{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analyse de survie en pratique"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quelques données\n",
    "\n",
    "On récupère les données disponibles sur *open.data.gouv.fr* [Données hospitalières relatives à l'épidémie de COVID-19](https://www.data.gouv.fr/fr/datasets/donnees-hospitalieres-relatives-a-lepidemie-de-covid-19/). Ces données ne permettent pas de construire la courbe de [Kaplan-Meier](https://fr.wikipedia.org/wiki/Estimateur_de_Kaplan-Meier). On sait combien de personnes rentrent et sortent chaque jour mais on ne sait pas quand une personne qui sort un 1er avril est entrée."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>jour</th>\n",
       "      <th>rad</th>\n",
       "      <th>dc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2020-03-18</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2020-03-19</td>\n",
       "      <td>695.0</td>\n",
       "      <td>207.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2020-03-20</td>\n",
       "      <td>806.0</td>\n",
       "      <td>248.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2020-03-21</td>\n",
       "      <td>452.0</td>\n",
       "      <td>151.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2020-03-22</td>\n",
       "      <td>608.0</td>\n",
       "      <td>210.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         jour    rad     dc\n",
       "0  2020-03-18    NaN    NaN\n",
       "1  2020-03-19  695.0  207.0\n",
       "2  2020-03-20  806.0  248.0\n",
       "3  2020-03-21  452.0  151.0\n",
       "4  2020-03-22  608.0  210.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy.random as rnd\n",
    "\n",
    "import pandas\n",
    "\n",
    "df = pandas.read_csv(\n",
    "    \"https://www.data.gouv.fr/fr/datasets/r/63352e38-d353-4b54-bfd1-f1b3ee1cabd7\",\n",
    "    sep=\";\",\n",
    ")\n",
    "gr = df[[\"jour\", \"rad\", \"dc\"]].groupby([\"jour\"]).sum()\n",
    "diff = gr.diff().reset_index(drop=False)\n",
    "diff.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>entree</th>\n",
       "      <th>sortie</th>\n",
       "      <th>issue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1905678</th>\n",
       "      <td>-148</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>577877</th>\n",
       "      <td>-147</td>\n",
       "      <td>40</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1126578</th>\n",
       "      <td>-140</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1140232</th>\n",
       "      <td>-140</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1205621</th>\n",
       "      <td>-131</td>\n",
       "      <td>26</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         entree  sortie  issue\n",
       "1905678    -148       3      1\n",
       "577877     -147      40      1\n",
       "1126578    -140       6      1\n",
       "1140232    -140      11      1\n",
       "1205621    -131      26      1"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def donnees_artificielles(hosp, mu=14, nu=21):\n",
    "    dt = pandas.to_datetime(hosp[\"jour\"])\n",
    "    res = []\n",
    "    for i in range(hosp.shape[0]):\n",
    "        date = dt[i].dayofyear\n",
    "        h1 = hosp.iloc[i, 1]\n",
    "        h2 = hosp.iloc[i, 2]\n",
    "        if h1 < 0 or h2 < 0:\n",
    "            continue\n",
    "        delay1 = rnd.exponential(mu, int(h1))\n",
    "        for j in range(delay1.shape[0]):\n",
    "            res.append([date - int(delay1[j]), date, 1])\n",
    "        delay2 = rnd.exponential(mu, int(h2))\n",
    "        for j in range(delay2.shape[0]):\n",
    "            res.append([date - int(delay2[j]), date, 0])\n",
    "    return pandas.DataFrame(res, columns=[\"entree\", \"sortie\", \"issue\"])\n",
    "\n",
    "\n",
    "data = donnees_artificielles(diff[1:].reset_index(drop=True)).sort_values(\"entree\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Chaque ligne est une personne, `entree` est le jour d'entrée à l'hôpital, `sortie` celui de la sortie, `issue`, 0 pour décès, 1 pour en vie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>entree</th>\n",
