Cox_Hazard_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
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    "id": "qzrBQpODSu0c",
    "outputId": "70f7ac7a-68db-4809-9983-ff2644016624"
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "pip install lifelines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "LXujyOj5SXZZ"
   },
   "outputs": [],
   "source": [
    "# importing libraries\n",
    "import pandas as pd\n",
    "import lifelines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "YOHMntKQSndS"
   },
   "outputs": [],
   "source": [
    "# reading dataset\n",
    "data = pd.read_csv('/content/drive/MyDrive/Data Mining for Business in Python-20210706T154929Z-001/Data Mining for Business in Python/1. Survival Analysis/lung.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 204
    },
    "id": "YZShc3IDSxLn",
    "outputId": "b5cb3d58-e622-4dd7-c8e1-e548cb6c5d67"
   },
   "outputs": [
    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>inst</th>\n",
       "      <th>time</th>\n",
       "      <th>status</th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>ph.ecog</th>\n",
       "      <th>ph.karno</th>\n",
       "      <th>pat.karno</th>\n",
       "      <th>meal.cal</th>\n",
       "      <th>wt.loss</th>\n",
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       "      <td>1.0</td>\n",
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       "      <td>90.0</td>\n",
       "      <td>1225.0</td>\n",
       "      <td>15.0</td>\n",
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       "      <th>2</th>\n",
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       "      <td>90.0</td>\n",
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      "text/plain": [
       "   inst  time  status  age  ...  ph.karno  pat.karno  meal.cal  wt.loss\n",
       "0   3.0   306       2   74  ...      90.0      100.0    1175.0      NaN\n",
       "1   3.0   455       2   68  ...      90.0       90.0    1225.0     15.0\n",
       "2   3.0  1010       1   56  ...      90.0       90.0       NaN     15.0\n",
       "3   5.0   210       2   57  ...      90.0       60.0    1150.0     11.0\n",
       "4   1.0   883       2   60  ...     100.0       90.0       NaN      0.0\n",
       "\n",
       "[5 rows x 10 columns]"
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     },
     "execution_count": 5,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# head\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "8u2378OfUAvB"
   },
   "outputs": [],
   "source": [
    "# dropping missing values\n",
    "data = data.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "1RXQpkPRUL3T",
    "outputId": "ff1a8cad-8dcc-4126-d8bc-b2108ecd2893"
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   "outputs": [
    {
     "data": {
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       "inst         0\n",
       "time         0\n",
       "status       0\n",
       "age          0\n",
       "sex          0\n",
       "ph.ecog      0\n",
       "ph.karno     0\n",
       "pat.karno    0\n",
       "meal.cal     0\n",
       "wt.loss      0\n",
       "dtype: int64"
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     },
     "execution_count": 7,
     "metadata": {
      "tags": []
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     "output_type": "execute_result"
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   "source": [
    "data.isnull().sum()"
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  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "GQDLbpwLT6fO"
   },
   "outputs": [],
   "source": [
    "#transforming dependent variable\n",
    "data.loc[data.status == 1, \"status\"] = 0\n",
    "data.loc[data.status == 2, \"status\"] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 204
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    "id": "CO6HxYqgT8ow",
    "outputId": "328c5a67-ada2-44e4-b359-374c65c84ec2"
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   "outputs": [
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       "      <th>time</th>\n",
       "      <th>status</th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>ph.ecog</th>\n",
       "      <th>ph.karno</th>\n",
       "      <th>pat.karno</th>\n",
       "      <th>meal.cal</th>\n",
       "      <th>wt.loss</th>\n",
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       "      <td>90.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>1150.0</td>\n",
       "      <td>11.0</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>12.0</td>\n",
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      "text/plain": [
       "   inst  time  status  age  ...  ph.karno  pat.karno  meal.cal  wt.loss\n",
       "1   3.0   455       1   68  ...      90.0       90.0    1225.0     15.0\n",
       "3   5.0   210       1   57  ...      90.0       60.0    1150.0     11.0\n",
       "5  12.0  1022       0   74  ...      50.0       80.0     513.0      0.0\n",
       "6   7.0   310       1   68  ...      70.0       60.0     384.0     10.0\n",
