(1)Univariate&MultivariateCoxModel.ipynb

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  "metadata": {
    "colab": {
      "name": "Univariate&MultivariateCoxModel.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/AnkushJamthikar/StatisticalModeling/blob/main/(1)Univariate%26MultivariateCoxModel.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "O_iuwaOUUuY7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cf164b0b-0319-4196-8932-ccb5005a49cb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting scikit-survival\n",
            "  Downloading scikit-survival-0.17.0.tar.gz (2.5 MB)\n",
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            "\u001b[?25h  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "    Preparing wheel metadata ... \u001b[?25l\u001b[?25hdone\n",
            "Requirement already satisfied: scipy!=1.3.0,>=1.0 in /usr/local/lib/python3.7/dist-packages (from scikit-survival) (1.4.1)\n",
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            "Building wheels for collected packages: scikit-survival\n",
            "  Building wheel for scikit-survival (PEP 517) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for scikit-survival: filename=scikit_survival-0.17.0-cp37-cp37m-linux_x86_64.whl size=4088323 sha256=82060060a2f0eea0ce5cef2b553ef62db400fd499128704f633279ad775237d8\n",
            "  Stored in directory: /root/.cache/pip/wheels/91/c1/99/2c2faacc82ff4f89d27612b1fd905ea35aa24f6a93dd4dcc0d\n",
            "Successfully built scikit-survival\n",
            "Installing collected packages: scikit-survival\n",
            "Successfully installed scikit-survival-0.17.0\n",
            "Collecting lifelines\n",
            "  Downloading lifelines-0.26.4-py3-none-any.whl (348 kB)\n",
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            "  Downloading autograd-gamma-0.5.0.tar.gz (4.0 kB)\n",
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            "  Downloading interface_meta-1.2.4-py2.py3-none-any.whl (14 kB)\n",
            "Requirement already satisfied: wrapt in /usr/local/lib/python3.7/dist-packages (from formulaic<0.3,>=0.2.2->lifelines) (1.13.3)\n",
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            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.1->matplotlib>=3.0->lifelines) (1.15.0)\n",
            "Building wheels for collected packages: autograd-gamma\n",
            "  Building wheel for autograd-gamma (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for autograd-gamma: filename=autograd_gamma-0.5.0-py3-none-any.whl size=4048 sha256=e18f0cddc119a6bb1099e281fe20ad54dcb015adc49ca07d92232ed1b36b9736\n",
            "  Stored in directory: /root/.cache/pip/wheels/9f/01/ee/1331593abb5725ff7d8c1333aee93a50a1c29d6ddda9665c9f\n",
            "Successfully built autograd-gamma\n",
            "Installing collected packages: interface-meta, formulaic, autograd-gamma, lifelines\n",
            "Successfully installed autograd-gamma-0.5.0 formulaic-0.2.4 interface-meta-1.2.4 lifelines-0.26.4\n"
          ]
        }
      ],
      "source": [
        "!pip install lifelines"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import os\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn_pandas import DataFrameMapper\n",
        "\n",
        "import joblib"
      ],
      "metadata": {
        "id": "O-wtVc7CeG9h"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "MTDD_TrainingData = pd.read_excel('/content/MTDD_TrainingDb.xlsx')\n",
        "MTDD_TestingData  = pd.read_excel('/content/MTDD_TestingDb.xlsx')\n",
        "MTDD_TrainingData.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "id": "BoUP1iN3eFGZ",
        "outputId": "adc6eef7-ba50-46af-8798-7f67bcecc267"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
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              "      <th>Unnamed: 47</th>\n",
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              "      <td>1.0</td>\n",
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              "      <td>0.95</td>\n",
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              "      <td>59.0</td>\n",
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              "      <td>-0.628468</td>\n",
              "      <td>1</td>\n",
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              "      <td>pEF</td>\n",
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              "      <td>177.8</td>\n",
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              "      <td>9.9</td>\n",
              "      <td>4.39</td>\n",
              "      <td>0.0</td>\n",
              "      <td>319.534722</td>\n",
              "      <td>59.0</td>\n",
              "      <td>0.7</td>\n",
              "      <td>1.1</td>\n",
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              "      <td>8.0</td>\n",
              "      <td>8.9</td>\n",
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              "      <td>35.6</td>\n",
              "      <td>64.79</td>\n",
              "      <td>1</td>\n",
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              "      <td>-0.631016</td>\n",
              "      <td>0.040995</td>\n",
              "      <td>-0.684295</td>\n",
              "      <td>1</td>\n",
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              "      <td>pEF</td>\n",
              "      <td>28</td>\n",
              "      <td>1</td>\n",
              "      <td>167.0</td>\n",
              "      <td>75.899</td>\n",
              "      <td>27.214672</td>\n",
              "      <td>1.85</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0</td>\n",
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              "      <td>12.4</td>\n",
              "      <td>1.11</td>\n",
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              "      <td>70.0</td>\n",
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              "      <td>2.3</td>\n",
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              "      <td>11.0</td>\n",
              "      <td>8.7</td>\n",
              "      <td>2.20</td>\n",
              "      <td>29.6</td>\n",
              "      <td>71.79</td>\n",
              "      <td>0</td>\n",
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              "      <td>926.677083</td>\n",
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              "      <td>-1.354255</td>\n",
              "      <td>1.699903</td>\n",
              "      <td>-0.675815</td>\n",
              "      <td>-0.255897</td>\n",
              "      <td>-0.371901</td>\n",
              "      <td>-0.463510</td>\n",
              "      <td>1</td>\n",
              "      <td>0.99902</td>\n",
              "      <td>0.00098</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>7</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>pEF</td>\n",
              "      <td>22</td>\n",
              "      <td>1</td>\n",
              "      <td>158.0</td>\n",
              "      <td>68.399</td>\n",
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              "      <td>0</td>\n",
              "      <td>12.9</td>\n",
              "      <td>0.67</td>\n",
              "      <td>0.0</td>\n",
              "      <td>902.565972</td>\n",
              "      <td>58.0</td>\n",
              "      <td>0.8</td>\n",
              "      <td>2.3</td>\n",
              "      <td>0.347826</td>\n",
              "      <td>13.0</td>\n",
              "      <td>6.6</td>\n",
              "      <td>2.52</td>\n",
              "      <td>18.9</td>\n",
              "      <td>65.17</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>902.565972</td>\n",
              "      <td>1</td>\n",
              "      <td>12.857639</td>\n",
              "      <td>0</td>\n",
              "      <td>902.565972</td>\n",