       "      <th>sortie</th>\n",
       "      <th>issue</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.993886e+06</td>\n",
       "      <td>1.993886e+06</td>\n",
       "      <td>1.993886e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.481621e+02</td>\n",
       "      <td>1.616597e+02</td>\n",
       "      <td>8.642781e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.152239e+02</td>\n",
       "      <td>1.143726e+02</td>\n",
       "      <td>3.424931e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-1.480000e+02</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.100000e+01</td>\n",
       "      <td>6.400000e+01</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.130000e+02</td>\n",
       "      <td>1.250000e+02</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.600000e+02</td>\n",
       "      <td>2.750000e+02</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.660000e+02</td>\n",
       "      <td>3.660000e+02</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             entree        sortie         issue\n",
       "count  1.993886e+06  1.993886e+06  1.993886e+06\n",
       "mean   1.481621e+02  1.616597e+02  8.642781e-01\n",
       "std    1.152239e+02  1.143726e+02  3.424931e-01\n",
       "min   -1.480000e+02  1.000000e+00  0.000000e+00\n",
       "25%    5.100000e+01  6.400000e+01  1.000000e+00\n",
       "50%    1.130000e+02  1.250000e+02  1.000000e+00\n",
       "75%    2.600000e+02  2.750000e+02  1.000000e+00\n",
       "max    3.660000e+02  3.660000e+02  1.000000e+00"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il y a environ 80% de survie dans ces données."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy\n",
    "\n",
    "duree = data.sortie - data.entree\n",
    "deces = (data.issue == 0).astype(numpy.int32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "from lifelines import KaplanMeierFitter\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(10, 4))\n",
    "kmf = KaplanMeierFitter()\n",
    "kmf.fit(duree, deces)\n",
    "kmf.plot(ax=ax)\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Régression de Cox\n",
    "\n",
    "On reprend les données artificiellement générées et on ajoute une variable identique à la durée plus un bruit mais quasi nul "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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>duree</th>\n",
       "      <th>deces</th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1905678</th>\n",
       "      <td>151</td>\n",
       "      <td>0</td>\n",
       "      <td>0.650961</td>\n",
       "      <td>-1.128843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>577877</th>\n",
       "      <td>187</td>\n",
       "      <td>0</td>\n",
       "      <td>-1.956525</td>\n",
       "      <td>0.108041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1126578</th>\n",
       "      <td>146</td>\n",
       "      <td>0</td>\n",
       "      <td>0.026987</td>\n",
       "      <td>-0.130392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1140232</th>\n",
       "      <td>151</td>\n",
       "      <td>0</td>\n",
       "      <td>1.149385</td>\n",
       "      <td>0.280224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1205621</th>\n",
       "      <td>157</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.032398</td>\n",
       "      <td>0.400499</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         duree  deces        X1        X2\n",
       "1905678    151      0  0.650961 -1.128843\n",
       "577877     187      0 -1.956525  0.108041\n",
       "1126578    146      0  0.026987 -0.130392\n",
       "1140232    151      0  1.149385  0.280224\n",
       "1205621    157      0 -0.032398  0.400499"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas\n",
    "\n",
    "data_simple = pandas.DataFrame(\n",
    "    {\n",
    "        \"duree\": duree,\n",
    "        \"deces\": deces,\n",
    "        \"X1\": duree * 0.57 * deces + numpy.random.randn(duree.shape[0]),\n",
    "        \"X2\": duree * (-0.57) * deces + numpy.random.randn(duree.shape[0]),\n",
    "    }\n",
    ")\n",
