sujitpal/lung_cancer_data_analysis.ipynb

## lung_cancer_data_analysis.ipynb
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  "name": ""
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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Using Correlation Coefficients to select most predictive Gene Expressions in Lung Cancer Data ###\n",
      "\n",
      "We use Lung Cancer data from the Dana Farber Cancer Institute, available from the [Kent Ridge Bio-Medical Datasets](http://datam.i2r.a-star.edu.sg/datasets/krbd/) page.\n",
      "\n",
      "The data contains gene expression data for 203 individuals. Each record has 12,600 gene expressions so its a very wide record. The target variable (ie, the type of Lung Cancer) can be one of 5 values each corresponding to one type of Lung Cancer - Adenocarcinoma of Lung (ADEN), Squamous Cell Carcinoma (SQUA), Carcinoid (COID), Small Cell Lung Cancer (SCLC) and Normal (NORMAL).\n",
      "\n",
      "Our objective is to analyze this data and find interesting information about Lung Cancer and different gene expressions from it.\n",
      "\n",
      "We will do our analysis with Python so we first import the necessary libraries."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from sklearn import preprocessing\n",
      "from operator import itemgetter\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we read the data into memory. The data is provided as a comma-separated set of 12,600 continuous variables, one line for each individual. The column names (the names of the gene expressions) are provided in a separate file, so we first import that. We also build a targets map that maps the response variable to a number between 0 and 4."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "colf = open(\"../data/lung-harvard.names\", 'rb')\n",
      "targets = {}\n",
      "colnames = []\n",
      "for col in colf:\n",
      "    col = col.strip()\n",
      "    if len(targets) == 0:\n",
      "        targets = {key:value for value, key in enumerate(col.split(\",\"))}\n",
      "        continue\n",
      "    if len(col) == 0: continue\n",
      "    colnames.append(col.split(\":\")[0].strip())\n",
      "colnames.append(\"clazz\")\n",
      "colf.close()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We then read in the data into a Pandas DataFrame object, passing in the column names that we just extracted."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = pd.read_csv(\"../data/lung-harvard.data\", names=colnames)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since we are going to use algorithms in Scikits-Learn to analyze our data, we need to convert this to a form that can be used by them. X is a 203x12600 matrix that contains all our features and y is a 203 element array containing all our response variables. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = data.values[:, 0:-1]\n",
      "y = np.array([targets[v] for v in list(data[\"clazz\"].values)])\n",
      "X, y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "(array([[-18.6, 10.54, 0.01, ..., 13.78, -103.49, 76.98],\n",
        "       [9.12, 9.12, 10.18, ..., -24.85, -34.41, 105.73],\n",
        "       [-2.175, -2.21, -0.0599999, ..., 10.465, -42.63, 73.735],\n",
        "       ..., \n",
        "       [-28.39, -6.2, -19.35, ..., 62.83, -66.2, 96.52],\n",
        "       [13.66, 16.82, -6.11, ..., 88.81, -89.93, 104.64],\n",
        "       [-14.29, -1.17, -0.23, ..., 100.11, -121.13, 87.92]], dtype=object),\n",
        " array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
        "       0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3,\n",
        "       3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
        "       1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]))"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given that the data has been generated from gene sequencers, it is very likely that they are in the same units and comparable, but for purposes of comparison we will just scale them so that they all have a mean of 0 and standard deviation of 1."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "scaler = preprocessing.StandardScaler()\n",
      "X_scaled = scaler.fit_transform(X)\n",
      "X_scaled"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array([[-0.5227063 ,  0.24721654, -0.02648143, ..., -0.40856216,\n",
        "        -0.988903  ,  0.1873709 ],\n",
        "       [ 0.82877933,  0.18378862,  0.50429811, ..., -1.27053044,\n",
        "         0.60904894,  1.18361986],\n",
        "       [ 0.27809282, -0.32229469, -0.03013477, ..., -0.48253122,\n",
        "         0.41890469,  0.07492472],\n",
        "       ..., \n",
        "       [-1.0000167 , -0.5005182 , -1.03689362, ...,  0.6859122 ,\n",
        "        -0.12631429,  0.86447367],\n",
        "       [ 1.05012654,  0.52772873, -0.34588859, ...,  1.26561544,\n",
        "        -0.67523438,  1.14584903],\n",
        "       [-0.31257271, -0.27584044, -0.0390072 , ...,  1.51775734,\n",
        "        -1.39694979,  0.56646529]])"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now try to find the features that are most important to decide the type of lung cancer, given the data. To do this, let us find the features that are most highly correlated (positively or negatively) with the target variable."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "corrs = []\n",
      "for col in range(0, np.shape(X)[1]):\n",
      "    corrs.append(np.abs(np.corrcoef(y, X_scaled[:, col])[0,1]))\n",
      "corrs_sorted = sorted(enumerate(corrs), key=itemgetter(1), reverse=True)\n",
      "print \"Top Gene Expression Features\"\n",
      "for corr in corrs_sorted[0:10]:\n",
      "    print \"%s: %f\" % (colnames[corr[0]], corr[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Top Gene Expression Features\n",
        "40841_at: 0.704324\n",
        "32542_at: 0.700063\n",
        "36569_at: 0.673899\n",
        "35868_at: 0.673499\n",
        "607_s_at: 0.670205\n",
        "32780_at: 0.660389\n",
        "38177_at: 0.659326\n",
        "36207_at: 0.658311\n",
        "38995_at: 0.656257\n",
        "40607_at: 0.654112\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Scatterplots of the top 2 features. Both variables are positively correlated."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(X[:,corrs_sorted[0][0]], y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.collections.PathCollection at 0x9920890>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eCAQC2LNnD8LCwkASSUlJaG1txZ49exAdHY2amhokJyfD7XZ/7TlqaWnBnj17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\nCnkRERtTyIuI2JhCXkTExhTyIiI29v8BRPfNApA6c2QAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5763c90>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.scatter(X[:,corrs_sorted[1][0]], y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.collections.PathCollection at 0x7610c10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x98791d0>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another way to look at the data is to look at the distribution of the features for each target variable. As before, we choose only the top 2 features and construct box plots for subsets of the data corresponding to the output variable."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def make_box_plot(feat_col):\n",
      "    distribs = []\n",
      "    for target in targets.keys():\n",
      "        data_filt = data[data[\"clazz\"] == target]\n",
      "        feats = list(data_filt[colnames[feat_col]])\n",
      "        distribs.append(feats)\n",
      "    bp = plt.boxplot(distribs)\n",
      "\n",
      "make_box_plot(corrs_sorted[0][0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DETwA5Bgjf2RN0+8iKSsstPf2AUAyMOAX/lXHGV/bAGChaNEAgKGMG8EDwFzEZUk2t3Ov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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x993fed0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "make_box_plot(corrs_sorted[1][0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x75f7f50>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As can be seen in the box plots for the two genes, both genes seem to be under-expressed for lung cancer patients. The 3rd boxplot represents NORMAL, and as you can see, in both cases, the distributions of values of expressions for the two genes we considered are on average much higher for NORMAL (ie not lung cancer patients)."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}