              "      <td>0</td>\n",
              "      <td>902.565972</td>\n",
              "      <td>0</td>\n",
              "      <td>902.565972</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>902.565972</td>\n",
              "      <td>0</td>\n",
              "      <td>902.565972</td>\n",
              "      <td>0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>157.656114</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>-0.192319</td>\n",
              "      <td>-0.035874</td>\n",
              "      <td>1.915233</td>\n",
              "      <td>-1.500805</td>\n",
              "      <td>2.474692</td>\n",
              "      <td>-0.925183</td>\n",
              "      <td>0.344292</td>\n",
              "      <td>-1.108233</td>\n",
              "      <td>-0.672309</td>\n",
              "      <td>1</td>\n",
              "      <td>0.99939</td>\n",
              "      <td>0.00061</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>10</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>pEF</td>\n",
              "      <td>56</td>\n",
              "      <td>1</td>\n",
              "      <td>188.0</td>\n",
              "      <td>83.699</td>\n",
              "      <td>23.681247</td>\n",
              "      <td>2.10</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>9.2</td>\n",
              "      <td>1.08</td>\n",
              "      <td>0.0</td>\n",
              "      <td>243.829861</td>\n",
              "      <td>63.0</td>\n",
              "      <td>0.6</td>\n",
              "      <td>0.9</td>\n",
              "      <td>0.666667</td>\n",
              "      <td>7.0</td>\n",
              "      <td>8.6</td>\n",
              "      <td>2.87</td>\n",
              "      <td>28.0</td>\n",
              "      <td>98.62</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>243.829861</td>\n",
              "      <td>1</td>\n",
              "      <td>190.318750</td>\n",
              "      <td>0</td>\n",
              "      <td>243.829861</td>\n",
              "      <td>0</td>\n",
              "      <td>243.829861</td>\n",
              "      <td>0</td>\n",
              "      <td>243.829861</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>243.829861</td>\n",
              "      <td>1</td>\n",
              "      <td>243.829861</td>\n",
              "      <td>0</td>\n",
              "      <td>0.328709</td>\n",
              "      <td>75.172633</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.280960</td>\n",
              "      <td>-0.853841</td>\n",
              "      <td>-0.416585</td>\n",
              "      <td>-0.426102</td>\n",
              "      <td>0.150325</td>\n",
              "      <td>-0.687689</td>\n",
              "      <td>1.000750</td>\n",
              "      <td>-0.482007</td>\n",
              "      <td>0.382729</td>\n",
              "      <td>1</td>\n",
              "      <td>0.55735</td>\n",
              "      <td>0.44265</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-35974faf-ec47-4a5b-a657-14308e958cef')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "  </svg>\n",
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              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
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              "      border-radius: 50%;\n",
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              "      fill: #1967D2;\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
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              "    [theme=dark] .colab-df-convert:hover {\n",
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              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-35974faf-ec47-4a5b-a657-14308e958cef');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
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              "          docLink.innerHTML = docLinkHtml;\n",
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              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   Row_ID  Region  ...  1 probability 2 probability\n",
              "0       2       1  ...        0.98608       0.01392\n",
              "1       3       1  ...        0.96694       0.03306\n",
              "2       6       1  ...        0.99902       0.00098\n",
              "3       7       1  ...        0.99939       0.00061\n",
              "4      10       1  ...        0.55735       0.44265\n",
              "\n",
              "[5 rows x 60 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "MTDD_TestingData.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        },
        "id": "ku_YM2BJstQU",
        "outputId": "f31f41cd-f013-4e14-baf6-ef42fcf058a3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-2af0f114-086e-4065-8a71-dcf5ddd9fdf9\">\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Row_ID</th>\n",
              "      <th>Region</th>\n",
              "      <th>Risk-Group (GroundTruth)</th>\n",
              "      <th>GROUP</th>\n",
              "      <th>AGE</th>\n",
              "      <th>GENDER</th>\n",
              "      <th>HEIGHT</th>\n",
              "      <th>WEIGHT</th>\n",
              "      <th>BMI</th>\n",
              "      <th>BSA</th>\n",
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              "      <th>DM</th>\n",
              "      <th>HTN</th>\n",
              "      <th>HLD</th>\n",
              "      <th>Hgb</th>\n",
              "      <th>Cr</th>\n",
              "      <th>COPD</th>\n",
              "      <th>EF_orig</th>\n",
              "      <th>E_orig</th>\n",
              "      <th>E_A_orig</th>\n",
              "      <th>A_orig</th>\n",
              "      <th>e_prime_orig</th>\n",
              "      <th>E_e_prime_orig</th>\n",
              "      <th>TRV_orig</th>\n",
              "      <th>LAVi_orig</th>\n",
              "      <th>LVMi_orig</th>\n",
              "      <th>FOLLOW_UP_DURATION</th>\n",
              "      <th>DEATH</th>\n",
              "      <th>MACCE_DEATH</th>\n",
              "      <th>TIME_TO_DEATH</th>\n",
              "      <th>ALL_REHOSPITALIZATION</th>\n",
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              "      <th>MACCE_REHOSPITALIZATION</th>\n",
              "      <th>TIME_TO_MACCE_REHOSPITALIZATION</th>\n",
              "      <th>MACE_REHOSPITALIZATION</th>\n",
              "      <th>TIME_TO_MACE_REHOSPITALIZATION</th>\n",
              "      <th>MACE_DEATH</th>\n",
              "      <th>TIME_TO_MACE_DEATH</th>\n",
              "      <th>MACE_CATEGORY</th>\n",
              "      <th>MACE_DEATH_REHOSPITALIZATION</th>\n",
              "      <th>TIME_TO_MACE_DEATH_REHOSPITALIZATION</th>\n",
              "      <th>Composite_Event</th>\n",
              "      <th>Time_To_CompositeEvent</th>\n",
              "      <th>Prospective</th>\n",
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              "      <th>GFR</th>\n",
              "      <th>CKD_GFR</th>\n",
              "      <th>Unnamed: 47</th>\n",
              "      <th>EF_norm</th>\n",
              "      <th>E_norm</th>\n",
              "      <th>E_A_norm</th>\n",
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              "      <th>e_prime_norm</th>\n",
              "      <th>E_e_prime_norm</th>\n",
              "      <th>TRV_norm</th>\n",
              "      <th>LAVi_norm</th>\n",
              "      <th>LVMi_norm</th>\n",
              "      <th>Risk-Group</th>\n",
              "      <th>1 probability</th>\n",
              "      <th>2 probability</th>\n",
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              "  </thead>\n",
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              "      <th>0</th>\n",
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              "      <td>1</td>\n",