    "data_simple.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "data_train, data_test = train_test_split(data_simple, test_size=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1: norm_delta = 5.01e-01, step_size = 0.9500, log_lik = -647954.57157, newton_decrement = 1.86e+04, seconds_since_start = 2.0\n",
      "Iteration 2: norm_delta = 1.29e-01, step_size = 0.9500, log_lik = -668348.17665, newton_decrement = 2.19e+04, seconds_since_start = 4.2\n",
      "Iteration 3: norm_delta = 8.30e-02, step_size = 0.9500, log_lik = -642917.75741, newton_decrement = 4.33e+03, seconds_since_start = 6.2\n",
      "Iteration 4: norm_delta = 3.36e-02, step_size = 1.0000, log_lik = -637879.13496, newton_decrement = 4.09e+02, seconds_since_start = 8.5\n",
      "Iteration 5: norm_delta = 3.94e-03, step_size = 1.0000, log_lik = -637443.76633, newton_decrement = 4.61e+00, seconds_since_start = 10.7\n",
      "Iteration 6: norm_delta = 4.65e-05, step_size = 1.0000, log_lik = -637439.12353, newton_decrement = 6.25e-04, seconds_since_start = 13.0\n",
      "Iteration 7: norm_delta = 6.33e-09, step_size = 1.0000, log_lik = -637439.12291, newton_decrement = 1.16e-11, seconds_since_start = 15.1\n",
      "Convergence success after 7 iterations.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<lifelines.CoxPHFitter: fitted with 398777 total observations, 344439 right-censored observations>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lifelines.fitters.coxph_fitter import CoxPHFitter\n",
    "\n",
    "cox = CoxPHFitter()\n",
    "cox.fit(\n",
    "    data_train[[\"duree\", \"deces\", \"X1\"]],\n",
    "    duration_col=\"duree\",\n",
    "    event_col=\"deces\",\n",
    "    show_progress=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
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   "outputs": [
    {
     "data": {
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model</th>\n",
       "      <td>lifelines.CoxPHFitter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>duration col</th>\n",
       "      <td>'duree'</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event col</th>\n",
       "      <td>'deces'</td>\n",
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       "      <th>baseline estimation</th>\n",
       "      <td>breslow</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of observations</th>\n",
       "      <td>398777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of events observed</th>\n",
       "      <td>54338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>partial log-likelihood</th>\n",
       "      <td>-637439.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>time fit was run</th>\n",
       "      <td>2024-10-07 10:42:15 UTC</td>\n",
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       "</div><table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th style=\"min-width: 12px;\"></th>\n",
       "      <th style=\"min-width: 12px;\">coef</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef)</th>\n",
       "      <th style=\"min-width: 12px;\">se(coef)</th>\n",
       "      <th style=\"min-width: 12px;\">coef lower 95%</th>\n",
       "      <th style=\"min-width: 12px;\">coef upper 95%</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef) lower 95%</th>\n",
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       "      <th style=\"min-width: 12px;\">-log2(p)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>X1</th>\n",
       "      <td>0.06</td>\n",
       "      <td>1.06</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.06</td>\n",
       "      <td>1.06</td>\n",
       "      <td>1.06</td>\n",
       "      <td>0.00</td>\n",
       "      <td>176.66</td>\n",
       "      <td>&lt;0.005</td>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Concordance</th>\n",
       "      <td>0.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Partial AIC</th>\n",
       "      <td>1274880.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log-likelihood ratio test</th>\n",
       "      <td>21030.90 on 1 df</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-log2(p) of ll-ratio test</th>\n",
       "      <td>inf</td>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/latex": [
       "\\begin{tabular}{lrrrrrrrrrrr}\n",
