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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Classifying pediatric IBD stool samples (work in progress)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This notebook is a recoding of the analysis used in the PLoSONE paper: [Non-Invasive Mapping of the Gastrointestinal Microbiota Identifies Children with Inflammatory Bowel Disease](http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0039242) using python, sklearn and pandas.\n",
      "\n",
      "[We](http://almlab.mit.edu) decided that the SLiME package, as it was packaged for the publication of the paper, should not be available anymore. This notebook replaces it, replicating the analysis executed on the paper with more up-to-date tools and (hopefully soon) expanding on its conclusion. \n",
      "I hope this can be the starting point for others trying to follow the same approach and improve upon it. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy import interp\n",
      "from sklearn.ensemble import RandomForestClassifier\n",
      "from sklearn.multiclass import OneVsRestClassifier\n",
      "from sklearn.cross_validation import cross_val_score, StratifiedKFold, train_test_split, KFold\n",
      "from sklearn.metrics import roc_curve, roc_auc_score, auc\n",
      "from sklearn.preprocessing import LabelEncoder, label_binarize"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Loading data\n",
      "The data came from two rounds of 16S sequencing of previously collected stool samples. Here we will use the OTU tables directly, which were created by using the RDP classifier and were subsequently normalized (details in the paper's methods).\n",
      "\n",
      "Sequencing was performed at the [Broad Institute](https://www.broadinstitute.org/). The first round of sequencing was dubbed CHIMP (Children Hospital IBD Pediatric), while the second round of sequencing -- performed following the request of an anonymous peer reviewer -- was termed 'blind validation'. Its purpose was to further validate the algorithm trained on the CHIMP dataset, as the reviewer did not think sufficient a \"leave 20% out\" approach on CHIMP was sufficient to demonstrate robust prediction. These were used as training and test set in the last figure of the paper respectively.\n",
      "\n",
      "It is useful to join the two data sets here."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#get the CHIMP training data\n",
      "\n",
      "X_chimp = pd.read_csv('data/chimp/chimp.Qsorted.rdpout.xtab.norm', delimiter=\"\\t\", index_col=0)\n",
      "y_chimp = pd.read_csv('data/chimp/sampledata.training.chimp.csv', index_col=0)\n",
      "\n",
      "#just make sure the labels are the same\n",
      "X_chimp.sort_index(inplace=True)\n",
      "y_chimp.sort_index(inplace=True)\n",
      "assert (X_chimp.index == y_chimp.index).all()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "## do the same for the blind validation test data\n",
      "X_blind = pd.read_csv('data/chimp/blind.sorted.rdpout.xtab.norm',\n",
      "                        delimiter=\"\\t\", index_col=0)\n",
      "y_blind = pd.read_csv('data/chimp/sampledata.validation.blind.csv',\n",
      "                        index_col=0)\n",
      "\n",
      "X_blind.sort_index(inplace=True)\n",
      "y_blind.sort_index(inplace=True)\n",
      "assert (X_blind.index == y_blind.index).all()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#concatenate using pandas\n",
      "X = pd.concat([X_chimp, X_blind], keys=['chimp','blind'])\n",
      "X.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th>cls_Actinobacteria</th>\n",
        "      <th>cls_Alphaproteobacteria</th>\n",
        "      <th>cls_Bacilli</th>\n",
        "      <th>cls_Bacteroidia</th>\n",
        "      <th>cls_Betaproteobacteria</th>\n",
        "      <th>cls_Clostridia</th>\n",
        "      <th>cls_Cyanobacteria</th>\n",
        "      <th>cls_Deltaproteobacteria</th>\n",
        "      <th>cls_Epsilonproteobacteria</th>\n",
        "      <th>cls_Erysipelotrichi</th>\n",
        "      <th>...</th>\n",
        "      <th>phylum_Euryarchaeota</th>\n",
        "      <th>phylum_Firmicutes</th>\n",
        "      <th>phylum_Fusobacteria</th>\n",
        "      <th>phylum_Lentisphaerae</th>\n",
        "      <th>phylum_NA</th>\n",
        "      <th>phylum_Proteobacteria</th>\n",
