BMD-Logistic Regression-GitHub.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistics Regression - BMD Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importing CSV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "bmd = pd.read_csv('../../bmd/bmd.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>fracture</th>\n",
       "      <th>weight_kg</th>\n",
       "      <th>height_cm</th>\n",
       "      <th>medication</th>\n",
       "      <th>waiting_time</th>\n",
       "      <th>bmd</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>469</td>\n",
       "      <td>57.052768</td>\n",
       "      <td>F</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>64.0</td>\n",
       "      <td>155.5</td>\n",
       "      <td>Anticonvulsant</td>\n",
       "      <td>18</td>\n",
       "      <td>0.8793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8724</td>\n",
       "      <td>75.741225</td>\n",
       "      <td>F</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>78.0</td>\n",
       "      <td>162.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>56</td>\n",
       "      <td>0.7946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6736</td>\n",
       "      <td>70.778900</td>\n",
       "      <td>M</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>73.0</td>\n",
       "      <td>170.5</td>\n",
       "      <td>No medication</td>\n",
       "      <td>10</td>\n",
       "      <td>0.9067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>24180</td>\n",
       "      <td>78.247175</td>\n",
       "      <td>F</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>60.0</td>\n",
       "      <td>148.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>14</td>\n",
       "      <td>0.7112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17072</td>\n",
       "      <td>54.191877</td>\n",
       "      <td>M</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>55.0</td>\n",
       "      <td>161.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>20</td>\n",
       "      <td>0.7909</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      id        age sex     fracture  weight_kg  height_cm      medication  \\\n",
       "0    469  57.052768   F  no fracture       64.0      155.5  Anticonvulsant   \n",
       "1   8724  75.741225   F  no fracture       78.0      162.0   No medication   \n",
       "2   6736  70.778900   M  no fracture       73.0      170.5   No medication   \n",
       "3  24180  78.247175   F  no fracture       60.0      148.0   No medication   \n",
       "4  17072  54.191877   M  no fracture       55.0      161.0   No medication   \n",
       "\n",
       "   waiting_time     bmd  \n",
       "0            18  0.8793  \n",
       "1            56  0.7946  \n",
       "2            10  0.9067  \n",
       "3            14  0.7112  \n",
       "4            20  0.7909  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmd.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analyzing numeric columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>age</th>\n",
       "      <th>weight_kg</th>\n",
       "      <th>height_cm</th>\n",
       "      <th>waiting_time</th>\n",
       "      <th>bmd</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>169.000000</td>\n",
       "      <td>169.000000</td>\n",
       "      <td>169.000000</td>\n",
       "      <td>169.000000</td>\n",
       "      <td>169.000000</td>\n",
       "      <td>169.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>9102.556213</td>\n",
       "      <td>63.631531</td>\n",
       "      <td>64.665680</td>\n",
       "      <td>160.254438</td>\n",
       "      <td>19.739645</td>\n",
       "      <td>0.783104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8744.623598</td>\n",
       "      <td>12.356936</td>\n",
       "      <td>11.537171</td>\n",
       "      <td>7.928272</td>\n",
       "      <td>15.800570</td>\n",
       "      <td>0.166529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>35.000000</td>\n",
       "      <td>35.814058</td>\n",
       "      <td>36.000000</td>\n",
       "      <td>142.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.407600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2018.000000</td>\n",
       "      <td>54.424211</td>\n",
       "      <td>56.000000</td>\n",
       "      <td>154.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>0.670800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>6702.000000</td>\n",
       "      <td>63.487837</td>\n",
       "      <td>64.500000</td>\n",
       "      <td>160.500000</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>0.786100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>17100.000000</td>\n",
       "      <td>72.080558</td>\n",
       "      <td>73.000000</td>\n",
       "      <td>166.000000</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>0.888800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>24208.000000</td>\n",
       "      <td>88.753795</td>\n",
       "      <td>96.000000</td>\n",
       "      <td>177.000000</td>\n",
       "      <td>96.000000</td>\n",
       "      <td>1.362400</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 id         age   weight_kg   height_cm  waiting_time  \\\n",
       "count    169.000000  169.000000  169.000000  169.000000    169.000000   \n",
       "mean    9102.556213   63.631531   64.665680  160.254438     19.739645   \n",
       "std     8744.623598   12.356936   11.537171    7.928272     15.800570   \n",
       "min       35.000000   35.814058   36.000000  142.000000      5.000000   \n",
       "25%     2018.000000   54.424211   56.000000  154.000000      9.000000   \n",
       "50%     6702.000000   63.487837   64.500000  160.500000     14.000000   \n",
       "75%    17100.000000   72.080558   73.000000  166.000000     24.000000   \n",
       "max    24208.000000   88.753795   96.000000  177.000000     96.000000   \n",
       "\n",
       "              bmd  \n",
       "count  169.000000  \n",
       "mean     0.783104  \n",
       "std      0.166529  \n",
       "min      0.407600  \n",
       "25%      0.670800  \n",
       "50%      0.786100  \n",
       "75%      0.888800  \n",
       "max      1.362400  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmd.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>age</th>\n",
       "      <th>weight_kg</th>\n",
       "      <th>height_cm</th>\n",
       "      <th>waiting_time</th>\n",
       "      <th>bmd</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fracture</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fracture</th>\n",
       "      <td>7869.040000</td>\n",
       "      <td>69.771320</td>\n",
       "      <td>58.410000</td>\n",
       "      <td>159.290000</td>\n",
       "      <td>23.300000</td>\n",
       "      <td>0.623308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>no fracture</th>\n",