       " & coef & exp(coef) & se(coef) & coef lower 95% & coef upper 95% & exp(coef) lower 95% & exp(coef) upper 95% & cmp to & z & p & -log2(p) \\\\\n",
       "covariate &  &  &  &  &  &  &  &  &  &  &  \\\\\n",
       "X1 & 0.06 & 1.06 & 0.00 & 0.06 & 0.06 & 1.06 & 1.06 & 0.00 & 176.66 & 0.00 & inf \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "<lifelines.CoxPHFitter: fitted with 398777 total observations, 344439 right-censored observations>\n",
       "             duration col = 'duree'\n",
       "                event col = 'deces'\n",
       "      baseline estimation = breslow\n",
       "   number of observations = 398777\n",
       "number of events observed = 54338\n",
       "   partial log-likelihood = -637439.12\n",
       "         time fit was run = 2024-10-07 10:42:15 UTC\n",
       "\n",
       "---\n",
       "           coef exp(coef)  se(coef)  coef lower 95%  coef upper 95% exp(coef) lower 95% exp(coef) upper 95%\n",
       "covariate                                                                                                  \n",
       "X1         0.06      1.06      0.00            0.06            0.06                1.06                1.06\n",
       "\n",
       "           cmp to      z      p  -log2(p)\n",
       "covariate                                \n",
       "X1           0.00 176.66 <0.005       inf\n",
       "---\n",
       "Concordance = 0.75\n",
       "Partial AIC = 1274880.25\n",
       "log-likelihood ratio test = 21030.90 on 1 df\n",
       "-log2(p) of ll-ratio test = inf"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cox.print_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 1: norm_delta = 5.01e-01, step_size = 0.9500, log_lik = -647954.57157, newton_decrement = 1.86e+04, seconds_since_start = 2.4\n",
      "Iteration 2: norm_delta = 1.31e-01, step_size = 0.9500, log_lik = -668036.09368, newton_decrement = 2.18e+04, seconds_since_start = 5.0\n",
      "Iteration 3: norm_delta = 8.29e-02, step_size = 0.9500, log_lik = -642745.26291, newton_decrement = 4.23e+03, seconds_since_start = 7.2\n",
      "Iteration 4: norm_delta = 3.27e-02, step_size = 1.0000, log_lik = -637838.96866, newton_decrement = 3.84e+02, seconds_since_start = 9.4\n",
      "Iteration 5: norm_delta = 3.70e-03, step_size = 1.0000, log_lik = -637430.64477, newton_decrement = 4.03e+00, seconds_since_start = 11.5\n",
      "Iteration 6: norm_delta = 4.05e-05, step_size = 1.0000, log_lik = -637426.59011, newton_decrement = 4.72e-04, seconds_since_start = 13.6\n",
      "Iteration 7: norm_delta = 4.77e-09, step_size = 1.0000, log_lik = -637426.58963, newton_decrement = 6.55e-12, seconds_since_start = 15.7\n",
      "Convergence success after 7 iterations.\n"
     ]
    },
    {
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       "      <td>2024-10-07 10:42:35 UTC</td>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th style=\"min-width: 12px;\"></th>\n",
       "      <th style=\"min-width: 12px;\">coef</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>X2</th>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.94</td>\n",
       "      <td>0.95</td>\n",
       "      <td>0.00</td>\n",
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       "      <th>Concordance</th>\n",
       "      <td>0.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Partial AIC</th>\n",
       "      <td>1274855.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log-likelihood ratio test</th>\n",
       "      <td>21055.96 on 1 df</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-log2(p) of ll-ratio test</th>\n",
       "      <td>inf</td>\n",
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       "</div>"
      ],
      "text/latex": [
       "\\begin{tabular}{lrrrrrrrrrrr}\n",
       " & coef & exp(coef) & se(coef) & coef lower 95% & coef upper 95% & exp(coef) lower 95% & exp(coef) upper 95% & cmp to & z & p & -log2(p) \\\\\n",
       "covariate &  &  &  &  &  &  &  &  &  &  &  \\\\\n",
       "X2 & -0.06 & 0.94 & 0.00 & -0.06 & -0.06 & 0.94 & 0.95 & 0.00 & -176.68 & 0.00 & inf \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "<lifelines.CoxPHFitter: fitted with 398777 total observations, 344439 right-censored observations>\n",