       "7  11.0   361       1   71  ...      60.0       80.0     538.0      1.0\n",
       "\n",
       "[5 rows x 10 columns]"
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     },
     "execution_count": 9,
     "metadata": {
      "tags": []
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     "output_type": "execute_result"
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   ],
   "source": [
    "data.head()"
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  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "_HECJ3iEUOBP"
   },
   "outputs": [],
   "source": [
    "# dropping instance variable\n",
    "data = data.drop(['inst'], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "NB3Cb8TrWNEC",
    "outputId": "2c4747dc-1bdf-480b-a295-5d04e38b82c9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['time', 'status', 'age', 'sex', 'ph.ecog', 'ph.karno', 'pat.karno',\n",
       "       'meal.cal', 'wt.loss'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 11,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wT5AcMB9hjME"
   },
   "source": [
    "# Cox Proportional Hazard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "eAzpVpsZhln_",
    "outputId": "c7ec2d53-9809-438a-e474-45c324d65239"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<lifelines.CoxPHFitter: fitted with 167 total observations, 47 right-censored observations>"
      ]
     },
     "execution_count": 12,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lifelines import CoxPHFitter\n",
    "model = CoxPHFitter()\n",
    "model.fit(data, 'time', event_col = 'status')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 672
    },
    "id": "Duk-SVq-iIo_",
    "outputId": "e899add0-ef42-4892-82b7-63a22b78e140"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model</th>\n",
       "      <td>lifelines.CoxPHFitter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>duration col</th>\n",
       "      <td>'time'</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event col</th>\n",
       "      <td>'status'</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>baseline estimation</th>\n",
       "      <td>breslow</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of observations</th>\n",
       "      <td>167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of events observed</th>\n",
       "      <td>120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>partial log-likelihood</th>\n",
       "      <td>-494.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>time fit was run</th>\n",
       "      <td>2021-07-29 16:03:25 UTC</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th style=\"min-width: 12px;\"></th>\n",
       "      <th style=\"min-width: 12px;\">coef</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef)</th>\n",
       "      <th style=\"min-width: 12px;\">se(coef)</th>\n",
       "      <th style=\"min-width: 12px;\">coef lower 95%</th>\n",
       "      <th style=\"min-width: 12px;\">coef upper 95%</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef) lower 95%</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef) upper 95%</th>\n",
       "      <th style=\"min-width: 12px;\">z</th>\n",
       "      <th style=\"min-width: 12px;\">p</th>\n",
       "      <th style=\"min-width: 12px;\">-log2(p)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>0.01</td>\n",
       "      <td>1.01</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.99</td>\n",
       "      <td>1.03</td>\n",
       "      <td>0.93</td>\n",
       "      <td>0.35</td>\n",
       "      <td>1.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sex</th>\n",
       "      <td>-0.55</td>\n",
       "      <td>0.57</td>\n",
       "      <td>0.20</td>\n",
       "      <td>-0.95</td>\n",
       "      <td>-0.16</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.85</td>\n",
       "      <td>-2.75</td>\n",
       "      <td>0.01</td>\n",
       "      <td>7.37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ph.ecog</th>\n",
       "      <td>0.74</td>\n",
       "      <td>2.09</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.30</td>\n",
       "      <td>1.18</td>\n",
       "      <td>1.35</td>\n",
       "      <td>3.26</td>\n",
       "      <td>3.29</td>\n",
       "      <td>&lt;0.005</td>\n",
       "      <td>9.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ph.karno</th>\n",
       "      <td>0.02</td>\n",
       "      <td>1.02</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.05</td>\n",
       "      <td>2.00</td>\n",
       "      <td>0.05</td>\n",
       "      <td>4.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pat.karno</th>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.97</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-1.49</td>\n",
       "      <td>0.14</td>\n",
       "      <td>2.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>meal.cal</th>\n",
       "      <td>0.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.91</td>\n",
       "      <td>0.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wt.loss</th>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.97</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-1.83</td>\n",