        "      <th>phylum_Spirochaetes</th>\n",
        "      <th>phylum_Synergistetes</th>\n",
        "      <th>phylum_TM7</th>\n",
        "      <th>phylum_Verrucomicrobia</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th rowspan=\"5\" valign=\"top\">chimp</th>\n",
        "      <th>003A</th>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.000549</td>\n",
        "      <td> 0.014827</td>\n",
        "      <td> 0.002197</td>\n",
        "      <td> 0.000275</td>\n",
        "      <td> 0.230917</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td>...</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.245744</td>\n",
        "      <td> 0.023064</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.728995</td>\n",
        "      <td> 0</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>004A</th>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.002486</td>\n",
        "      <td> 0.754195</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.230889</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000932</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.001865</td>\n",
        "      <td>...</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.238036</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.007147</td>\n",
        "      <td> 0</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>005A</th>\n",
        "      <td> 0.006521</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.026084</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.908706</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.054451</td>\n",
        "      <td>...</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.990545</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000326</td>\n",
        "      <td> 0.002608</td>\n",
        "      <td> 0</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>008A</th>\n",
        "      <td> 0.000315</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.000210</td>\n",
        "      <td> 0.837024</td>\n",
        "      <td> 0.035995</td>\n",
        "      <td> 0.112499</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000840</td>\n",
        "      <td>...</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.113758</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.048903</td>\n",
        "      <td> 0</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>009A</th>\n",
        "      <td> 0.001291</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.001550</td>\n",
        "      <td> 0.823864</td>\n",
        "      <td> 0.024277</td>\n",
        "      <td> 0.118027</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td>...</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.119576</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0</td>\n",
        "      <td> 0.000000</td>\n",
        "      <td> 0.055269</td>\n",
        "      <td> 0</td>\n",
        "      <td>NaN</td>\n",
        "      <td>NaN</td>\n",
        "      <td> 0</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>5 rows \u00d7 284 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "            cls_Actinobacteria  cls_Alphaproteobacteria  cls_Bacilli  \\\n",
        "chimp 003A            0.000000                 0.000549     0.014827   \n",
        "      004A            0.000000                 0.000000     0.002486   \n",
        "      005A            0.006521                 0.000000     0.026084   \n",
        "      008A            0.000315                 0.000000     0.000210   \n",
        "      009A            0.001291                 0.000000     0.001550   \n",
        "\n",
        "            cls_Bacteroidia  cls_Betaproteobacteria  cls_Clostridia  \\\n",
        "chimp 003A         0.002197                0.000275        0.230917   \n",
        "      004A         0.754195                0.000000        0.230889   \n",
        "      005A         0.000000                0.000000        0.908706   \n",
        "      008A         0.837024                0.035995        0.112499   \n",
        "      009A         0.823864                0.024277        0.118027   \n",
        "\n",
        "            cls_Cyanobacteria  cls_Deltaproteobacteria  \\\n",
        "chimp 003A                  0                 0.000000   \n",
        "      004A                  0                 0.000932   \n",