       "      <td>9620.840336</td>\n",
       "      <td>61.051787</td>\n",
       "      <td>67.294118</td>\n",
       "      <td>160.659664</td>\n",
       "      <td>18.243697</td>\n",
       "      <td>0.850245</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      id        age  weight_kg   height_cm  waiting_time  \\\n",
       "fracture                                                                   \n",
       "fracture     7869.040000  69.771320  58.410000  159.290000     23.300000   \n",
       "no fracture  9620.840336  61.051787  67.294118  160.659664     18.243697   \n",
       "\n",
       "                  bmd  \n",
       "fracture               \n",
       "fracture     0.623308  \n",
       "no fracture  0.850245  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmd.groupby('fracture').mean()\n",
    "\n",
    "# id: To be removed\n",
    "# Age: The oldest you get, the biggest the probability to fracture.\n",
    "# Weight: A higher weight helps preventing a fracture.\n",
    "# Height: It does not really impact.\n",
    "# Waiting time (time the patient had to wait for the densitometry (in minutes): the longest the time, the more probability to fracture.\n",
    "# Bdm (bone mineral density): The most dense your bones ares, the less likely they are to fracture."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analyzing string columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>sex</th>\n",
       "      <th>F</th>\n",
       "      <th>M</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fracture</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fracture</th>\n",
       "      <td>25</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>no fracture</th>\n",
       "      <td>58</td>\n",
       "      <td>61</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "sex           F   M\n",
       "fracture           \n",
       "fracture     25  25\n",
       "no fracture  58  61"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_sex = pd.crosstab(bmd['fracture'], bmd['sex'])\n",
    "cross_sex\n",
    "\n",
    "# There is not a lot of difference between Men and Women"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.30120481927710846"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Female_Fracture = cross_sex['F']['fracture'] / (cross_sex['F']['fracture']  + cross_sex['F']['no fracture'])\n",
    "Female_Fracture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.29069767441860467"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Male_Fracture = cross_sex['M']['fracture'] / (cross_sex['M']['fracture']  + cross_sex['M']['no fracture'])\n",
    "Male_Fracture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>medication</th>\n",
       "      <th>Anticonvulsant</th>\n",
       "      <th>Glucocorticoids</th>\n",
       "      <th>No medication</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fracture</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>fracture</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>no fracture</th>\n",
       "      <td>5</td>\n",
       "      <td>19</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "medication   Anticonvulsant  Glucocorticoids  No medication\n",
       "fracture                                                   \n",
       "fracture                  4                5             41\n",
       "no fracture               5               19             95"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_med = pd.crosstab(bmd['fracture'], bmd['medication'])\n",
    "cross_med\n",
    "\n",
    "# Medication prevents fractures, especially for Gluco. For Anticonvulsant there are not many cases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4444444444444444"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Anticonvulsant_fracture = cross_med['Anticonvulsant']['fracture'] / (cross_med['Anticonvulsant']['fracture']  \n",
    "+ cross_med['Anticonvulsant']['no fracture'])\n",
    "\n",
    "Anticonvulsant_fracture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20833333333333334"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Glucocorticoids_fracture = cross_med['Glucocorticoids']['fracture'] / (cross_med['Glucocorticoids']['fracture']  \n",
    "+ cross_med['Glucocorticoids']['no fracture'])\n",
    "\n",
    "Glucocorticoids_fracture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3014705882352941"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "No_medication_fracture = cross_med['No medication']['fracture'] / (cross_med['No medication']['fracture']  \n",
    "+ cross_med['No medication']['no fracture'])\n",
    "\n",
    "No_medication_fracture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Removing columns \"id\" and sending \"fracture\" column to the end."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['id',\n",
       " 'age',\n",
       " 'sex',\n",
       " 'fracture',\n",
       " 'weight_kg',\n",
       " 'height_cm',\n",
       " 'medication',\n",
       " 'waiting_time',\n",
       " 'bmd']"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols = bmd.columns.values.tolist()\n",
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols_new = ['age',\n",
    " 'sex',\n",
    " 'weight_kg',\n",
    " 'height_cm',\n",
    " 'medication',\n",
    " 'waiting_time',\n",
    " 'bmd',\n",
    " 'fracture']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "bmd = bmd[cols_new]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "dum_sex = pd.get_dummies(bmd['sex'], prefix = 'sex')\n",
    "new_bmd = bmd.join(dum_sex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>weight_kg</th>\n",
       "      <th>height_cm</th>\n",
       "      <th>medication</th>\n",
       "      <th>waiting_time</th>\n",
       "      <th>bmd</th>\n",
       "      <th>fracture</th>\n",
       "      <th>sex_F</th>\n",
       "      <th>sex_M</th>\n",
       "      <th>medication_Anticonvulsant</th>\n",
       "      <th>medication_Glucocorticoids</th>\n",
       "      <th>medication_No medication</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>57.052768</td>\n",
       "      <td>F</td>\n",
       "      <td>64.0</td>\n",
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       "      <td>Anticonvulsant</td>\n",
       "      <td>18</td>\n",
       "      <td>0.8793</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>75.741225</td>\n",
       "      <td>F</td>\n",
       "      <td>78.0</td>\n",
       "      <td>162.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>56</td>\n",
       "      <td>0.7946</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>70.778900</td>\n",
       "      <td>M</td>\n",
       "      <td>73.0</td>\n",
       "      <td>170.5</td>\n",
       "      <td>No medication</td>\n",
       "      <td>10</td>\n",