              "      <td>175.3</td>\n",
              "      <td>64.410</td>\n",
              "      <td>20.959913</td>\n",
              "      <td>1.79</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>13.3</td>\n",
              "      <td>1.24</td>\n",
              "      <td>0.0</td>\n",
              "      <td>70</td>\n",
              "      <td>0.9</td>\n",
              "      <td>1.9</td>\n",
              "      <td>0.473684</td>\n",
              "      <td>9.0</td>\n",
              "      <td>10.5</td>\n",
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              "      <td>45.8</td>\n",
              "      <td>79.45</td>\n",
              "      <td>1047.533333</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1047.533333</td>\n",
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              "      <td>1047.533333</td>\n",
              "      <td>0</td>\n",
              "      <td>1047.533333</td>\n",
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              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>1047.533333</td>\n",
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              "      <td>1047.533333</td>\n",
              "      <td>0</td>\n",
              "      <td>1.098393</td>\n",
              "      <td>62.580379</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.943550</td>\n",
              "      <td>0.373110</td>\n",
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              "      <td>0.925114</td>\n",
              "      <td>-0.462070</td>\n",
              "      <td>-0.255897</td>\n",
              "      <td>0.742918</td>\n",
              "      <td>-0.221907</td>\n",
              "      <td>1</td>\n",
              "      <td>0.96557</td>\n",
              "      <td>0.03443</td>\n",
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              "      <td>62.899</td>\n",
              "      <td>25.037168</td>\n",
              "      <td>1.64</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0</td>\n",
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              "      <td>1</td>\n",
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              "      <td>0.76</td>\n",
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              "      <td>78</td>\n",
              "      <td>0.8</td>\n",
              "      <td>1.1</td>\n",
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              "      <td>11.0</td>\n",
              "      <td>7.3</td>\n",
              "      <td>1.7</td>\n",
              "      <td>28.0</td>\n",
              "      <td>61.63</td>\n",
              "      <td>923.497222</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>923.497222</td>\n",
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              "      <td>923.497222</td>\n",
              "      <td>0</td>\n",
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              "      <td>923.497222</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>923.497222</td>\n",
              "      <td>0</td>\n",
              "      <td>923.497222</td>\n",
              "      <td>0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>86.700599</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.700796</td>\n",
              "      <td>-0.035874</td>\n",
              "      <td>-0.083468</td>\n",
              "      <td>-0.221819</td>\n",
              "      <td>1.699903</td>\n",
              "      <td>-0.842061</td>\n",
              "      <td>-1.193694</td>\n",
              "      <td>-0.482007</td>\n",
              "      <td>-0.783964</td>\n",
              "      <td>1</td>\n",
              "      <td>0.99977</td>\n",
              "      <td>0.00023</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>8</td>\n",
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              "      <td>1</td>\n",
              "      <td>pEF</td>\n",
              "      <td>50</td>\n",
              "      <td>1</td>\n",
              "      <td>180.0</td>\n",
              "      <td>58.967</td>\n",
              "      <td>18.199691</td>\n",
              "      <td>1.75</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>11.9</td>\n",
              "      <td>1.21</td>\n",
              "      <td>0.0</td>\n",
              "      <td>63</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.9</td>\n",
              "      <td>0.555556</td>\n",
              "      <td>7.0</td>\n",
              "      <td>7.3</td>\n",
              "      <td>2.0</td>\n",
              "      <td>13.4</td>\n",
              "      <td>83.05</td>\n",
              "      <td>362.465278</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>362.465278</td>\n",
              "      <td>0</td>\n",
              "      <td>362.465278</td>\n",
              "      <td>0</td>\n",
              "      <td>362.465278</td>\n",
              "      <td>0</td>\n",
              "      <td>362.465278</td>\n",
              "      <td>0</td>\n",
              "      <td>362.465278</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>362.465278</td>\n",
              "      <td>0</td>\n",
              "      <td>362.465278</td>\n",
              "      <td>0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>67.466428</td>\n",
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              "      <td>NaN</td>\n",
              "      <td>0.280960</td>\n",
              "      <td>-1.262825</td>\n",
              "      <td>-0.416585</td>\n",
              "      <td>-0.800620</td>\n",
              "      <td>0.150325</td>\n",
              "      <td>-0.842061</td>\n",
              "      <td>-0.631016</td>\n",
              "      <td>-1.486721</td>\n",
              "      <td>-0.108361</td>\n",
              "      <td>1</td>\n",
              "      <td>0.99307</td>\n",
              "      <td>0.00693</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>18</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>pEF</td>\n",
              "      <td>49</td>\n",
              "      <td>0</td>\n",
              "      <td>167.6</td>\n",
              "      <td>70.760</td>\n",
              "      <td>25.190674</td>\n",
              "      <td>1.80</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>11.6</td>\n",
              "      <td>0.86</td>\n",
              "      <td>0.0</td>\n",
              "      <td>63</td>\n",
              "      <td>0.6</td>\n",
              "      <td>0.8</td>\n",
              "      <td>0.750000</td>\n",
              "      <td>10.0</td>\n",
              "      <td>5.9</td>\n",
              "      <td>1.7</td>\n",
              "      <td>25.8</td>\n",
              "      <td>58.68</td>\n",
              "      <td>1038.513194</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1038.513194</td>\n",
              "      <td>0</td>\n",
              "      <td>1038.513194</td>\n",
              "      <td>0</td>\n",
              "      <td>1038.513194</td>\n",
              "      <td>0</td>\n",
              "      <td>1038.513194</td>\n",
              "      <td>0</td>\n",
              "      <td>1038.513194</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>1038.513194</td>\n",
              "      <td>0</td>\n",
              "      <td>1038.513194</td>\n",
              "      <td>0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>74.541106</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.280960</td>\n",
              "      <td>-0.853841</td>\n",
              "      <td>-0.583144</td>\n",
              "      <td>-0.145213</td>\n",
              "      <td>1.312508</td>\n",
              "      <td>-1.008306</td>\n",
              "      <td>-1.193694</td>\n",
              "      <td>-0.633402</td>\n",
              "      <td>-0.877009</td>\n",
              "      <td>1</td>\n",