        "      005A                  0                 0.000000   \n",
        "      008A                  0                 0.000000   \n",
        "      009A                  0                 0.000000   \n",
        "\n",
        "            cls_Epsilonproteobacteria  cls_Erysipelotrichi  \\\n",
        "chimp 003A                          0             0.000000   \n",
        "      004A                          0             0.001865   \n",
        "      005A                          0             0.054451   \n",
        "      008A                          0             0.000840   \n",
        "      009A                          0             0.000000   \n",
        "\n",
        "                     ...            phylum_Euryarchaeota  phylum_Firmicutes  \\\n",
        "chimp 003A           ...                               0           0.245744   \n",
        "      004A           ...                               0           0.238036   \n",
        "      005A           ...                               0           0.990545   \n",
        "      008A           ...                               0           0.113758   \n",
        "      009A           ...                               0           0.119576   \n",
        "\n",
        "            phylum_Fusobacteria  phylum_Lentisphaerae  phylum_NA  \\\n",
        "chimp 003A             0.023064                     0   0.000000   \n",
        "      004A             0.000000                     0   0.000000   \n",
        "      005A             0.000000                     0   0.000326   \n",
        "      008A             0.000000                     0   0.000000   \n",
        "      009A             0.000000                     0   0.000000   \n",
        "\n",
        "            phylum_Proteobacteria  phylum_Spirochaetes  phylum_Synergistetes  \\\n",
        "chimp 003A               0.728995                    0                   NaN   \n",
        "      004A               0.007147                    0                   NaN   \n",
        "      005A               0.002608                    0                   NaN   \n",
        "      008A               0.048903                    0                   NaN   \n",
        "      009A               0.055269                    0                   NaN   \n",
        "\n",
        "            phylum_TM7  phylum_Verrucomicrobia  \n",
        "chimp 003A         NaN                       0  \n",
        "      004A         NaN                       0  \n",
        "      005A         NaN                       0  \n",
        "      008A         NaN                       0  \n",
        "      009A         NaN                       0  \n",
        "\n",
        "[5 rows x 284 columns]"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X.fillna(value=0,inplace=True) #replace NAs with zeroes"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_dx = pd.concat([y_chimp.dx, y_blind.dx], keys=['chimp','blind'])\n",
      "y_dx #btw, what joy is to use pandas over R/dplyr for this. so intuitive and fast."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "       sample\n",
        "chimp  003A      UC\n",
        "       004A      UC\n",
        "       005A      NM\n",
        "       008A      CD\n",
        "       009A      UC\n",
        "       012A      UC\n",
        "       016A      CD\n",
        "       018A      CD\n",
        "       024A      NM\n",
        "       025A      CD\n",
        "       026A      UC\n",
        "       027A      UC\n",
        "       030A      NM\n",
        "       031A      NM\n",
        "       034B      UC\n",
        "...\n",
        "blind  251-AX    CD\n",
        "       252-AX    CD\n",
        "       253-AZ    UC\n",
        "       254-AX    CD\n",
        "       255-AZ    UC\n",
        "       256-AX    CD\n",
        "       258-AZ    CD\n",
        "       259-AX    NM\n",
        "       260-AY    CD\n",
        "       261-AX    UC\n",
        "       262-AZ    CD\n",
        "       263-AX    UC\n",
        "       264-AX    NM\n",
        "       265-AX    UC\n",
        "       291-AX    CD\n",
        "Name: dx, Length: 158, dtype: object"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#convert the training and testing labels to numerical values\n",
      "le = LabelEncoder()\n",
      "le.fit(y_dx)\n",
      "y = le.transform(y_dx)\n",
      "\n",