       "      <td>0.9067</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         age sex  weight_kg  height_cm      medication  waiting_time     bmd  \\\n",
       "0  57.052768   F       64.0      155.5  Anticonvulsant            18  0.8793   \n",
       "1  75.741225   F       78.0      162.0   No medication            56  0.7946   \n",
       "2  70.778900   M       73.0      170.5   No medication            10  0.9067   \n",
       "\n",
       "      fracture  sex_F  sex_M  medication_Anticonvulsant  \\\n",
       "0  no fracture      1      0                          1   \n",
       "1  no fracture      1      0                          0   \n",
       "2  no fracture      0      1                          0   \n",
       "\n",
       "   medication_Glucocorticoids  medication_No medication  \n",
       "0                           0                         0  \n",
       "1                           0                         1  \n",
       "2                           0                         1  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dum_med = pd.get_dummies(new_bmd['medication'], prefix = 'medication')\n",
    "new_bmd = new_bmd.join(dum_med)\n",
    "new_bmd.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['age',\n",
       " 'sex',\n",
       " 'weight_kg',\n",
       " 'height_cm',\n",
       " 'medication',\n",
       " 'waiting_time',\n",
       " 'bmd',\n",
       " 'fracture',\n",
       " 'sex_F',\n",
       " 'sex_M',\n",
       " 'medication_Anticonvulsant',\n",
       " 'medication_Glucocorticoids',\n",
       " 'medication_No medication']"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols = new_bmd.columns.values.tolist()\n",
    "cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols_new = ['age',\n",
    " 'weight_kg',\n",
    " 'height_cm',\n",
    " 'waiting_time',\n",
    " 'bmd',\n",
    " 'fracture',\n",
    " 'sex_F',\n",
    " 'sex_M',\n",
    " 'medication_Anticonvulsant',\n",
    " 'medication_Glucocorticoids',\n",
    " 'medication_No medication']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_bmd = new_bmd[cols_new]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>weight_kg</th>\n",
       "      <th>height_cm</th>\n",
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       "      <td>18</td>\n",
       "      <td>0.8793</td>\n",
       "      <td>no fracture</td>\n",
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       "      <td>0</td>\n",
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       "      <td>73.0</td>\n",
       "      <td>170.5</td>\n",
       "      <td>10</td>\n",
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       "      <td>no fracture</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>78.247175</td>\n",
       "      <td>60.0</td>\n",
       "      <td>148.0</td>\n",
       "      <td>14</td>\n",
       "      <td>0.7112</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>54.191877</td>\n",
       "      <td>55.0</td>\n",
       "      <td>161.0</td>\n",
       "      <td>20</td>\n",
       "      <td>0.7909</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         age  weight_kg  height_cm  waiting_time     bmd     fracture  sex_F  \\\n",
       "0  57.052768       64.0      155.5            18  0.8793  no fracture      1   \n",
       "1  75.741225       78.0      162.0            56  0.7946  no fracture      1   \n",
       "2  70.778900       73.0      170.5            10  0.9067  no fracture      0   \n",
       "3  78.247175       60.0      148.0            14  0.7112  no fracture      1   \n",
       "4  54.191877       55.0      161.0            20  0.7909  no fracture      0   \n",
       "\n",
       "   sex_M  medication_Anticonvulsant  medication_Glucocorticoids  \\\n",
       "0      0                          1                           0   \n",
       "1      0                          0                           0   \n",
       "2      1                          0                           0   \n",
       "3      0                          0                           0   \n",
       "4      1                          0                           0   \n",
       "\n",
       "   medication_No medication  \n",
       "0                         0  \n",
       "1                         1  \n",
       "2                         1  \n",
       "3                         1  \n",
       "4                         1  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_bmd.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We change the Fracture columns from string to numeric. True=1, False=0.\n",
    "\n",
    "new_bmd['fracture'] = (new_bmd['fracture'] == 'fracture').astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>148.0</td>\n",
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       "      <td>0.7112</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>54.191877</td>\n",
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       "      <td>161.0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         age  weight_kg  height_cm  waiting_time     bmd  fracture  sex_F  \\\n",
       "0  57.052768       64.0      155.5            18  0.8793         0      1   \n",
       "1  75.741225       78.0      162.0            56  0.7946         0      1   \n",
       "2  70.778900       73.0      170.5            10  0.9067         0      0   \n",
       "3  78.247175       60.0      148.0            14  0.7112         0      1   \n",
       "4  54.191877       55.0      161.0            20  0.7909         0      0   \n",
       "\n",
       "   sex_M  medication_Anticonvulsant  medication_Glucocorticoids  \\\n",
       "0      0                          1                           0   \n",
       "1      0                          0                           0   \n",
       "2      1                          0                           0   \n",
       "3      0                          0                           0   \n",
       "4      1                          0                           0   \n",
       "\n",
       "   medication_No medication  \n",
       "0                         0  \n",
       "1                         1  \n",
       "2                         1  \n",
       "3                         1  \n",
       "4                         1  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_bmd.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    119\n",
       "1     50\n",
       "Name: fracture, dtype: int64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_bmd.fracture.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Select columns to build the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['age',\n",
       " 'weight_kg',\n",
       " 'height_cm',\n",
       " 'waiting_time',\n",
       " 'bmd',\n",
       " 'fracture',\n",
       " 'sex_F',\n",
       " 'sex_M',\n",
       " 'medication_Anticonvulsant',\n",
       " 'medication_Glucocorticoids',\n",