              "      <td>0.99932</td>\n",
              "      <td>0.00068</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>47</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>pEF</td>\n",
              "      <td>57</td>\n",
              "      <td>1</td>\n",
              "      <td>182.9</td>\n",
              "      <td>122.470</td>\n",
              "      <td>36.610217</td>\n",
              "      <td>2.42</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>13.7</td>\n",
              "      <td>1.05</td>\n",
              "      <td>0.0</td>\n",
              "      <td>66</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.8</td>\n",
              "      <td>0.625000</td>\n",
              "      <td>8.0</td>\n",
              "      <td>7.1</td>\n",
              "      <td>2.7</td>\n",
              "      <td>38.1</td>\n",
              "      <td>81.00</td>\n",
              "      <td>508.342361</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>508.342361</td>\n",
              "      <td>0</td>\n",
              "      <td>508.342361</td>\n",
              "      <td>0</td>\n",
              "      <td>508.342361</td>\n",
              "      <td>0</td>\n",
              "      <td>508.342361</td>\n",
              "      <td>0</td>\n",
              "      <td>508.342361</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>508.342361</td>\n",
              "      <td>0</td>\n",
              "      <td>508.342361</td>\n",
              "      <td>0</td>\n",
              "      <td>0.381645</td>\n",
              "      <td>77.378071</td>\n",
              "      <td>0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.564927</td>\n",
              "      <td>-1.262825</td>\n",
              "      <td>-0.583144</td>\n",
              "      <td>-0.566546</td>\n",
              "      <td>0.537719</td>\n",
              "      <td>-0.865810</td>\n",
              "      <td>0.681899</td>\n",
              "      <td>0.213035</td>\n",
              "      <td>-0.173019</td>\n",
              "      <td>1</td>\n",
              "      <td>0.86290</td>\n",
              "      <td>0.13710</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-2af0f114-086e-4065-8a71-dcf5ddd9fdf9')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
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              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
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              "      fill: #FFFFFF;\n",
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              "  </style>\n",
              "\n",
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              "        const buttonEl =\n",
              "          document.querySelector('#df-2af0f114-086e-4065-8a71-dcf5ddd9fdf9 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-2af0f114-086e-4065-8a71-dcf5ddd9fdf9');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "   Row_ID  Region  ...  1 probability 2 probability\n",
              "0       1       1  ...        0.96557       0.03443\n",
              "1       5       1  ...        0.99977       0.00023\n",
              "2       8       1  ...        0.99307       0.00693\n",
              "3      18       1  ...        0.99932       0.00068\n",
              "4      47       1  ...        0.86290       0.13710\n",
              "\n",
              "[5 rows x 60 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Functions for Confidence Intervals of C-index"
      ],
      "metadata": {
        "id": "FoEV_xdvfm2A"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def score_stat_ci(\n",
        "    X,\n",
        "    score_fun,\n",
        "    stat_fun=np.mean,\n",
        "    n_bootstraps=2000,\n",
        "    confidence_level=0.95,\n",
        "    seed=None,\n",
        "    reject_one_class_samples=True,\n",
        "    ):\n",
        "       \n",
        "    np.random.seed(seed)\n",
        "    \n",
        "    scores = []\n",
        "    for i in range(n_bootstraps):\n",
        "        indices   = np.random.randint(0, len(X), len(X))  \n",
        "        Sampled_X = X.iloc[indices,:]\n",
        "        scores.append(score_fun(Sampled_X, scoring_method = 'concordance_index'))\n",
        "    \n",
        "    mean_score = np.mean(scores)\n",
        "    sorted_scores = np.array(sorted(scores))\n",
        "    alpha = (1.0 - confidence_level) / 2.0\n",
        "    ci_lower = sorted_scores[int(round(alpha * len(sorted_scores)))]\n",
        "    ci_upper = sorted_scores[int(round((1.0 - alpha) * len(sorted_scores)))]\n",
        "    return mean_score, ci_lower, ci_upper, scores\n",
        "    \n",
        "    \n",
        "\n",
        "def score_ci(X,\n",
        "    score_fun,\n",
        "    n_bootstraps=1000,\n",
        "    confidence_level=0.95,\n",
        "    seed=None,\n",
        "    reject_one_class_samples=True):\n",
        "       \n",
        "    score = score_fun(X, scoring_method = 'concordance_index')\n",
        "    \n",
        "    _, ci_lower, ci_upper, scores = score_stat_ci(\n",
        "    X=X,\n",
        "    score_fun=score_fun,\n",
        "    n_bootstraps=n_bootstraps,\n",
        "    confidence_level=confidence_level,\n",
        "    seed=seed,\n",
        "    reject_one_class_samples=reject_one_class_samples,\n",
        "    )\n",
        "    \n",
        "    return score, ci_lower, ci_upper, scores"
      ],
      "metadata": {
        "id": "VAVa4bt7fkm4"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Using lifelines package"
      ],
      "metadata": {
        "id": "3GHc6xELb670"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Univariate Cox Proportional Hazard Analysis"
      ],
      "metadata": {
        "id": "_Caw9aNjd42y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from lifelines import CoxPHFitter"
      ],
      "metadata": {
        "id": "t_yEGqUtb6n-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def function_train_CoxModel(TrainingData, Time, Event):\n",
        "\n",
        "  trained_model     = CoxPHFitter().fit(TrainingData, Time, Event)\n",
        "  c_index_training  = trained_model.score(TrainingData, scoring_method = 'concordance_index')\n",
        "  model_summary     = trained_model.summary  \n",
        "\n",
        "  return trained_model, c_index_training, model_summary\n",
        "\n",
        "def function_test_CoxModel(Trained_CoxModel, TestingData):\n",
        "  c_index               = Trained_CoxModel.score(TestingData, scoring_method = 'concordance_index')\n",
        "  _, lower, upper, _    = score_ci(TestingData, Trained_CoxModel.score)\n",
        "  c_index_df            = pd.DataFrame([[c_index, lower, upper]]).round(decimals = 2)  \n",
        "  return c_index_df"
      ],
      "metadata": {
        "id": "LsUIfNe8gXMP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#FeaturesForUnivariateAnalysis = [\"2 probability\", \"AGE\", \"GENDER\"] \n",
        "FeaturesForUnivariateAnalysis = [\"AGE\", \"GENDER\", \"EF_orig\", \"E_orig\", \"E_A_orig\", \"A_orig\", \"e_prime_orig\", \"E_e_prime_orig\", \"TRV_orig\", \"LAVi_orig\", \"LVMi_orig\", \"2 probability\"]"
      ],
      "metadata": {
        "id": "lWzTqXirqIyP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "univariate_c_index      = list()\n",
        "univariate_modelsummary = list()\n",
        "\n",
        "for feature in FeaturesForUnivariateAnalysis:\n",
        "  ColumnsToBeUsed   = [feature, \"Composite_Event\", \"Time_To_CompositeEvent\"]\n",
        "  E                 = ColumnsToBeUsed[-2]\n",
        "  T                 = ColumnsToBeUsed[-1]\n",
        "\n",
        "  TrainingData      = MTDD_TrainingData[ColumnsToBeUsed]\n",
        "  TrainingData      = TrainingData.fillna(TrainingData.median())\n",
        "\n",
        "  TestingData       = MTDD_TestingData[ColumnsToBeUsed]\n",