      "# just for reference, the columns of the binarized label read respectively:\n",
      "le.inverse_transform([0,1,2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array(['CD', 'NM', 'UC'], dtype=object)"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Label classification\n",
      "*Please note that the ROC plots will look different everytime the notebook is run due to the random nature of the cross-validation split*\n",
      "\n",
      "### Vanilla classifier\n",
      "We will go straight to using RandomForest and a 10-fold cross validation. Many other models were tried but RandomForest consistently prevented overfitting. First let's get an idea of how it looks like when you try to classify all the labels at the same time. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf = RandomForestClassifier(n_estimators=50, oob_score=True)\n",
      "clf.fit(X.values, y)\n",
      "scores = cross_val_score(clf, X.values, y, cv=10)\n",
      "\n",
      "print(\"Cross validation score:\")\n",
      "print(scores.mean())\n",
      "\n",
      "importances = clf.feature_importances_\n",
      "std = np.std([tree.feature_importances_ for tree in clf.estimators_],axis = 0)\n",
      "indices = np.argsort(importances)[::-1]\n",
      "\n",
      "print(\"feature ranking:\")\n",
      "\n",
      "for f in range(20):\n",
      "    print(\"%d. feature %d (%f)\" % (f + 1, indices[f], importances[indices[f]]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Cross validation score:\n",
        "0.567471988796\n",
        "feature ranking:\n",
        "1. feature 71 (0.030080)\n",
        "2. feature 92 (0.029311)\n",
        "3. feature 52 (0.021462)\n",
        "4. feature 223 (0.019596)\n",
        "5. feature 12 (0.018157)\n",
        "6. feature 66 (0.017697)\n",
        "7. feature 45 (0.017373)\n",
        "8. feature 145 (0.016363)\n",
        "9. feature 216 (0.015820)\n",
        "10. feature 79 (0.015636)\n",
        "11. feature 65 (0.014432)\n",
        "12. feature 99 (0.014312)\n",
        "13. feature 109 (0.014086)\n",
        "14. feature 72 (0.014012)\n",
        "15. feature 51 (0.013417)\n",
        "16. feature 37 (0.013062)\n",
        "17. feature 27 (0.013053)\n",
        "18. feature 2 (0.012811)\n",
        "19. feature 0 (0.012587)\n",
        "20. feature 272 (0.012439)\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Build a One-vs-all ROC curve (not cross validated)\n",
      "To build a ROC curve we need to binarize the variable and run the classifier as one class vs. all others"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_bin = label_binarize(y,classes=[0,1,2])\n",
      "n_classes = y_bin.shape[1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X_train, X_test, y_train, y_test = train_test_split(X.values, y_bin, test_size=.3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "clf1 = OneVsRestClassifier(RandomForestClassifier(n_estimators=50))\n",
      "y_score = clf1.fit(X_train, y_train).predict_proba(X_test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/local/lib/python3.4/site-packages/sklearn/utils/__init__.py:93: DeprecationWarning: Function multilabel_ is deprecated; Attribute multilabel_ is deprecated and will be removed in 0.17. Use 'y_type_.startswith('multilabel')' instead\n",
        "  warnings.warn(msg, category=DeprecationWarning)\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The probabilities of each class are now in a numpy array where each row corresponds to sample and each column to the label in question (CD, NM or UC). Let's take a pick at the first 10:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_score[:10,:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "array([[ 0.48,  0.1 ,  0.34],\n",
        "       [ 0.56,  0.08,  0.56],\n",
        "       [ 0.02,  0.74,  0.14],\n",
        "       [ 0.32,  0.16,  0.58],\n",
        "       [ 0.16,  0.4 ,  0.58],\n",
        "       [ 0.28,  0.02,  0.76],\n",
        "       [ 0.34,  0.42,  0.34],\n",
        "       [ 0.48,  0.06,  0.58],\n",
        "       [ 0.3 ,  0.08,  0.48],\n",
        "       [ 0.28,  0.64,  0.2 ]])"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Compute ROC curve and ROC area for each class\n",
      "fpr = dict()\n",
      "tpr = dict()\n",
      "roc_auc = dict()\n",
      "for i in range(n_classes):\n",
      "    fpr[i], tpr[i], _ = roc_curve(y_test[:, i], y_score[:, i])\n",