       " 'medication_No medication']"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_bmd.columns.values.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = ['age',\n",
    " 'weight_kg',\n",
    " 'height_cm',\n",
    " 'waiting_time',\n",
    " 'bmd',\n",
    " 'sex_F',\n",
    " 'sex_M',\n",
    " 'medication_Anticonvulsant',\n",
    " 'medication_Glucocorticoids',\n",
    " 'medication_No medication']\n",
    "\n",
    "Y = ['fracture']\n",
    "\n",
    "# We put under X the columns to be used as predictors.\n",
    "# Y is the column we want to predict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We evaluate dtypes and assign numeric type to them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "age                           float64\n",
       "weight_kg                     float64\n",
       "height_cm                     float64\n",
       "waiting_time                    int64\n",
       "bmd                           float64\n",
       "fracture                        int32\n",
       "sex_F                           uint8\n",
       "sex_M                           uint8\n",
       "medication_Anticonvulsant       uint8\n",
       "medication_Glucocorticoids      uint8\n",
       "medication_No medication        uint8\n",
       "dtype: object"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_bmd.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\pandas\\core\\ops\\array_ops.py:253: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  res_values = method(rvalues)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "age                           float64\n",
       "weight_kg                     float64\n",
       "height_cm                     float64\n",
       "waiting_time                    int64\n",
       "bmd                           float64\n",
       "fracture                        int32\n",
       "sex_F                           int32\n",
       "sex_M                           int32\n",
       "medication_Anticonvulsant       int32\n",
       "medication_Glucocorticoids      int32\n",
       "medication_No medication        int32\n",
       "dtype: object"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_bmd['sex_F'] = (new_bmd['sex_F'] == 'sex_F').astype(int)\n",
    "new_bmd['sex_M'] = (new_bmd['sex_M'] == 'sex_M').astype(int)\n",
    "new_bmd['medication_Anticonvulsant'] = (new_bmd['medication_Anticonvulsant'] == 'medication_Anticonvulsant').astype(int)\n",
    "new_bmd['medication_Glucocorticoids'] = (new_bmd['medication_Glucocorticoids'] == 'medication_Glucocorticoids').astype(int)\n",
    "new_bmd['medication_No medication'] = (new_bmd['medication_No medication'] == 'medication_No medication').astype(int) \n",
    "new_bmd.dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# We import the needed libraries and fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.feature_selection import RFE\n",
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "rfe = RFE(lr, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    }
   ],
   "source": [
    "rfe = rfe.fit(new_bmd[X], new_bmd[Y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, False,  True, False, False, False, False,\n",
       "       False])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfe.support_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3,  2,  4,  5,  1, 10,  9,  8,  7,  6])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rfe.ranking_\n",
    "# Ranking allows us to rank the impact of every columns on the final model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('age', 3),\n",
       " ('weight_kg', 2),\n",
       " ('height_cm', 4),\n",
       " ('waiting_time', 5),\n",
       " ('bmd', 1),\n",
       " ('sex_F', 10),\n",
       " ('sex_M', 9),\n",
       " ('medication_Anticonvulsant', 8),\n",
       " ('medication_Glucocorticoids', 7),\n",
       " ('medication_No medication', 6)]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(zip(new_bmd[X],rfe.ranking_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Implementation with SKLEARN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "logit_model = linear_model.LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_model.fit(new_bmd[X], new_bmd[Y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8224852071005917"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_model.score(new_bmd[X], new_bmd[Y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create and Actual vs Prediction column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "Actual_and_Prediction = pd.DataFrame(\n",
    "    {\n",
    "    'Prediction': logit_model.predict(new_bmd[X]).tolist()\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "Actual_and_Prediction['Actual'] = new_bmd[Y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "Actual_and_Prediction['Result'] = Actual_and_Prediction['Actual'] == Actual_and_Prediction['Prediction']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "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",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Prediction</th>\n",
       "      <th>Actual</th>\n",
       "      <th>Result</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Prediction  Actual  Result\n",
       "0           0       0    True\n",
       "1           0       0    True\n",
       "2           0       0    True\n",
       "3           0       0    True\n",
       "4           0       0    True"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Actual_and_Prediction.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True     139\n",
       "False     30\n",
       "Name: Result, dtype: int64"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Actual_and_Prediction['Result'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8224852071005917"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Percentage of hits\n",
    "139 / (30 + 139)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# As seen, Score can be calcaulated as True / (True+False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Can the model work with less variables?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# As seen, Gender does not really a big impact on Y. Let's remove the Gender related columns and re run the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = ['age',\n",
    " 'weight_kg',\n",
    " 'height_cm',\n",
    " 'waiting_time',\n",
    " 'bmd',\n",
    " 'medication_Anticonvulsant',\n",
    " 'medication_Glucocorticoids',\n",
    " 'medication_No medication']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_model.fit(new_bmd[X], new_bmd[Y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8224852071005917"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_model.score(new_bmd[X], new_bmd[Y])\n",
    "\n",
    "# Removing the gender columns has no impact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's now remove the medication fields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8224852071005917"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = ['age',\n",