        "  TestingData       = TestingData.fillna(TestingData.median())\n",
        "\n",
        "  trained_model, c_index_training, model_summary \\\n",
        "                    = function_train_CoxModel(TrainingData, T, E)                    \n",
        "  c_index_df        = function_test_CoxModel(trained_model, TestingData)  \n",
        "  \n",
        "  univariate_modelsummary.append(model_summary)\n",
        "  univariate_c_index.append(c_index_df)\n",
        "\n",
        "univariate_model_summary_df = pd.concat(univariate_modelsummary)\n",
        "univariate_c_index          = pd.concat(univariate_c_index)\n",
        "univariate_c_index.columns  = [\"C-index\", \"95% lowerCI\", \"95% upper CI\"]\n",
        "\n",
        "univariate_model_summary_df = pd.concat([univariate_c_index.reset_index(drop=True), univariate_model_summary_df.reset_index(drop=True)], axis=1)\n",
        "univariate_model_summary_df.index = FeaturesForUnivariateAnalysis\n",
        "univariate_model_summary_df"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "7vJDsGNQjb-l",
        "outputId": "5d424510-aa95-4eb5-bede-3d0520243389"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n",
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-ad0f2108-a72e-48de-ae1d-82ad6c21a62c\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>C-index</th>\n",
              "      <th>95% lowerCI</th>\n",
              "      <th>95% upper CI</th>\n",
              "      <th>coef</th>\n",
              "      <th>exp(coef)</th>\n",
              "      <th>se(coef)</th>\n",
              "      <th>coef lower 95%</th>\n",
              "      <th>coef upper 95%</th>\n",
              "      <th>exp(coef) lower 95%</th>\n",
              "      <th>exp(coef) upper 95%</th>\n",
              "      <th>z</th>\n",
              "      <th>p</th>\n",
              "      <th>-log2(p)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>AGE</th>\n",
              "      <td>0.76</td>\n",
              "      <td>0.68</td>\n",
              "      <td>0.84</td>\n",
              "      <td>0.035825</td>\n",
              "      <td>1.036475</td>\n",
              "      <td>0.005127</td>\n",
              "      <td>0.025777</td>\n",
              "      <td>0.045874</td>\n",
              "      <td>1.026112</td>\n",
              "      <td>1.046943</td>\n",
              "      <td>6.987577</td>\n",
              "      <td>2.796746e-12</td>\n",
              "      <td>38.379388</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GENDER</th>\n",
              "      <td>0.51</td>\n",
              "      <td>0.42</td>\n",
              "      <td>0.61</td>\n",
              "      <td>0.528049</td>\n",
              "      <td>1.695622</td>\n",
              "      <td>0.158018</td>\n",
              "      <td>0.218339</td>\n",
              "      <td>0.837760</td>\n",
              "      <td>1.244009</td>\n",
              "      <td>2.311184</td>\n",
              "      <td>3.341695</td>\n",
              "      <td>8.326855e-04</td>\n",
              "      <td>10.229941</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>EF_orig</th>\n",
              "      <td>0.54</td>\n",
              "      <td>0.41</td>\n",
              "      <td>0.67</td>\n",
              "      <td>-0.029496</td>\n",
              "      <td>0.970935</td>\n",
              "      <td>0.005537</td>\n",
              "      <td>-0.040347</td>\n",
              "      <td>-0.018644</td>\n",
              "      <td>0.960456</td>\n",
              "      <td>0.981529</td>\n",
              "      <td>-5.327364</td>\n",
              "      <td>9.964847e-08</td>\n",
              "      <td>23.258577</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E_orig</th>\n",
              "      <td>0.71</td>\n",
              "      <td>0.62</td>\n",
              "      <td>0.80</td>\n",
              "      <td>1.461526</td>\n",
              "      <td>4.312536</td>\n",
              "      <td>0.234447</td>\n",
              "      <td>1.002018</td>\n",
              "      <td>1.921034</td>\n",
              "      <td>2.723773</td>\n",
              "      <td>6.828015</td>\n",
              "      <td>6.233926</td>\n",
              "      <td>4.548874e-10</td>\n",
              "      <td>31.033771</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E_A_orig</th>\n",
              "      <td>0.49</td>\n",
              "      <td>0.36</td>\n",
              "      <td>0.63</td>\n",
              "      <td>0.367181</td>\n",
              "      <td>1.443660</td>\n",
              "      <td>0.117638</td>\n",
              "      <td>0.136616</td>\n",
              "      <td>0.597747</td>\n",
              "      <td>1.146387</td>\n",
              "      <td>1.818018</td>\n",
              "      <td>3.121290</td>\n",
              "      <td>1.800605e-03</td>\n",
              "      <td>9.117302</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>A_orig</th>\n",
              "      <td>0.60</td>\n",
              "      <td>0.49</td>\n",
              "      <td>0.73</td>\n",
              "      <td>0.924777</td>\n",
              "      <td>2.521306</td>\n",
              "      <td>0.232407</td>\n",
              "      <td>0.469267</td>\n",
              "      <td>1.380287</td>\n",
              "      <td>1.598823</td>\n",
              "      <td>3.976042</td>\n",
              "      <td>3.979125</td>\n",
              "      <td>6.916937e-05</td>\n",
              "      <td>13.819507</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>e_prime_orig</th>\n",
              "      <td>0.72</td>\n",
              "      <td>0.64</td>\n",
              "      <td>0.80</td>\n",
              "      <td>-0.245590</td>\n",
              "      <td>0.782243</td>\n",
              "      <td>0.037481</td>\n",
              "      <td>-0.319051</td>\n",
              "      <td>-0.172129</td>\n",
              "      <td>0.726839</td>\n",
              "      <td>0.841871</td>\n",
              "      <td>-6.552428</td>\n",
              "      <td>5.660905e-11</td>\n",
              "      <td>34.040176</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E_e_prime_orig</th>\n",
              "      <td>0.79</td>\n",
              "      <td>0.72</td>\n",
              "      <td>0.86</td>\n",
              "      <td>0.050143</td>\n",
              "      <td>1.051422</td>\n",
              "      <td>0.005668</td>\n",
              "      <td>0.039034</td>\n",
              "      <td>0.061252</td>\n",
              "      <td>1.039806</td>\n",
              "      <td>1.063167</td>\n",
              "      <td>8.846745</td>\n",
              "      <td>9.010915e-19</td>\n",
              "      <td>59.944960</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TRV_orig</th>\n",
              "      <td>0.67</td>\n",
              "      <td>0.57</td>\n",
              "      <td>0.76</td>\n",
              "      <td>0.630556</td>\n",
              "      <td>1.878656</td>\n",
              "      <td>0.130986</td>\n",
              "      <td>0.373828</td>\n",
              "      <td>0.887285</td>\n",
              "      <td>1.453287</td>\n",
              "      <td>2.428527</td>\n",
              "      <td>4.813912</td>\n",
              "      <td>1.480042e-06</td>\n",
              "      <td>19.365930</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>LAVi_orig</th>\n",
              "      <td>0.77</td>\n",
              "      <td>0.69</td>\n",
              "      <td>0.84</td>\n",
              "      <td>0.031279</td>\n",
              "      <td>1.031774</td>\n",
              "      <td>0.003828</td>\n",
              "      <td>0.023777</td>\n",
              "      <td>0.038782</td>\n",
              "      <td>1.024062</td>\n",
              "      <td>1.039544</td>\n",
              "      <td>8.171325</td>\n",