      "    roc_auc[i] = roc_auc_score(y_test[:,i], y_score[:,i],average=\"micro\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot of a ROC curve for a specific class\n",
      "plt.figure()\n",
      "plt.plot(fpr[2], tpr[2], label='ROC curve (area = %0.2f)' % roc_auc[2])\n",
      "plt.plot([0, 1], [0, 1], 'k--')\n",
      "plt.xlim([0.0, 1.0])\n",
      "plt.ylim([0.0, 1.05])\n",
      "plt.xlabel('False Positive Rate')\n",
      "plt.ylabel('True Positive Rate')\n",
      "plt.title('ROC - UC vs all')\n",
      "plt.legend(loc=\"lower right\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Cw4YN/Y5jcpHnEYOIdBaRDThDaCMiLUXkdc+TGWOKlFKlSjF16lQrCoVAIKeSXgG6AwcB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\nQJwja4+hjLeePXtm+54mTZq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       "text": [
        "<matplotlib.figure.Figure at 0x113cdd358>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot ROC curves all together now\n",
      "plt.figure()\n",
      "\n",
      "for i in range(n_classes):\n",
      "    plt.plot(fpr[i], tpr[i], label='ROC curve {0} (area = {1:0.2f})'\n",
      "                                   ''.format(le.inverse_transform(i), roc_auc[i]))\n",
      "\n",
      "plt.plot([0, 1], [0, 1], 'k--')\n",
      "plt.xlim([0.0, 1.0])\n",
      "plt.ylim([0.0, 1.05])\n",
      "plt.xlabel('False Positive Rate')\n",
      "plt.ylabel('True Positive Rate')\n",
      "plt.title('ROC - one random 1/3 split')\n",
      "plt.legend(loc=\"lower right\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BEUFVb9nip9WVVBuooqrxIpILOAGUU9WzGRVpcBP79sHzz1sLwBxGAeCjPz+i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\nFuA3xWT6AUud5S7A+kDrHUBbdAUineW+F7ItisitAD4BBgV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       "text": [
        "<matplotlib.figure.Figure at 0x113d5dc50>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### ROC cross validated [Figure 6A](http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0039242#pone-0039242-g006)\n",
      "#### top panel: one vs all"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Run classifier with cross-validation and plot ROC curves\n",
      "\n",
      "for dx in range(n_classes):\n",
      "    cv = StratifiedKFold(y_bin[:,dx], n_folds=10)\n",
      "    classifier = RandomForestClassifier()\n",
      "\n",
      "    mean_tpr = 0.0\n",
      "    mean_fpr = np.linspace(0, 1, 100)\n",
      "    all_tpr = []\n",
      "\n",
      "    for i, (train, test) in enumerate(cv):\n",
      "        probas_ = classifier.fit(X.iloc[train], y_bin[train,dx]).predict_proba(X.iloc[test])\n",
      "        # Compute ROC curve and area the curve\n",
      "        fpr, tpr, thresholds = roc_curve(y_bin[test,dx], probas_[:, 1])\n",
      "        mean_tpr += interp(mean_fpr, fpr, tpr)\n",
      "        mean_tpr[0] = 0.0\n",
      "        roc_auc = auc(fpr, tpr)\n",
      "        #plt.plot(fpr, tpr, lw=1, label='ROC fold %d (area = %0.2f)' % (i, roc_auc))\n",
      "\n",
      "\n",
      "    mean_tpr /= len(cv)\n",
      "    mean_tpr[-1] = 1.0\n",
      "    mean_auc = auc(mean_fpr, mean_tpr)\n",
      "    plt.plot(mean_fpr, mean_tpr, \n",
      "             label='Mean ROC %s (area = %0.2f)' % (le.inverse_transform(dx), mean_auc), lw=1)\n",
      "\n",
      "plt.xlim([-0.05, 1.05])\n",
      "plt.ylim([-0.05, 1.05])\n",
      "plt.xlabel('False Positive Rate')\n",
      "plt.ylabel('True Positive Rate')\n",
      "plt.title('Figure 6A - ROC - crossvalidated - one vs. all')\n",
      "plt.legend(loc=\"lower right\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FWLkS7nCD5HFuQFycdudMmAAjRsBrr5mkarmNPcJ/WinVGkApVQh4CTjoUKsM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\ns2dPPDw8Miy9WK1atRSlF+2tEmXNhx9+SLNmzXj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       "text": [
        "<matplotlib.figure.Figure at 0x113da3278>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### bottom panel: CD vs UC"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Only CD vs UC\n",
      "\n",
      "X_cduc = X[(y == 0) | (y == 2)]\n",
      "y_cduc = y[(y == 0) | (y == 2)]\n",
      "np.place(y_cduc,y_cduc == 2, 1)\n",
      "\n",
      "cv = StratifiedKFold(y_cduc, n_folds=10)\n",
      "clf_cduc = RandomForestClassifier()\n",
      "\n",
      "mean_tpr = 0.0\n",
      "mean_fpr = np.linspace(0, 1, 100)\n",