    " 'weight_kg',\n",
    " 'height_cm',\n",
    " 'waiting_time',\n",
    " 'bmd']\n",
    "\n",
    "logit_model.fit(new_bmd[X], new_bmd[Y])\n",
    "logit_model.score(new_bmd[X], new_bmd[Y])\n",
    "\n",
    "# As we see, if we remove this field, the model losses part of its predictive capabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8106508875739645"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's now remove the waiting time\n",
    "\n",
    "X = ['age',\n",
    "'weight_kg',\n",
    " 'height_cm',\n",
    " 'bmd']\n",
    "\n",
    "logit_model.fit(new_bmd[X], new_bmd[Y])\n",
    "logit_model.score(new_bmd[X], new_bmd[Y])\n",
    "\n",
    "# As per the result, when removing waiting time, the model losses part of its capabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8402366863905325"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = [\n",
    " 'age',\n",
    " #'weight_kg',\n",
    " #'height_cm',\n",
    " 'medication_No medication',\n",
    " 'waiting_time',\n",
    " 'bmd'\n",
    "    ]\n",
    "\n",
    "\n",
    "logit_model.fit(new_bmd[X], new_bmd[Y])\n",
    "logit_model.score(new_bmd[X], new_bmd[Y])\n",
    "\n",
    "# We include waiting_time again. \n",
    "# We have finally four fields. We can manually check, which fields we can remove to see how we impact the model results.\n",
    "\n",
    "# Is 84% a good result? Initially, we had a list with 119 cases in which a fracture did not ocurr, and 50 in which it did.\n",
    "# If we always predict \"no fracture\", we will be right in 70,4 percent of the cases (1-(50 / (50+119)))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "Actual_and_Prediction = pd.DataFrame(\n",
    "    {\n",
    "    'Prediction': logit_model.predict(new_bmd[X]).tolist()\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_bmd['Prediction'] = Actual_and_Prediction['Prediction']\n",
    "new_bmd['Result'] = new_bmd['fracture'] == new_bmd['Prediction']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True     142\n",
       "False     27\n",
       "Name: Result, dtype: int64"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_bmd['Result'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, Y_train, Y_test = train_test_split(new_bmd[X], new_bmd[Y], test_size=0.3, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train:  118\n",
      "X_test:  51\n",
      "Y_train:  118\n",
      "Y_test:  51\n"
     ]
    }
   ],
   "source": [
    "# Length:\n",
    "print('X_train: ', len(X_train))\n",
    "print('X_test: ', len(X_test))\n",
    "print('Y_train: ', len(Y_train))\n",
    "print('Y_test: ', len(Y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8389830508474576"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = linear_model.LogisticRegression()\n",
    "lm.fit(X_train, Y_train)\n",
    "lm.score(X_train, Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs = lm.predict_proba(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1,\n",
       "       1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,\n",
       "       0, 0, 1, 1, 0, 0, 0])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction = lm.predict(X_test)\n",
    "prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.201424</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.611834</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.369244</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.093150</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0  prediction\n",
       "0  0.531768           0\n",
       "1  0.201424           0\n",
       "2  0.611834           1\n",
       "3  0.369244           0\n",
       "4  0.093150           0"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob = probs[:,1]\n",
    "prob_df = pd.DataFrame(prob)\n",
    "threshold = 0.6\n",
    "prob_df['prediction'] = np.where(prob_df[0] > threshold, 1, 0)\n",
    "prob_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8431372549019608\n"
     ]
    }
   ],
   "source": [
    "print(len(prob_df[prob_df['prediction']==0])/ len(prob_df))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    43\n",
       "1     8\n",
       "Name: prediction, dtype: int64"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob_df.prediction.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.803921568627451"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.accuracy_score(Y_test, prediction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n",
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n",
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n",
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n",
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n",
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n",
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n",
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    }
   ],
   "source": [
    "scores = cross_val_score(linear_model.LogisticRegression(), new_bmd[X], new_bmd[Y], scoring = 'accuracy', cv=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.90909091, 0.9047619 , 0.85714286, 0.95238095, 0.85714286,\n",
       "       0.80952381, 0.71428571, 0.66666667])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8338744588744589"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scores.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# # Confussion Matrix and ROC Curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X:  169\n",
      "Y:  169\n",
      "X_train:  118\n",
      "X_test:  51\n",
      "Y_train:  118\n",
      "Y_test:  51\n"
     ]
    }
   ],
   "source": [
    "# Length:\n",
    "print('X: ', len(new_bmd[X]))\n",
    "print('Y: ', len(new_bmd[Y]))\n",
    "print('X_train: ', len(X_train))\n",
    "print('X_test: ', len(X_test))\n",
    "print('Y_train: ', len(Y_train))\n",
    "print('Y_test: ', len(Y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = linear_model.LogisticRegression()\n",
    "lm.fit(X_train, Y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs = lm.predict_proba(X_test)\n",
    "prob = probs[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "51"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(Y_test)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_test2 = pd.DataFrame.reset_index(Y_test) \n",
    "Y_test2 = Y_test2['fracture']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob_df = pd.DataFrame(prob) \n",
    "threshold = 0.60\n",
    "prob_df[\"prediction\"] = np.where(prob_df[0]>= threshold, 1, 0)\n",
    "prob_df['actual'] = Y_test2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "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",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>actual</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prediction</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "actual       0  1\n",