       "             duration col = 'duree'\n",
       "                event col = 'deces'\n",
       "      baseline estimation = breslow\n",
       "   number of observations = 398777\n",
       "number of events observed = 54338\n",
       "   partial log-likelihood = -637426.59\n",
       "         time fit was run = 2024-10-07 10:42:35 UTC\n",
       "\n",
       "---\n",
       "           coef exp(coef)  se(coef)  coef lower 95%  coef upper 95% exp(coef) lower 95% exp(coef) upper 95%\n",
       "covariate                                                                                                  \n",
       "X2        -0.06      0.94      0.00           -0.06           -0.06                0.94                0.95\n",
       "\n",
       "           cmp to       z      p  -log2(p)\n",
       "covariate                                 \n",
       "X2           0.00 -176.68 <0.005       inf\n",
       "---\n",
       "Concordance = 0.75\n",
       "Partial AIC = 1274855.18\n",
       "log-likelihood ratio test = 21055.96 on 1 df\n",
       "-log2(p) of ll-ratio test = inf"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cox2 = CoxPHFitter()\n",
    "cox2.fit(\n",
    "    data_train[[\"duree\", \"deces\", \"X2\"]],\n",
    "    duration_col=\"duree\",\n",
    "    event_col=\"deces\",\n",
    "    show_progress=True,\n",
    ")\n",
    "cox2.print_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>1369970</th>\n",
       "      <th>834048</th>\n",
       "      <th>1217055</th>\n",
       "      <th>1119706</th>\n",
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       "      <th>0.0</th>\n",
       "      <td>0.008909</td>\n",
       "      <td>0.008111</td>\n",
       "      <td>0.020118</td>\n",
       "      <td>0.008601</td>\n",
       "      <td>0.008080</td>\n",
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       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.017592</td>\n",
       "      <td>0.016017</td>\n",
       "      <td>0.039727</td>\n",
       "      <td>0.016985</td>\n",
       "      <td>0.015956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.026273</td>\n",
       "      <td>0.023921</td>\n",
       "      <td>0.059330</td>\n",
       "      <td>0.025366</td>\n",
       "      <td>0.023830</td>\n",
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       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>0.035119</td>\n",
       "      <td>0.031975</td>\n",
       "      <td>0.079308</td>\n",
       "      <td>0.033908</td>\n",
       "      <td>0.031854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>0.043795</td>\n",
       "      <td>0.039875</td>\n",
       "      <td>0.098901</td>\n",
       "      <td>0.042284</td>\n",
       "      <td>0.039724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>156.0</th>\n",
       "      <td>0.532402</td>\n",
       "      <td>0.484742</td>\n",
       "      <td>1.202293</td>\n",
       "      <td>0.514034</td>\n",
       "      <td>0.482903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>158.0</th>\n",
       "      <td>0.538375</td>\n",
       "      <td>0.490181</td>\n",
       "      <td>1.215783</td>\n",
       "      <td>0.519801</td>\n",
       "      <td>0.488322</td>\n",
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       "    <tr>\n",
       "      <th>163.0</th>\n",
       "      <td>0.538375</td>\n",
       "      <td>0.490181</td>\n",
       "      <td>1.215783</td>\n",
       "      <td>0.519801</td>\n",
       "      <td>0.488322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>170.0</th>\n",
       "      <td>0.538375</td>\n",
       "      <td>0.490181</td>\n",
       "      <td>1.215783</td>\n",
       "      <td>0.519801</td>\n",
       "      <td>0.488322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>186.0</th>\n",
       "      <td>0.538375</td>\n",
       "      <td>0.490181</td>\n",
       "      <td>1.215783</td>\n",
       "      <td>0.519801</td>\n",
       "      <td>0.488322</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>151 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        1369970   834048    1217055   1119706   1444869\n",
