:len(nullGenes1), len(nullGenes1):]), 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And next using the Binomial test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_mutex0_binom = discover.pairwise_discover_test(modelBinom0[numpy.r_[nullGenes1, nullGenes2]], group)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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scLTuiTx82AEWaCXkXAkZwZzLzZzLa6XkfPSi16iqo+4DeMOwMxwtOVdCRnOac9Q/juac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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80587de2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    plt.hist(numpy.diag(result_mutex0_binom.pvalues.values[:len(nullGenes1), len(nullGenes1):]), 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing for co-occurrences"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we test for co-occurrence using the DISCOVER test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_cooc0_poisbinom = discover.pairwise_discover_test(model0[numpy.r_[nullGenes1, nullGenes2]], group, \"greater\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4XuBJ4+W1ftXPXYxC9Fidtp2rITA2A/dPLB9Ksu446x5gtPewVh13LGrkfwCSvBV4clX9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f805b114050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    plt.hist(numpy.diag(result_cooc0_poisbinom.pvalues.values[:len(nullGenes1), len(nullGenes1):]), 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And using the Binomial test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_cooc0_binom = discover.pairwise_discover_test(modelBinom0[numpy.r_[nullGenes1, nullGenes2]], group, \"greater\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UVd84oAeVJM2LA14ikqSFyxvckqRmlogkqZklIklqZolIkppZIpKkZpaIJKnZgvt7Ikmu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\n+wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f805b6b4210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    plt.hist(numpy.diag(result_cooc0_binom.pvalues.values[:len(nullGenes1), len(nullGenes1):]), 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mutual exclusivities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we add simulated mutual exclusivities to the alteration matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eventsWithMutex, indexes = nbsupport.simulations.add_mutual_exclusivities(events)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We test for mutual exclusivity using the DISCOVER test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "modelMutex = discover.DiscoverMatrix(pandas.DataFrame(eventsWithMutex))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "groupMutex = numpy.repeat([0, 1], 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_mutex_poisbinom = discover.pairwise_discover_test(modelMutex[numpy.r_[indexes[:, 0], indexes[:, 1]]], groupMutex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gSJKaGBiSpCYGhiSpiYEhSWqyqgPjP/7j30jS93HOORtHXaYkrQhLvkXrSlB1GKi+Y558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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f805b52c450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    plt.hist(numpy.diag(result_mutex_poisbinom.pvalues.values[:len(indexes), len(indexes):]), 20)\n",
    "    plt.xlim(0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And using the Binomial test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "modelMutexBinom = discover.DiscoverMatrix(\n",
    "    pandas.DataFrame(eventsWithMutex),\n",
    "    pandas.DataFrame(estimate_binomial_background(eventsWithMutex)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_mutex_binom = discover.pairwise_discover_test(modelMutexBinom[numpy.r_[indexes[:, 0], indexes[:, 1]]], groupMutex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aDIYkqcVgSJJaDIYkqcVgSJJaDIYkqeX/AK9lg0XX+24hAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7fb765a6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    plt.hist(numpy.diag(result_mutex_binom.pvalues.values[:len(indexes), len(indexes):]), 20)\n",
    "    plt.xlim(0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Co-occurrences"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we add simulated co-occurrences to the alteration matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eventsWithCooc, coocIndexes = nbsupport.simulations.add_cooccurrences(events)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We test for co-occurrence using the DISCOVER test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "modelCooc = discover.DiscoverMatrix(pandas.DataFrame(eventsWithCooc))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "groupCooc = numpy.repeat([0, 1], 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_cooc_poisbinom = discover.pairwise_discover_test(modelCooc[numpy.r_[coocIndexes[:, 0], coocIndexes[:, 1]]], groupCooc, \"greater\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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p1vxzMeBcQ1jv78ivA3+WBEY3P28datAZWG8tPgksJ3kE+A7wJwPNOWsFo5+k5Ek8d/pJ\nb0lSy3Z4S0qStAUYDElSi8GQJLUYDElSi8GQJLUYDElSi8GQJLUYDElSy/8BbP1sres2w/wAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f805b127490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    bins = numpy.linspace(0, 1, 20)\n",