       "prediction       \n",
       "0           34  9\n",
       "1            1  7"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confussion_matrix = pd.crosstab(prob_df[\"prediction\"], prob_df[\"actual\"])\n",
    "confussion_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "TN = confussion_matrix[0][0]\n",
    "TP = confussion_matrix[1][1]\n",
    "FP = confussion_matrix[0][1]\n",
    "FN = confussion_matrix[1][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4375"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sens = TP / (TP+FN)\n",
    "sens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02857142857142858"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "espc_1 = 1 - (TN / (TN+FP))\n",
    "espc_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.803921568627451"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Overall_performance = (TP + TN) / (FP + FN + TP + TN)\n",
    "Overall_performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "threshold = [0.08, 0.10, 0.12,0.15, 0.18, 0.20, 0.25, 0.3, 0.37,0.4, 0.5]\n",
    "sensitivity = [1]\n",
    "especifity_1 = [1]\n",
    "\n",
    "for t in threshold:\n",
    "    prob_df[\"prediction\"] = np.where(prob_df[0]>= t, 1, 0)\n",
    "    prob_df[\"actual\"] = Y_test2\n",
    "    confusion_matrix = pd.crosstab(prob_df.prediction, prob_df.actual)\n",
    "    TN = confusion_matrix[0][0]\n",
    "    TP = confusion_matrix[1][1]\n",
    "    FP = confusion_matrix[0][1]\n",
    "    FN = confusion_matrix[1][0]\n",
    "    sens = TP / (TP+FN)\n",
    "    espc_1= 1-TN/(TN+FP)\n",
    "    sensitivity.append(sens)\n",
    "    especifity_1.append(espc_1)\n",
    "\n",
    "sensitivity.append(0)\n",
    "especifity_1.append(0)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 1.0, 1.0, 1.0, 1.0, 0.875, 0.875, 0.875, 0.875, 0.75, 0.6875, 0.5625, 0]"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sensitivity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1,\n",
       " 0.9714285714285714,\n",
       " 0.9142857142857143,\n",
       " 0.8857142857142857,\n",
       " 0.8,\n",
       " 0.6,\n",
       " 0.5142857142857142,\n",
       " 0.4285714285714286,\n",
       " 0.37142857142857144,\n",
       " 0.22857142857142854,\n",
       " 0.22857142857142854,\n",
       " 0.08571428571428574,\n",
       " 0]"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "especifity_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Sensibilidad')"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.plot(especifity_1,sensitivity, marker='o', color='r')\n",
    "x = [i*0.01 for i in range(100)]\n",
    "y = [i*0.01 for i in range(100)]\n",
    "plt.plot(x,y)\n",
    "plt.title('ROC Curve')\n",
    "plt.xlabel('1-Especifidad')\n",
    "plt.ylabel('Sensibilidad')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "espc_1, sens, _ = metrics.roc_curve(Y_test, prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({\n",
    "    'x' : espc_1,\n",
    "    'y' : sens    \n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "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",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0625</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     x       y\n",
       "0  0.0  0.0000\n",
       "1  0.0  0.0625"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8169642857142856"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auc = metrics.auc(especifity_1,sensitivity)\n",
    "auc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Validation without splitting the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Usuario\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:760: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = linear_model.LogisticRegression()\n",
    "lm.fit(new_bmd[X], new_bmd[Y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs = lm.predict_proba(new_bmd[X])\n",
    "prob = probs[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "169"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(new_bmd[X])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob_df = pd.DataFrame(prob) \n",
    "threshold = 0.50\n",
    "prob_df[\"prediction\"] = np.where(prob_df[0]>= threshold, 1, 0)\n",
    "prob_df['actual'] = new_bmd[Y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "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",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>actual</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prediction</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>115</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "actual        0   1\n",
       "prediction         \n",
       "0           115  23\n",
       "1             4  27"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confussion_matrix = pd.crosstab(prob_df[\"prediction\"], prob_df[\"actual\"])\n",
    "confussion_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "TN = confussion_matrix[0][0]\n",
    "TP = confussion_matrix[1][1]\n",
    "FP = confussion_matrix[0][1]\n",
    "FN = confussion_matrix[1][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.54"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sens = TP / (TP+FN)\n",
    "sens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03361344537815125"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "espc_1 = 1 - (TN / (TN+FP))\n",
    "espc_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8402366863905325"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Overall_performance = (TP + TN) / (FP + FN + TP + TN)\n",
    "Overall_performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [],
   "source": [
    "threshold = [0.04, 0.05, 0.07, 0.10, 0.12,0.15, 0.18, 0.20, 0.25, 0.3, 0.37,0.4, 0.5]\n",
    "sensitivity = [1]\n",
    "especifity_1 = [1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "for t in threshold:\n",
    "    prob_df[\"prediction\"] = np.where(prob_df[0]>= t, 1, 0)\n",
    "    prob_df[\"actual\"] = new_bmd[Y]\n",
    "    confusion_matrix = pd.crosstab(prob_df.prediction, prob_df.actual)\n",
    "    TN = confusion_matrix[0][0]\n",
    "    TP = confusion_matrix[1][1]\n",
    "    FP = confusion_matrix[0][1]\n",
    "    FN = confusion_matrix[1][0]\n",
    "    sens = TP / (TP+FN)\n",
    "    espc_1= 1-TN/(TN+FP)\n",
    "    sensitivity.append(sens)\n",
    "    especifity_1.append(espc_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "sensitivity.append(0)\n",
    "especifity_1.append(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1,\n",
       " 1.0,\n",
       " 1.0,\n",
       " 1.0,\n",
       " 1.0,\n",
       " 0.94,\n",
       " 0.92,\n",
       " 0.88,\n",
       " 0.88,\n",
       " 0.86,\n",
       " 0.78,\n",
       " 0.72,\n",
       " 0.66,\n",
       " 0.54,\n",
       " 0]"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sensitivity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1,\n",
