{
 "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": 2,
   "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": 3,
     "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/e3d83ab3-dc52-4c99-abaf-8a38050cc68c\",\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": 3,
   "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>518488</th>\n",
       "      <td>-200</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>541408</th>\n",
       "      <td>-192</td>\n",
       "      <td>27</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476735</th>\n",
       "      <td>-187</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>587013</th>\n",
       "      <td>-185</td>\n",
       "      <td>42</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476057</th>\n",
       "      <td>-180</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        entree  sortie  issue\n",
       "518488    -200      19      0\n",
       "541408    -192      27      0\n",
       "476735    -187       2      0\n",
       "587013    -185      42      0\n",
       "476057    -180       1      0"
      ]
     },
     "execution_count": 4,
     "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",
    "        h = hosp.iloc[i, 1]\n",
    "        delay = rnd.exponential(mu, int(h))\n",
    "        for j in range(delay.shape[0]):\n",
    "            res.append([date - int(delay[j]), date, 1])\n",
    "        h = hosp.iloc[i, 2]\n",
    "        delay = rnd.exponential(nu, int(h))\n",
    "        for j in range(delay.shape[0]):\n",
    "            res.append([date - int(delay[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": 4,
   "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>624130.000000</td>\n",
       "      <td>624130.000000</td>\n",
       "      <td>624130.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>169.704510</td>\n",
       "      <td>184.532815</td>\n",
       "      <td>0.806729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>125.420957</td>\n",
       "      <td>124.343186</td>\n",
       "      <td>0.394864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-200.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>53.000000</td>\n",
       "      <td>84.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>133.000000</td>\n",
       "      <td>144.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>301.000000</td>\n",
       "      <td>315.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>366.000000</td>\n",
       "      <td>366.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              entree         sortie          issue\n",
       "count  624130.000000  624130.000000  624130.000000\n",
       "mean      169.704510     184.532815       0.806729\n",
       "std       125.420957     124.343186       0.394864\n",
       "min      -200.000000       1.000000       0.000000\n",
       "25%        53.000000      84.000000       1.000000\n",
       "50%       133.000000     144.000000       1.000000\n",
       "75%       301.000000     315.000000       1.000000\n",
       "max       366.000000     366.000000       1.000000"
      ]
     },
     "execution_count": 5,
     "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": 5,
   "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": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 7,
   "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>518488</th>\n",
       "      <td>219</td>\n",
       "      <td>1</td>\n",
       "      <td>125.653230</td>\n",
       "      <td>-125.666662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>541408</th>\n",
       "      <td>219</td>\n",
       "      <td>1</td>\n",
       "      <td>126.006024</td>\n",
       "      <td>-125.327549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476735</th>\n",
       "      <td>189</td>\n",
       "      <td>1</td>\n",
       "      <td>107.920779</td>\n",
       "      <td>-108.358230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>587013</th>\n",
       "      <td>227</td>\n",
       "      <td>1</td>\n",
       "      <td>129.788930</td>\n",
       "      <td>-130.045019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476057</th>\n",
       "      <td>181</td>\n",
       "      <td>1</td>\n",
       "      <td>103.642440</td>\n",
       "      <td>-103.793008</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        duree  deces          X1          X2\n",
       "518488    219      1  125.653230 -125.666662\n",
       "541408    219      1  126.006024 -125.327549\n",
       "476735    189      1  107.920779 -108.358230\n",
       "587013    227      1  129.788930 -130.045019\n",
       "476057    181      1  103.642440 -103.793008"
      ]
     },
     "execution_count": 8,
     "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": 8,
   "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": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r\n",
      "Iteration 1: norm_delta = 0.13943, step_size = 0.9000, log_lik = -250658.36250, newton_decrement = 889.93933, seconds_since_start = 0.0\n",
      "\r\n",
      "Iteration 2: norm_delta = 0.00660, step_size = 0.9000, log_lik = -249862.37270, newton_decrement = 2.81312, seconds_since_start = 0.0\n",
      "\r\n",
      "Iteration 3: norm_delta = 0.00073, step_size = 0.9000, log_lik = -249859.57376, newton_decrement = 0.03357, seconds_since_start = 0.1\n",
      "\r\n",
      "Iteration 4: norm_delta = 0.00000, step_size = 1.0000, log_lik = -249859.54017, newton_decrement = 0.00000, seconds_since_start = 0.1\n",
      "Convergence success after 4 iterations.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<lifelines.CoxPHFitter: fitted with 124826 total observations, 100754 right-censored observations>"
      ]
     },
     "execution_count": 10,
     "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": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model</th>\n",
       "      <td>lifelines.CoxPHFitter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>duration col</th>\n",
       "      <td>'duree'</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event col</th>\n",
       "      <td>'deces'</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>baseline estimation</th>\n",