    "    plt.hist(numpy.diag(result_cooc_poisbinom.pvalues.values[:len(coocIndexes), len(coocIndexes):]), bins)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And using the Binomial test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "modelCoocBinom = discover.DiscoverMatrix(\n",
    "    pandas.DataFrame(eventsWithCooc),\n",
    "    pandas.DataFrame(estimate_binomial_background(eventsWithCooc)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_cooc_binom = discover.pairwise_discover_test(modelCoocBinom[numpy.r_[coocIndexes[:, 0], coocIndexes[:, 1]]], groupCooc, \"greater\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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p1vxzMeBcQ1jv78ivA3+WBEY3P28datAZWG8tPgksJ3kE+A7wJwPNOWsFo5+k5Ek8d/pJ\nb0lSy3Z4S0qStAUYDElSi8GQJLUYDElSi8GQJLUYDElSi8GQJLUYDElSy/8BbP1sres2w/wAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f805b5f3490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    bins = numpy.linspace(0, 1, 20)\n",
    "    plt.hist(numpy.diag(result_cooc_binom.pvalues.values[:len(coocIndexes), len(coocIndexes):]), bins)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fisher's exact test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To illustrate that the issues observed with the Binomial test also affect Fisher's exact test, we repeat the same analyses below, this time using Fisher's exact test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing for co-occurrence in independent alterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pCoocFisher0 = numpy.array([\n",
    "        scipy.stats.fisher_exact(numpy.histogram2d(events.values[gene1], events.values[gene2], 2)[0], \"greater\")[1]\n",
    "        for gene1, gene2 in zip(nullGenes1, nullGenes2)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+s/WAO3ZMDMGfNc3t5D88+3h2HmrQfPKEt49jMXipmo8T1QwH6LyM/RhwZrfpmqp6/Kge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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8058474250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    plt.hist(pCoocFisher0, numpy.linspace(0, 1, 21))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing for mutual exclusivity in independent data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pMutexFisher0 = numpy.array([\n",
    "        scipy.stats.fisher_exact(numpy.histogram2d(events.values[gene1], events.values[gene2], 2)[0], \"less\")[1]\n",
    "        for gene1, gene2 in zip(nullGenes1, nullGenes2)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f805b301b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    plt.hist(pMutexFisher0, numpy.linspace(0, 1, 21))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing for co-occurrence in co-occurring gene pairs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pCoocFisher = numpy.array([\n",
    "        scipy.stats.fisher_exact(numpy.histogram2d(eventsWithCooc[gene1], eventsWithCooc[gene2], 2)[0], \"greater\")[1]\n",
    "        for gene1, gene2 in coocIndexes])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qbh1m1A236vfFgHMNYa2/I28F/iwJjC5+3jbUoDOw1lp8ElhK8gjwL8BnBppz1gpGv0nJ\nk3ju9JPekqSWrfCWlCRpEzAYkqQWgyFJajEYkqQWgyFJajEYkqQWgyFJajEYkqSW/wfgdW0C4pdy\nWQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8058b0cd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    plt.hist(pCoocFisher, numpy.linspace(0, 1, 21))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing for mutual exclusivity in mutually exclusive gene pairs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pMutexFisher = numpy.array([\n",
    "        scipy.stats.fisher_exact(numpy.histogram2d(eventsWithMutex[gene1], eventsWithMutex[gene2], 2)[0], \"less\")[1]\n",
    "        for gene1, gene2 in indexes])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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A5oHrJ1TV0YH75gbu2wwcGNdgHVhpWzx5/PZjwGuBXx33cGO20rZ4C/DTwN8Dvw/8RpK3\njXm+cVppWzwCPFBV36uqRXq/fR/7W/csOe62SPIS4ALg+cB2YGuSXxv7hJNhqOfOaQjGncCvACR5\nJb3fDJ50P/DzSU7tn8g7D/jH8Y84NittC4Av0DuH8eaBQ1Oz6rjboqo+VVUvr6rXAH8CfKWqvtzN\nmGOx0s/Fg8BzBk7+/iK937Jn1Urb4iDwGPB49Q7k/xe9w1PPBMfuaQ/13DkNHz54I/D6JHf2r78j\nycX0Drl8Mcn7gFvpbZAvVtV/djXoGBx3W9DbzX4HsLv/iogC/ryqbu5m1HW34s9Fh3N1YbV/I+8E\n/joJ9E5+3tLVoGOw2rb4ArAnyePAvwFf6mjOcSvovZKSNTx3+k5vSVKTaTgkJUmaAAZDktTEYEiS\nmhgMSVITgyFJamIwJElNDIYkqYnBkCQ1+T/PwBQpFsj/YAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80587fbc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    plt.hist(pMutexFisher, numpy.linspace(0, 1, 21))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Similar alteration rates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we show that the Binomial test does not have problems if the alteration rates per tumour are more homogeneous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "iidEvents = numpy.row_stack([\n",