      "all_tpr = []\n",
      "\n",
      "for i, (train, test) in enumerate(cv):\n",
      "    fitted = classifier.fit(X_cduc.iloc[train], y_cduc[train])\n",
      "    probas_ = fitted.predict_proba(X_cduc.iloc[test])\n",
      "    scored_ = fitted.predict(X_cduc.iloc[test])\n",
      "    # Compute ROC curve and area the curve\n",
      "    fpr, tpr, thresholds = roc_curve(y_cduc[test], probas_[:, 1])\n",
      "    mean_tpr += interp(mean_fpr, fpr, tpr)\n",
      "    mean_tpr[0] = 0.0\n",
      "    #roc_auc = auc(fpr, tpr)\n",
      "    roc_auc = roc_auc_score(scored_, y_cduc[test], average=\"micro\")\n",
      "    #plt.plot(fpr, tpr, lw=1, label='ROC fold %d (area = %0.2f)' % (i, roc_auc))\n",
      "\n",
      "\n",
      "mean_tpr /= len(cv)\n",
      "mean_tpr[-1] = 1.0\n",
      "mean_auc = auc(mean_fpr, mean_tpr)\n",
      "plt.plot(mean_fpr, mean_tpr, \n",
      "         label='Mean ROC (area = %0.2f)' % mean_auc, lw=1)\n",
      "\n",
      "plt.xlim([-0.05, 1.05])\n",
      "plt.ylim([-0.05, 1.05])\n",
      "plt.xlabel('False Positive Rate')\n",
      "plt.ylabel('True Positive Rate')\n",
      "plt.title('Figure 6A - ROC - crossvalidated - CD vs UC')\n",
      "plt.legend(loc=\"lower right\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fu6qqvqqqK1X1SYo+DHMHYK03T+8h4G2gbz7lbgGmkPcEsomAzEw3Dn6rVlCx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\nh0o+F+SsW7eOCy+8MPc1atW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       "text": [
        "<matplotlib.figure.Figure at 0x113976748>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Comparison with the Frank et al. dataset\n",
      "The [original paper](http://www.pnas.org/content/104/34/13780.full) links to the available dataset. As outlined in the paper, the SLiME pipeline runs RDP on the fasta files and outputs a matrix of normalized abundance of each family, class, genus, etc. \n",
      "\n",
      "I am going to load directly that table, which has had the ibd classification label appended to it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "frank = pd.read_csv('data/pace/pace.rdpout.xtab.norm.ibd.csv')\n",
      "frank_label = frank['ibd']\n",
      "del frank['ibd']\n",
      "frank_label = (frank_label == 'yes')\n",
      "frank_label.value_counts()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "True     129\n",
        "False     61\n",
        "dtype: int64"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def crossval_roc(X, y):\n",
      "    cv = StratifiedKFold(y, n_folds=10)\n",
      "    clf = RandomForestClassifier()\n",
      "\n",
      "    mean_tpr = 0.0\n",
      "    mean_fpr = np.linspace(0, 1, 100)\n",
      "    all_tpr = []\n",
      "\n",
      "    for i, (train, test) in enumerate(cv):\n",
      "        fitted = clf.fit(X[train], y[train])\n",
      "        probas_ = fitted.predict_proba(X[test])\n",
      "        scored_ = fitted.predict(X[test])\n",
      "        # Compute ROC curve and area the curve\n",
      "        fpr, tpr, thresholds = roc_curve(y[test], probas_[:, 1])\n",
      "        mean_tpr += interp(mean_fpr, fpr, tpr)\n",
      "        mean_tpr[0] = 0.0\n",
      "        #roc_auc = auc(fpr, tpr)\n",
      "        roc_auc = roc_auc_score(scored_, y[test], average=\"micro\")\n",
      "        #plt.plot(fpr, tpr, lw=1, label='ROC fold %d (area = %0.2f)' % (i, roc_auc))\n",
      "\n",
      "\n",
      "    mean_tpr /= len(cv)\n",
      "    mean_tpr[-1] = 1.0\n",
      "    mean_auc = auc(mean_fpr, mean_tpr)\n",
      "    return plt.plot(mean_fpr, mean_tpr, \n",
      "                    label='Mean ROC (area = %0.2f)' % mean_auc, lw=1)\n",
      "\n",
      "fig = crossval_roc(frank.values,frank_label.values)\n",
      "plt.xlim([-0.05, 1.05])\n",
      "plt.ylim([-0.05, 1.05])\n",
      "plt.xlabel('False Positive Rate')\n",
      "plt.ylabel('True Positive Rate')\n",
      "plt.title('Frank et al. cross-validated ROC')\n",
      "plt.legend(loc=\"lower right\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ISFBdjX8moT3/A+CfZvYsYYYsCHPu7jRhSkOmGr+ISFBd4i+r5e8GrCNMiB5L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\nFxHJMkr8IiJZ5v8Dm6Sx2xo9sdkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113f40b00>"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "array([False,  True], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}