              "      <td>3.050218e-16</td>\n",
              "      <td>51.541937</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>LVMi_orig</th>\n",
              "      <td>0.76</td>\n",
              "      <td>0.68</td>\n",
              "      <td>0.84</td>\n",
              "      <td>0.016569</td>\n",
              "      <td>1.016707</td>\n",
              "      <td>0.001901</td>\n",
              "      <td>0.012842</td>\n",
              "      <td>0.020296</td>\n",
              "      <td>1.012925</td>\n",
              "      <td>1.020503</td>\n",
              "      <td>8.714003</td>\n",
              "      <td>2.933295e-18</td>\n",
              "      <td>58.242183</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2 probability</th>\n",
              "      <td>0.81</td>\n",
              "      <td>0.75</td>\n",
              "      <td>0.87</td>\n",
              "      <td>1.852788</td>\n",
              "      <td>6.377573</td>\n",
              "      <td>0.247072</td>\n",
              "      <td>1.368535</td>\n",
              "      <td>2.337040</td>\n",
              "      <td>3.929591</td>\n",
              "      <td>10.350553</td>\n",
              "      <td>7.498977</td>\n",
              "      <td>6.431787e-14</td>\n",
              "      <td>43.821774</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "  "
            ],
            "text/plain": [
              "                C-index  95% lowerCI  ...             p   -log2(p)\n",
              "AGE                0.76         0.68  ...  2.796746e-12  38.379388\n",
              "GENDER             0.51         0.42  ...  8.326855e-04  10.229941\n",
              "EF_orig            0.54         0.41  ...  9.964847e-08  23.258577\n",
              "E_orig             0.71         0.62  ...  4.548874e-10  31.033771\n",
              "E_A_orig           0.49         0.36  ...  1.800605e-03   9.117302\n",
              "A_orig             0.60         0.49  ...  6.916937e-05  13.819507\n",
              "e_prime_orig       0.72         0.64  ...  5.660905e-11  34.040176\n",
              "E_e_prime_orig     0.79         0.72  ...  9.010915e-19  59.944960\n",
              "TRV_orig           0.67         0.57  ...  1.480042e-06  19.365930\n",
              "LAVi_orig          0.77         0.69  ...  3.050218e-16  51.541937\n",
              "LVMi_orig          0.76         0.68  ...  2.933295e-18  58.242183\n",
              "2 probability      0.81         0.75  ...  6.431787e-14  43.821774\n",
              "\n",
              "[12 rows x 13 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "univariate_model_summary_df.to_excel('UnivariateCoxModel.xlsx')"
      ],
      "metadata": {
        "id": "yO6j5AkntVBy"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Select only those predictor with p<0.05 i.e. significant\n",
        "univariate_model_summary_df.loc[univariate_model_summary_df['p']<0.05]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 695
        },
        "id": "RCcn8QrBuYmh",
        "outputId": "3d367df4-e3d5-4e72-d4c1-4eba7527770e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-0bf4934a-187a-42ac-a1d8-7e8eb55ee652\">\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>C-index</th>\n",
              "      <th>95% lowerCI</th>\n",
              "      <th>95% upper CI</th>\n",
              "      <th>coef</th>\n",
              "      <th>exp(coef)</th>\n",
              "      <th>se(coef)</th>\n",
              "      <th>coef lower 95%</th>\n",
              "      <th>coef upper 95%</th>\n",
              "      <th>exp(coef) lower 95%</th>\n",
              "      <th>exp(coef) upper 95%</th>\n",
              "      <th>z</th>\n",
              "      <th>p</th>\n",
              "      <th>-log2(p)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>AGE</th>\n",
              "      <td>0.76</td>\n",
              "      <td>0.68</td>\n",
              "      <td>0.84</td>\n",
              "      <td>0.035825</td>\n",
              "      <td>1.036475</td>\n",
              "      <td>0.005127</td>\n",
              "      <td>0.025777</td>\n",
              "      <td>0.045874</td>\n",
              "      <td>1.026112</td>\n",
              "      <td>1.046943</td>\n",
              "      <td>6.987577</td>\n",
              "      <td>2.796746e-12</td>\n",
              "      <td>38.379388</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GENDER</th>\n",
              "      <td>0.51</td>\n",
              "      <td>0.42</td>\n",
              "      <td>0.61</td>\n",
              "      <td>0.528049</td>\n",
              "      <td>1.695622</td>\n",
              "      <td>0.158018</td>\n",
              "      <td>0.218339</td>\n",
              "      <td>0.837760</td>\n",
              "      <td>1.244009</td>\n",
              "      <td>2.311184</td>\n",
              "      <td>3.341695</td>\n",
              "      <td>8.326855e-04</td>\n",
              "      <td>10.229941</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>EF_orig</th>\n",
              "      <td>0.54</td>\n",
              "      <td>0.41</td>\n",
              "      <td>0.67</td>\n",
              "      <td>-0.029496</td>\n",
              "      <td>0.970935</td>\n",
              "      <td>0.005537</td>\n",
              "      <td>-0.040347</td>\n",
              "      <td>-0.018644</td>\n",
              "      <td>0.960456</td>\n",
              "      <td>0.981529</td>\n",
              "      <td>-5.327364</td>\n",
              "      <td>9.964847e-08</td>\n",
              "      <td>23.258577</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E_orig</th>\n",
              "      <td>0.71</td>\n",
              "      <td>0.62</td>\n",
              "      <td>0.80</td>\n",
              "      <td>1.461526</td>\n",
              "      <td>4.312536</td>\n",
              "      <td>0.234447</td>\n",
              "      <td>1.002018</td>\n",
              "      <td>1.921034</td>\n",
              "      <td>2.723773</td>\n",
              "      <td>6.828015</td>\n",
              "      <td>6.233926</td>\n",
              "      <td>4.548874e-10</td>\n",
              "      <td>31.033771</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E_A_orig</th>\n",
              "      <td>0.49</td>\n",
              "      <td>0.36</td>\n",
              "      <td>0.63</td>\n",
              "      <td>0.367181</td>\n",
              "      <td>1.443660</td>\n",
              "      <td>0.117638</td>\n",
              "      <td>0.136616</td>\n",
              "      <td>0.597747</td>\n",
              "      <td>1.146387</td>\n",
              "      <td>1.818018</td>\n",
              "      <td>3.121290</td>\n",
              "      <td>1.800605e-03</td>\n",
              "      <td>9.117302</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>A_orig</th>\n",
              "      <td>0.60</td>\n",
              "      <td>0.49</td>\n",
              "      <td>0.73</td>\n",
              "      <td>0.924777</td>\n",
              "      <td>2.521306</td>\n",
              "      <td>0.232407</td>\n",
              "      <td>0.469267</td>\n",
              "      <td>1.380287</td>\n",
              "      <td>1.598823</td>\n",
              "      <td>3.976042</td>\n",
              "      <td>3.979125</td>\n",
              "      <td>6.916937e-05</td>\n",
              "      <td>13.819507</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>e_prime_orig</th>\n",
              "      <td>0.72</td>\n",
              "      <td>0.64</td>\n",
              "      <td>0.80</td>\n",
              "      <td>-0.245590</td>\n",
              "      <td>0.782243</td>\n",
              "      <td>0.037481</td>\n",
              "      <td>-0.319051</td>\n",
              "      <td>-0.172129</td>\n",
              "      <td>0.726839</td>\n",