       " 0.9831932773109243,\n",
       " 0.9663865546218487,\n",
       " 0.9159663865546218,\n",
       " 0.8403361344537815,\n",
       " 0.7563025210084033,\n",
       " 0.680672268907563,\n",
       " 0.5042016806722689,\n",
       " 0.4453781512605042,\n",
       " 0.31932773109243695,\n",
       " 0.2016806722689075,\n",
       " 0.12605042016806722,\n",
       " 0.10924369747899154,\n",
       " 0.03361344537815125,\n",
       " 0]"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "especifity_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Sensibilidad')"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "plt.plot(especifity_1,sensitivity, marker='o', color='r')\n",
    "x = [i*0.01 for i in range(100)]\n",
    "y = [i*0.01 for i in range(100)]\n",
    "plt.plot(x,y)\n",
    "plt.title('ROC Curve')\n",
    "plt.xlabel('1-Especifidad')\n",
    "plt.ylabel('Sensibilidad')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [],
   "source": [
    "espc_1, sens, _ = metrics.roc_curve(new_bmd[Y], prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({\n",
    "    'x' : espc_1,\n",
    "    'y' : sens    \n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8510084033613445"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auc = metrics.auc(especifity_1,sensitivity)\n",
    "auc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adding results to original dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "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",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>weight_kg</th>\n",
       "      <th>height_cm</th>\n",
       "      <th>medication</th>\n",
       "      <th>waiting_time</th>\n",
       "      <th>bmd</th>\n",
       "      <th>fracture</th>\n",
       "      <th>Prediction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>57.052768</td>\n",
       "      <td>F</td>\n",
       "      <td>64.0</td>\n",
       "      <td>155.5</td>\n",
       "      <td>Anticonvulsant</td>\n",
       "      <td>18</td>\n",
       "      <td>0.8793</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>75.741225</td>\n",
       "      <td>F</td>\n",
       "      <td>78.0</td>\n",
       "      <td>162.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>56</td>\n",
       "      <td>0.7946</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>70.778900</td>\n",
       "      <td>M</td>\n",
       "      <td>73.0</td>\n",
       "      <td>170.5</td>\n",
       "      <td>No medication</td>\n",
       "      <td>10</td>\n",
       "      <td>0.9067</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>78.247175</td>\n",
       "      <td>F</td>\n",
       "      <td>60.0</td>\n",
       "      <td>148.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>14</td>\n",
       "      <td>0.7112</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>54.191877</td>\n",
       "      <td>M</td>\n",
       "      <td>55.0</td>\n",
       "      <td>161.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>20</td>\n",
       "      <td>0.7909</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         age sex  weight_kg  height_cm      medication  waiting_time     bmd  \\\n",
       "0  57.052768   F       64.0      155.5  Anticonvulsant            18  0.8793   \n",
       "1  75.741225   F       78.0      162.0   No medication            56  0.7946   \n",
       "2  70.778900   M       73.0      170.5   No medication            10  0.9067   \n",
       "3  78.247175   F       60.0      148.0   No medication            14  0.7112   \n",
       "4  54.191877   M       55.0      161.0   No medication            20  0.7909   \n",
       "\n",
       "      fracture  Prediction  \n",
       "0  no fracture           0  \n",
       "1  no fracture           0  \n",
       "2  no fracture           0  \n",
       "3  no fracture           0  \n",
       "4  no fracture           0  "
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmd['Prediction'] = new_bmd['Prediction']\n",
    "bmd.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "bmd['Prediction'] = bmd['Prediction'].replace(0, 'no fracture')\n",
    "bmd['Prediction'] = bmd['Prediction'].replace(1, 'fracture')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>weight_kg</th>\n",
       "      <th>height_cm</th>\n",
       "      <th>medication</th>\n",
       "      <th>waiting_time</th>\n",
       "      <th>bmd</th>\n",
       "      <th>fracture</th>\n",
       "      <th>Prediction</th>\n",
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       "      <td>Anticonvulsant</td>\n",
       "      <td>18</td>\n",
       "      <td>0.8793</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>75.741225</td>\n",
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       "      <td>No medication</td>\n",
       "      <td>56</td>\n",
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       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>70.778900</td>\n",
       "      <td>M</td>\n",
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       "      <td>No medication</td>\n",
       "      <td>10</td>\n",
       "      <td>0.9067</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>78.247175</td>\n",
       "      <td>F</td>\n",
       "      <td>60.0</td>\n",
       "      <td>148.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>14</td>\n",
       "      <td>0.7112</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>54.191877</td>\n",
       "      <td>M</td>\n",
       "      <td>55.0</td>\n",
       "      <td>161.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>20</td>\n",
       "      <td>0.7909</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         age sex  weight_kg  height_cm      medication  waiting_time     bmd  \\\n",
       "0  57.052768   F       64.0      155.5  Anticonvulsant            18  0.8793   \n",
       "1  75.741225   F       78.0      162.0   No medication            56  0.7946   \n",
       "2  70.778900   M       73.0      170.5   No medication            10  0.9067   \n",
       "3  78.247175   F       60.0      148.0   No medication            14  0.7112   \n",
       "4  54.191877   M       55.0      161.0   No medication            20  0.7909   \n",
       "\n",
       "      fracture   Prediction  \n",
       "0  no fracture  no fracture  \n",
       "1  no fracture  no fracture  \n",
       "2  no fracture  no fracture  \n",
       "3  no fracture  no fracture  \n",
       "4  no fracture  no fracture  "
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmd.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>height_cm</th>\n",
       "      <th>medication</th>\n",
       "      <th>waiting_time</th>\n",
       "      <th>bmd</th>\n",
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       "      <td>Anticonvulsant</td>\n",