       "      <td>0.07</td>\n",
       "      <td>3.89</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table><br><div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Concordance</th>\n",
       "      <td>0.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Partial AIC</th>\n",
       "      <td>1002.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log-likelihood ratio test</th>\n",
       "      <td>28.16 on 7 df</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-log2(p) of ll-ratio test</th>\n",
       "      <td>12.25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/latex": [
       "\\begin{tabular}{lrrrrrrrrrr}\n",
       "\\toprule\n",
       "{} &  coef &  exp(coef) &  se(coef) &  coef lower 95\\% &  coef upper 95\\% &  exp(coef) lower 95\\% &  exp(coef) upper 95\\% &     z &    p &  -log2(p) \\\\\n",
       "covariate &       &            &           &                 &                 &                      &                      &       &      &           \\\\\n",
       "\\midrule\n",
       "age       &  0.01 &       1.01 &      0.01 &           -0.01 &            0.03 &                 0.99 &                 1.03 &  0.93 & 0.35 &      1.51 \\\\\n",
       "sex       & -0.55 &       0.57 &      0.20 &           -0.95 &           -0.16 &                 0.39 &                 0.85 & -2.75 & 0.01 &      7.37 \\\\\n",
       "ph.ecog   &  0.74 &       2.09 &      0.22 &            0.30 &            1.18 &                 1.35 &                 3.26 &  3.29 & 0.00 &      9.95 \\\\\n",
       "ph.karno  &  0.02 &       1.02 &      0.01 &            0.00 &            0.04 &                 1.00 &                 1.05 &  2.00 & 0.05 &      4.45 \\\\\n",
       "pat.karno & -0.01 &       0.99 &      0.01 &           -0.03 &            0.00 &                 0.97 &                 1.00 & -1.49 & 0.14 &      2.87 \\\\\n",
       "meal.cal  &  0.00 &       1.00 &      0.00 &           -0.00 &            0.00 &                 1.00 &                 1.00 &  0.11 & 0.91 &      0.13 \\\\\n",
       "wt.loss   & -0.01 &       0.99 &      0.01 &           -0.03 &            0.00 &                 0.97 &                 1.00 & -1.83 & 0.07 &      3.89 \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "<lifelines.CoxPHFitter: fitted with 167 total observations, 47 right-censored observations>\n",
       "             duration col = 'time'\n",
       "                event col = 'status'\n",
       "      baseline estimation = breslow\n",
       "   number of observations = 167\n",
       "number of events observed = 120\n",
       "   partial log-likelihood = -494.03\n",
       "         time fit was run = 2021-07-29 16:03:25 UTC\n",
       "\n",
       "---\n",
       "            coef  exp(coef)   se(coef)   coef lower 95%   coef upper 95%  exp(coef) lower 95%  exp(coef) upper 95%\n",
       "covariate                                                                                                         \n",
       "age         0.01       1.01       0.01            -0.01             0.03                 0.99                 1.03\n",
       "sex        -0.55       0.57       0.20            -0.95            -0.16                 0.39                 0.85\n",
       "ph.ecog     0.74       2.09       0.22             0.30             1.18                 1.35                 3.26\n",
       "ph.karno    0.02       1.02       0.01             0.00             0.04                 1.00                 1.05\n",
       "pat.karno  -0.01       0.99       0.01            -0.03             0.00                 0.97                 1.00\n",
       "meal.cal    0.00       1.00       0.00            -0.00             0.00                 1.00                 1.00\n",
       "wt.loss    -0.01       0.99       0.01            -0.03             0.00                 0.97                 1.00\n",
       "\n",
       "              z      p   -log2(p)\n",
       "covariate                        \n",
       "age        0.93   0.35       1.51\n",
       "sex       -2.75   0.01       7.37\n",
       "ph.ecog    3.29 <0.005       9.95\n",
       "ph.karno   2.00   0.05       4.45\n",
       "pat.karno -1.49   0.14       2.87\n",
       "meal.cal   0.11   0.91       0.13\n",
       "wt.loss   -1.83   0.07       3.89\n",
       "---\n",
       "Concordance = 0.65\n",
       "Partial AIC = 1002.07\n",
       "log-likelihood ratio test = 28.16 on 7 df\n",
       "-log2(p) of ll-ratio test = 12.25"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.print_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 296
    },
    "id": "LDR1OovQiREi",
    "outputId": "62497d50-995b-4d92-cd1b-9cf2b5ab2c39"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fe29defee10>"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualising the results\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "viCi9hMuAUqG"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "name": "Cox Hazard Regression.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}