       "0.0    0.008909  0.008111  0.020118  0.008601  0.008080\n",
       "1.0    0.017592  0.016017  0.039727  0.016985  0.015956\n",
       "2.0    0.026273  0.023921  0.059330  0.025366  0.023830\n",
       "3.0    0.035119  0.031975  0.079308  0.033908  0.031854\n",
       "4.0    0.043795  0.039875  0.098901  0.042284  0.039724\n",
       "...         ...       ...       ...       ...       ...\n",
       "156.0  0.532402  0.484742  1.202293  0.514034  0.482903\n",
       "158.0  0.538375  0.490181  1.215783  0.519801  0.488322\n",
       "163.0  0.538375  0.490181  1.215783  0.519801  0.488322\n",
       "170.0  0.538375  0.490181  1.215783  0.519801  0.488322\n",
       "186.0  0.538375  0.490181  1.215783  0.519801  0.488322\n",
       "\n",
       "[151 rows x 5 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cox.predict_cumulative_hazard(data_test[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.980083</td>\n",
       "      <td>0.991435</td>\n",
       "      <td>0.991952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.982562</td>\n",
       "      <td>0.984111</td>\n",
       "      <td>0.961052</td>\n",
       "      <td>0.983159</td>\n",
       "      <td>0.984170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.974069</td>\n",
       "      <td>0.976363</td>\n",
       "      <td>0.942396</td>\n",
       "      <td>0.974953</td>\n",
       "      <td>0.976452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>0.965490</td>\n",
       "      <td>0.968530</td>\n",
       "      <td>0.923755</td>\n",
       "      <td>0.966661</td>\n",
       "      <td>0.968648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>0.957150</td>\n",
       "      <td>0.960910</td>\n",
       "      <td>0.905833</td>\n",
       "      <td>0.958597</td>\n",
       "      <td>0.961055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>156.0</th>\n",
       "      <td>0.587193</td>\n",
       "      <td>0.615856</td>\n",
       "      <td>0.300504</td>\n",
       "      <td>0.598078</td>\n",
       "      <td>0.616989</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>158.0</th>\n",
       "      <td>0.583696</td>\n",
       "      <td>0.612516</td>\n",
       "      <td>0.296478</td>\n",
       "      <td>0.594639</td>\n",
       "      <td>0.613656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>163.0</th>\n",
       "      <td>0.583696</td>\n",
       "      <td>0.612516</td>\n",
       "      <td>0.296478</td>\n",
       "      <td>0.594639</td>\n",
       "      <td>0.613656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>170.0</th>\n",
       "      <td>0.583696</td>\n",
       "      <td>0.612516</td>\n",
       "      <td>0.296478</td>\n",
       "      <td>0.594639</td>\n",
       "      <td>0.613656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>186.0</th>\n",
       "      <td>0.583696</td>\n",
       "      <td>0.612516</td>\n",
       "      <td>0.296478</td>\n",
       "      <td>0.594639</td>\n",
       "      <td>0.613656</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>151 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        1369970   834048    1217055   1119706   1444869\n",
       "0.0    0.991131  0.991922  0.980083  0.991435  0.991952\n",
       "1.0    0.982562  0.984111  0.961052  0.983159  0.984170\n",
       "2.0    0.974069  0.976363  0.942396  0.974953  0.976452\n",
       "3.0    0.965490  0.968530  0.923755  0.966661  0.968648\n",
       "4.0    0.957150  0.960910  0.905833  0.958597  0.961055\n",
       "...         ...       ...       ...       ...       ...\n",
       "156.0  0.587193  0.615856  0.300504  0.598078  0.616989\n",
       "158.0  0.583696  0.612516  0.296478  0.594639  0.613656\n",
       "163.0  0.583696  0.612516  0.296478  0.594639  0.613656\n",
       "170.0  0.583696  0.612516  0.296478  0.594639  0.613656\n",
       "186.0  0.583696  0.612516  0.296478  0.594639  0.613656\n",
       "\n",
       "[151 rows x 5 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cox.predict_survival_function(data_test[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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