    "        numpy.random.permutation(row == 2).astype(int)\n",
    "        for row in cn.values])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plot shows that the alteration frequences per gene still resemble those of the TCGA breast tumours. In contrast, the alteration frequencies per tumour are much more homogeneous than in the breast cancer data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fvpy6ujrq6+tZuXIl4No2K1dxwEiqAv4ReDltuha4PCIagHGSPiJpKnAJcCpw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\nykn4aGT+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f805b6af710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Fch1wg6QGsrOupgAvA9dK2h5YBtwRESFpLtBItotrVkS8UZ5um22dadOmMXXqVKqrq6mo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\nIZ18xwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f805862fc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    bins = numpy.linspace(0, max(iidEvents.sum(1).max(), (cn == 2).sum(1).max()), 20)\n",
    "    plt.suptitle(\"Gene marginals\")\n",
    "    plt.subplot(121)\n",
    "    plt.title(\"Simulated\")\n",
    "    plt.hist(iidEvents.sum(1), bins)\n",
    "    plt.subplot(122, sharex=plt.gca(), sharey=plt.gca())\n",
    "    plt.title(\"TCGA BRCA\")\n",
    "    plt.hist((cn == 2).sum(1), bins)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "with nbsupport.plots.use_custom_style():\n",
    "    bins = numpy.linspace(0, max(iidEvents.sum(0).max(), (cn == 2).sum(0).max()), 20)\n",
    "    plt.suptitle(\"Sample marginals\")\n",
    "    plt.subplot(121)\n",
    "    plt.title(\"Simulated\")\n",
    "    plt.hist(iidEvents.sum(0), bins)\n",
    "    plt.subplot(122, sharex=plt.gca(), sharey=plt.gca())\n",
    "    plt.title(\"TCGA BRCA\")\n",
    "    plt.hist((cn == 2).sum(0), bins)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing for mutual exclusivity in independent data results in a much more uniform $P$-value distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "modelBinomIid0 = discover.DiscoverMatrix(\n",
    "    pandas.DataFrame(iidEvents),\n",
    "    pandas.DataFrame(estimate_binomial_background(iidEvents)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_iid_mutex0_binom = discover.pairwise_discover_test(modelBinomIid0[numpy.r_[nullGenes1, nullGenes2]], group)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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N/DdAkrcBp1fV3wxQ46wcty+SLAG/DvwSkAFqm7W1/kaeDpwHfAi4CLgoycpsy5uptfoC\n4F+ALwG3AZ+rqoOzLG7Wquo64NAxVnX67lyEwDgIbJ1Y3lRVhyfWbZtYtxU4MKvCBrBWXzx2/PYD\nwA8BPzLr4mZsrb74MeBpwF8C7wJ+PMlPzbi+WVqrL+4D7qqqO6rqEKO976P3ujeS4/ZFku8HXgU8\nG1gGdiT50ZlXOB86fXcuQmDcBLwSIMm5jPYMHrMP+J4kTx2fyLsA+LvZlzgza/UFwEcZncN47cSh\nqY3quH1RVb9XVS+qqpcBvw18qqo+OUyZM7HW78W/A98ycfL3pYz2sjeqtfrifuAh4JEaHcj/GqPD\nU08ER4+0O313LsLNB68DXp7kpvHypUnewOiQyzVJ3g78NaMOuaaq/muoQmfguH3BaJh9KbBnPCOi\ngA9W1WeHKXXdrfl7MWBdQzjR38jPAX+cBEYnP3cNVegMnKgvPgrsTfII8BXgEwPVOWsFo5mUTPHd\n6ZXekqQmi3BISpI0BwwMSVITA0OS1MTAkCQ1MTAkSU0MDElSEwNDktTEwJAkNfk/gjXDnwMB31sA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80585a2b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    bins = numpy.linspace(0, 1, 20)\n",
    "    plt.hist(numpy.diag(result_iid_mutex0_binom.pvalues.values[:len(nullGenes1), len(nullGenes1):]), bins)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same is true for co-occurrences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_iid_cooc0_binom = discover.pairwise_discover_test(modelBinomIid0[numpy.r_[nullGenes1, nullGenes2]], group, \"greater\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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k8C17Vq3XF08BTwPP5mBH/lcZ7J46FZw40m702TkNkw/eBrwpIu4ZLl8REe9gsMvl5oh4\nD/BFBh1yc2b+V1eFTsCafcFgmH0FsDT8RUQCv5+Zf9pNqRtu3fdFh3V14WT/I78E/GFEwODg54Gu\nCp2Ak/XFp4C7I+JZ4N+AWzuqc9ISBr+kZIzPTs/0liSVTMMuKUlSDxgYkqQSA0OSVGJgSJJKDAxJ\nUomBIUkqMTAkSSUGhiSp5P8B+x1U9HmVKToAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f805b410d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with nbsupport.plots.use_custom_style():\n",
    "    bins = numpy.linspace(0, 1, 21)\n",
    "    plt.hist(numpy.diag(result_iid_cooc0_binom.pvalues.values[:len(nullGenes1), len(nullGenes1):]), bins)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}