              "      <td>0.841871</td>\n",
              "      <td>-6.552428</td>\n",
              "      <td>5.660905e-11</td>\n",
              "      <td>34.040176</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E_e_prime_orig</th>\n",
              "      <td>0.79</td>\n",
              "      <td>0.72</td>\n",
              "      <td>0.86</td>\n",
              "      <td>0.050143</td>\n",
              "      <td>1.051422</td>\n",
              "      <td>0.005668</td>\n",
              "      <td>0.039034</td>\n",
              "      <td>0.061252</td>\n",
              "      <td>1.039806</td>\n",
              "      <td>1.063167</td>\n",
              "      <td>8.846745</td>\n",
              "      <td>9.010915e-19</td>\n",
              "      <td>59.944960</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TRV_orig</th>\n",
              "      <td>0.67</td>\n",
              "      <td>0.57</td>\n",
              "      <td>0.76</td>\n",
              "      <td>0.630556</td>\n",
              "      <td>1.878656</td>\n",
              "      <td>0.130986</td>\n",
              "      <td>0.373828</td>\n",
              "      <td>0.887285</td>\n",
              "      <td>1.453287</td>\n",
              "      <td>2.428527</td>\n",
              "      <td>4.813912</td>\n",
              "      <td>1.480042e-06</td>\n",
              "      <td>19.365930</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>LAVi_orig</th>\n",
              "      <td>0.77</td>\n",
              "      <td>0.69</td>\n",
              "      <td>0.84</td>\n",
              "      <td>0.031279</td>\n",
              "      <td>1.031774</td>\n",
              "      <td>0.003828</td>\n",
              "      <td>0.023777</td>\n",
              "      <td>0.038782</td>\n",
              "      <td>1.024062</td>\n",
              "      <td>1.039544</td>\n",
              "      <td>8.171325</td>\n",
              "      <td>3.050218e-16</td>\n",
              "      <td>51.541937</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>LVMi_orig</th>\n",
              "      <td>0.76</td>\n",
              "      <td>0.68</td>\n",
              "      <td>0.84</td>\n",
              "      <td>0.016569</td>\n",
              "      <td>1.016707</td>\n",
              "      <td>0.001901</td>\n",
              "      <td>0.012842</td>\n",
              "      <td>0.020296</td>\n",
              "      <td>1.012925</td>\n",
              "      <td>1.020503</td>\n",
              "      <td>8.714003</td>\n",
              "      <td>2.933295e-18</td>\n",
              "      <td>58.242183</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2 probability</th>\n",
              "      <td>0.81</td>\n",
              "      <td>0.75</td>\n",
              "      <td>0.87</td>\n",
              "      <td>1.852788</td>\n",
              "      <td>6.377573</td>\n",
              "      <td>0.247072</td>\n",
              "      <td>1.368535</td>\n",
              "      <td>2.337040</td>\n",
              "      <td>3.929591</td>\n",
              "      <td>10.350553</td>\n",
              "      <td>7.498977</td>\n",
              "      <td>6.431787e-14</td>\n",
              "      <td>43.821774</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-0bf4934a-187a-42ac-a1d8-7e8eb55ee652')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
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              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
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              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-0bf4934a-187a-42ac-a1d8-7e8eb55ee652 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-0bf4934a-187a-42ac-a1d8-7e8eb55ee652');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "                C-index  95% lowerCI  ...             p   -log2(p)\n",
              "AGE                0.76         0.68  ...  2.796746e-12  38.379388\n",
              "GENDER             0.51         0.42  ...  8.326855e-04  10.229941\n",
              "EF_orig            0.54         0.41  ...  9.964847e-08  23.258577\n",
              "E_orig             0.71         0.62  ...  4.548874e-10  31.033771\n",
              "E_A_orig           0.49         0.36  ...  1.800605e-03   9.117302\n",
              "A_orig             0.60         0.49  ...  6.916937e-05  13.819507\n",
              "e_prime_orig       0.72         0.64  ...  5.660905e-11  34.040176\n",
              "E_e_prime_orig     0.79         0.72  ...  9.010915e-19  59.944960\n",
              "TRV_orig           0.67         0.57  ...  1.480042e-06  19.365930\n",
              "LAVi_orig          0.77         0.69  ...  3.050218e-16  51.541937\n",
              "LVMi_orig          0.76         0.68  ...  2.933295e-18  58.242183\n",
              "2 probability      0.81         0.75  ...  6.431787e-14  43.821774\n",
              "\n",
              "[12 rows x 13 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Multivariate Cox Proportional Hazard Analysis"
      ],
      "metadata": {
        "id": "xtzt22S9o0IP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "FeaturesForMultivariateAnalysis = univariate_model_summary_df.index.to_list()\n",
        "\n",
        "ColumnsToBeUsed   = FeaturesForMultivariateAnalysis + [\"Composite_Event\", \"Time_To_CompositeEvent\"]\n",
        "E                 = ColumnsToBeUsed[-2]\n",
        "T                 = ColumnsToBeUsed[-1]"
      ],
      "metadata": {
        "id": "dDMKE-Xxmnrh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "TrainingData      = MTDD_TrainingData[ColumnsToBeUsed]\n",
        "TrainingData      = TrainingData.fillna(TrainingData.median())\n",
        "\n",
        "TestingData       = MTDD_TestingData[ColumnsToBeUsed]\n",
        "TestingData       = TestingData.fillna(TestingData.median())\n",
        "\n",
        "trained_model, c_index_training, model_summary \\\n",
        "                  = function_train_CoxModel(TrainingData, T, E)                    \n",
        "c_index_df        = function_test_CoxModel(trained_model, TestingData)  \n",
        "\n",
        "MultiVariateCox = model_summary\n",
        "MultiVariateCox.to_excel('MultiVariateCox.xlsx')\n",
        "MultiVariateCox"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 494
        },
        "id": "F5PAzg6YnULo",
        "outputId": "826f5c3e-ae74-4b25-e517-3a8f74655062"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/lifelines/utils/__init__.py:936: UserWarning: DataFrame Index is not unique, defaulting to incrementing index instead.\n",
            "  warnings.warn(\"DataFrame Index is not unique, defaulting to incrementing index instead.\")\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-38e254bd-eb6b-4be6-8fef-0d638c4adff5\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
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              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>coef</th>\n",
              "      <th>exp(coef)</th>\n",
              "      <th>se(coef)</th>\n",
              "      <th>coef lower 95%</th>\n",
              "      <th>coef upper 95%</th>\n",
              "      <th>exp(coef) lower 95%</th>\n",
              "      <th>exp(coef) upper 95%</th>\n",
              "      <th>z</th>\n",
              "      <th>p</th>\n",
              "      <th>-log2(p)</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>covariate</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>AGE</th>\n",
              "      <td>0.019561</td>\n",
              "      <td>1.019753</td>\n",
              "      <td>0.006440</td>\n",
              "      <td>0.006938</td>\n",
              "      <td>0.032184</td>\n",
              "      <td>1.006962</td>\n",
              "      <td>1.032707</td>\n",
              "      <td>3.037275</td>\n",
              "      <td>0.002387</td>\n",