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       "      <td>0.8793</td>\n",
       "      <td>no fracture</td>\n",
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       "      <th>1</th>\n",
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       "      <td>F</td>\n",
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       "      <td>162.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>56</td>\n",
       "      <td>0.7946</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>70.778900</td>\n",
       "      <td>M</td>\n",
       "      <td>73.0</td>\n",
       "      <td>170.5</td>\n",
       "      <td>No medication</td>\n",
       "      <td>10</td>\n",
       "      <td>0.9067</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>78.247175</td>\n",
       "      <td>F</td>\n",
       "      <td>60.0</td>\n",
       "      <td>148.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>14</td>\n",
       "      <td>0.7112</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>54.191877</td>\n",
       "      <td>M</td>\n",
       "      <td>55.0</td>\n",
       "      <td>161.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>20</td>\n",
       "      <td>0.7909</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         age sex  weight_kg  height_cm      medication  waiting_time     bmd  \\\n",
       "0  57.052768   F       64.0      155.5  Anticonvulsant            18  0.8793   \n",
       "1  75.741225   F       78.0      162.0   No medication            56  0.7946   \n",
       "2  70.778900   M       73.0      170.5   No medication            10  0.9067   \n",
       "3  78.247175   F       60.0      148.0   No medication            14  0.7112   \n",
       "4  54.191877   M       55.0      161.0   No medication            20  0.7909   \n",
       "\n",
       "      fracture   Prediction  Result  \n",
       "0  no fracture  no fracture    True  \n",
       "1  no fracture  no fracture    True  \n",
       "2  no fracture  no fracture    True  \n",
       "3  no fracture  no fracture    True  \n",
       "4  no fracture  no fracture    True  "
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmd['Result'] = bmd['fracture']==bmd['Prediction'] \n",
    "bmd.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True     142\n",
       "False     27\n",
       "Name: Result, dtype: int64"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmd['Result'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Renaming columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_cols = ['Age',\n",
    " 'Gender',\n",
    " 'Weight (kg)',\n",
    " 'Height (cm)',\n",
    " 'Medication',\n",
    " 'Densitometry Waiting_Time',\n",
    " 'Bone Mineral Density',\n",
    " 'Fracture (Actual)',\n",
    " 'Fracture (Prediction)',\n",
    " 'Prediction Result']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "bmd.columns = new_cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Fracture (Prediction)</th>\n",
       "      <th>fracture</th>\n",
       "      <th>no fracture</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fracture (Actual)</th>\n",
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       "      <th>fracture</th>\n",
       "      <td>27</td>\n",
       "      <td>23</td>\n",
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       "      <th>no fracture</th>\n",
       "      <td>4</td>\n",
       "      <td>115</td>\n",
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      ],
      "text/plain": [
       "Fracture (Prediction)  fracture  no fracture\n",
       "Fracture (Actual)                           \n",
       "fracture                     27           23\n",
       "no fracture                   4          115"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.crosstab(bmd['Fracture (Actual)'], bmd['Fracture (Prediction)'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Medication</th>\n",
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       "      <td>no fracture</td>\n",
       "      <td>True</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
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       "      <td>F</td>\n",
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       "      <td>162.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>56</td>\n",
       "      <td>0.7946</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>70.778900</td>\n",
       "      <td>M</td>\n",
       "      <td>73.0</td>\n",
       "      <td>170.5</td>\n",
       "      <td>No medication</td>\n",
       "      <td>10</td>\n",
       "      <td>0.9067</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>78.247175</td>\n",
       "      <td>F</td>\n",
       "      <td>60.0</td>\n",
       "      <td>148.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>14</td>\n",
       "      <td>0.7112</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>54.191877</td>\n",
       "      <td>M</td>\n",
       "      <td>55.0</td>\n",
       "      <td>161.0</td>\n",
       "      <td>No medication</td>\n",
       "      <td>20</td>\n",
       "      <td>0.7909</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>no fracture</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Age Gender  Weight (kg)  Height (cm)      Medication  \\\n",
       "0  57.052768      F         64.0        155.5  Anticonvulsant   \n",
       "1  75.741225      F         78.0        162.0   No medication   \n",
       "2  70.778900      M         73.0        170.5   No medication   \n",
       "3  78.247175      F         60.0        148.0   No medication   \n",
       "4  54.191877      M         55.0        161.0   No medication   \n",
       "\n",
       "   Densitometry Waiting_Time  Bone Mineral Density Fracture (Actual)  \\\n",
       "0                         18                0.8793       no fracture   \n",
       "1                         56                0.7946       no fracture   \n",
       "2                         10                0.9067       no fracture   \n",
       "3                         14                0.7112       no fracture   \n",
       "4                         20                0.7909       no fracture   \n",
       "\n",
       "  Fracture (Prediction)  Prediction Result  \n",
       "0           no fracture               True  \n",
       "1           no fracture               True  \n",
       "2           no fracture               True  \n",
       "3           no fracture               True  \n",
       "4           no fracture               True  "
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmd.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [],
   "source": [
    "bmd.to_excel('bmd_logistic_regression.xlsx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['age', 'medication_No medication', 'waiting_time', 'bmd']"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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