              "      <td>8.710418</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>GENDER</th>\n",
              "      <td>0.155249</td>\n",
              "      <td>1.167949</td>\n",
              "      <td>0.182620</td>\n",
              "      <td>-0.202679</td>\n",
              "      <td>0.513177</td>\n",
              "      <td>0.816540</td>\n",
              "      <td>1.670591</td>\n",
              "      <td>0.850122</td>\n",
              "      <td>0.395257</td>\n",
              "      <td>1.339137</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>EF_orig</th>\n",
              "      <td>-0.018059</td>\n",
              "      <td>0.982103</td>\n",
              "      <td>0.007093</td>\n",
              "      <td>-0.031962</td>\n",
              "      <td>-0.004156</td>\n",
              "      <td>0.968544</td>\n",
              "      <td>0.995853</td>\n",
              "      <td>-2.545841</td>\n",
              "      <td>0.010901</td>\n",
              "      <td>6.519332</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E_orig</th>\n",
              "      <td>-0.109925</td>\n",
              "      <td>0.895901</td>\n",
              "      <td>0.618130</td>\n",
              "      <td>-1.321437</td>\n",
              "      <td>1.101587</td>\n",
              "      <td>0.266752</td>\n",
              "      <td>3.008936</td>\n",
              "      <td>-0.177835</td>\n",
              "      <td>0.858852</td>\n",
              "      <td>0.219518</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E_A_orig</th>\n",
              "      <td>0.361656</td>\n",
              "      <td>1.435705</td>\n",
              "      <td>0.237888</td>\n",
              "      <td>-0.104596</td>\n",
              "      <td>0.827908</td>\n",
              "      <td>0.900688</td>\n",
              "      <td>2.288527</td>\n",
              "      <td>1.520277</td>\n",
              "      <td>0.128441</td>\n",
              "      <td>2.960818</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>A_orig</th>\n",
              "      <td>0.886391</td>\n",
              "      <td>2.426358</td>\n",
              "      <td>0.483997</td>\n",
              "      <td>-0.062226</td>\n",
              "      <td>1.835008</td>\n",
              "      <td>0.939671</td>\n",
              "      <td>6.265186</td>\n",
              "      <td>1.831398</td>\n",
              "      <td>0.067041</td>\n",
              "      <td>3.898808</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>e_prime_orig</th>\n",
              "      <td>0.020429</td>\n",
              "      <td>1.020639</td>\n",
              "      <td>0.080654</td>\n",
              "      <td>-0.137649</td>\n",
              "      <td>0.178507</td>\n",
              "      <td>0.871404</td>\n",
              "      <td>1.195431</td>\n",
              "      <td>0.253290</td>\n",
              "      <td>0.800044</td>\n",
              "      <td>0.321848</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>E_e_prime_orig</th>\n",
              "      <td>0.000765</td>\n",
              "      <td>1.000766</td>\n",
              "      <td>0.019897</td>\n",
              "      <td>-0.038232</td>\n",
              "      <td>0.039763</td>\n",
              "      <td>0.962490</td>\n",
              "      <td>1.040564</td>\n",
              "      <td>0.038465</td>\n",
              "      <td>0.969317</td>\n",
              "      <td>0.044959</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>TRV_orig</th>\n",
              "      <td>0.066456</td>\n",
              "      <td>1.068714</td>\n",
              "      <td>0.133520</td>\n",
              "      <td>-0.195239</td>\n",
              "      <td>0.328151</td>\n",
              "      <td>0.822638</td>\n",
              "      <td>1.388399</td>\n",
              "      <td>0.497722</td>\n",
              "      <td>0.618680</td>\n",
              "      <td>0.692735</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>LAVi_orig</th>\n",
              "      <td>0.005490</td>\n",
              "      <td>1.005505</td>\n",
              "      <td>0.005538</td>\n",
              "      <td>-0.005363</td>\n",
              "      <td>0.016344</td>\n",
              "      <td>0.994651</td>\n",
              "      <td>1.016478</td>\n",
              "      <td>0.991482</td>\n",
              "      <td>0.321450</td>\n",
              "      <td>1.637332</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>LVMi_orig</th>\n",
              "      <td>0.006935</td>\n",
              "      <td>1.006959</td>\n",
              "      <td>0.002385</td>\n",
              "      <td>0.002261</td>\n",
              "      <td>0.011609</td>\n",
              "      <td>1.002263</td>\n",
              "      <td>1.011677</td>\n",
              "      <td>2.907903</td>\n",
              "      <td>0.003639</td>\n",
              "      <td>8.102395</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2 probability</th>\n",
              "      <td>0.647279</td>\n",
              "      <td>1.910337</td>\n",
              "      <td>0.359932</td>\n",
              "      <td>-0.058175</td>\n",
              "      <td>1.352734</td>\n",
              "      <td>0.943485</td>\n",
              "      <td>3.867986</td>\n",
              "      <td>1.798336</td>\n",
              "      <td>0.072124</td>\n",
              "      <td>3.793381</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-38e254bd-eb6b-4be6-8fef-0d638c4adff5')\"\n",
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              "              style=\"display:none;\">\n",
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              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "\n",
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              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
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              "  </style>\n",
              "\n",
              "      <script>\n",
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              "          document.querySelector('#df-38e254bd-eb6b-4be6-8fef-0d638c4adff5 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-38e254bd-eb6b-4be6-8fef-0d638c4adff5');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "                    coef  exp(coef)  se(coef)  ...         z         p  -log2(p)\n",
              "covariate                                      ...                              \n",
              "AGE             0.019561   1.019753  0.006440  ...  3.037275  0.002387  8.710418\n",
              "GENDER          0.155249   1.167949  0.182620  ...  0.850122  0.395257  1.339137\n",
              "EF_orig        -0.018059   0.982103  0.007093  ... -2.545841  0.010901  6.519332\n",
              "E_orig         -0.109925   0.895901  0.618130  ... -0.177835  0.858852  0.219518\n",
              "E_A_orig        0.361656   1.435705  0.237888  ...  1.520277  0.128441  2.960818\n",
              "A_orig          0.886391   2.426358  0.483997  ...  1.831398  0.067041  3.898808\n",
              "e_prime_orig    0.020429   1.020639  0.080654  ...  0.253290  0.800044  0.321848\n",
              "E_e_prime_orig  0.000765   1.000766  0.019897  ...  0.038465  0.969317  0.044959\n",
              "TRV_orig        0.066456   1.068714  0.133520  ...  0.497722  0.618680  0.692735\n",
              "LAVi_orig       0.005490   1.005505  0.005538  ...  0.991482  0.321450  1.637332\n",
              "LVMi_orig       0.006935   1.006959  0.002385  ...  2.907903  0.003639  8.102395\n",
              "2 probability   0.647279   1.910337  0.359932  ...  1.798336  0.072124  3.793381\n",
              "\n",
              "[12 rows x 10 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "M8Uy_yDKpeSO"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}