       "      <td>breslow</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of observations</th>\n",
       "      <td>124826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of events observed</th>\n",
       "      <td>24072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>partial log-likelihood</th>\n",
       "      <td>-249859.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>time fit was run</th>\n",
       "      <td>2021-02-24 23:48:57 UTC</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th style=\"min-width: 12px;\"></th>\n",
       "      <th style=\"min-width: 12px;\">coef</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef)</th>\n",
       "      <th style=\"min-width: 12px;\">se(coef)</th>\n",
       "      <th style=\"min-width: 12px;\">coef lower 95%</th>\n",
       "      <th style=\"min-width: 12px;\">coef upper 95%</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef) lower 95%</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef) upper 95%</th>\n",
       "      <th style=\"min-width: 12px;\">z</th>\n",
       "      <th style=\"min-width: 12px;\">p</th>\n",
       "      <th style=\"min-width: 12px;\">-log2(p)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>X1</th>\n",
       "      <td>0.02</td>\n",
       "      <td>1.02</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.02</td>\n",
       "      <td>1.02</td>\n",
       "      <td>1.02</td>\n",
       "      <td>42.23</td>\n",
       "      <td>&lt;0.005</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table><br><div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Concordance</th>\n",
       "      <td>0.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Partial AIC</th>\n",
       "      <td>499721.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log-likelihood ratio test</th>\n",
       "      <td>1597.64 on 1 df</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-log2(p) of ll-ratio test</th>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/latex": [
       "\\begin{tabular}{lrrrrrrrrrr}\n",
       "\\toprule\n",
       "{} &  coef &  exp(coef) &  se(coef) &  coef lower 95\\% &  coef upper 95\\% &  exp(coef) lower 95\\% &  exp(coef) upper 95\\% &     z &    p &  -log2(p) \\\\\n",
       "covariate &       &            &           &                 &                 &                      &                      &       &      &           \\\\\n",
       "\\midrule\n",
       "X1        &  0.02 &       1.02 &      0.00 &            0.02 &            0.02 &                 1.02 &                 1.02 & 42.23 & 0.00 &       inf \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "<lifelines.CoxPHFitter: fitted with 124826 total observations, 100754 right-censored observations>\n",
       "             duration col = 'duree'\n",
       "                event col = 'deces'\n",
       "      baseline estimation = breslow\n",
       "   number of observations = 124826\n",
       "number of events observed = 24072\n",
       "   partial log-likelihood = -249859.54\n",
       "         time fit was run = 2021-02-24 23:48:57 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          0.02       1.02       0.00             0.02             0.02                 1.02                 1.02\n",
       "\n",
       "              z      p   -log2(p)\n",
       "covariate                        \n",
       "X1        42.23 <0.005        inf\n",
       "---\n",
       "Concordance = 0.69\n",
       "Partial AIC = 499721.08\n",
       "log-likelihood ratio test = 1597.64 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": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r\n",
      "Iteration 1: norm_delta = 0.13946, step_size = 0.9000, log_lik = -250658.36250, newton_decrement = 888.92089, seconds_since_start = 0.0\n",
      "\r\n",
      "Iteration 2: norm_delta = 0.00667, step_size = 0.9000, log_lik = -249863.61089, newton_decrement = 2.86434, seconds_since_start = 0.0\n",
      "\r\n",
      "Iteration 3: norm_delta = 0.00074, step_size = 0.9000, log_lik = -249860.76079, newton_decrement = 0.03426, seconds_since_start = 0.1\n",
      "\r\n",
      "Iteration 4: norm_delta = 0.00000, step_size = 1.0000, log_lik = -249860.72650, newton_decrement = 0.00000, seconds_since_start = 0.1\n",
      "Convergence success after 4 iterations.\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model</th>\n",
       "      <td>lifelines.CoxPHFitter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>duration col</th>\n",
       "      <td>'duree'</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>event col</th>\n",
       "      <td>'deces'</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>baseline estimation</th>\n",
       "      <td>breslow</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of observations</th>\n",
       "      <td>124826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>number of events observed</th>\n",
       "      <td>24072</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>partial log-likelihood</th>\n",
       "      <td>-249860.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>time fit was run</th>\n",
       "      <td>2021-02-24 23:48:59 UTC</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div><table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th style=\"min-width: 12px;\"></th>\n",
       "      <th style=\"min-width: 12px;\">coef</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef)</th>\n",
       "      <th style=\"min-width: 12px;\">se(coef)</th>\n",
       "      <th style=\"min-width: 12px;\">coef lower 95%</th>\n",
       "      <th style=\"min-width: 12px;\">coef upper 95%</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef) lower 95%</th>\n",
       "      <th style=\"min-width: 12px;\">exp(coef) upper 95%</th>\n",
       "      <th style=\"min-width: 12px;\">z</th>\n",
       "      <th style=\"min-width: 12px;\">p</th>\n",
       "      <th style=\"min-width: 12px;\">-log2(p)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>X2</th>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.98</td>\n",
       "      <td>0.98</td>\n",
       "      <td>-42.21</td>\n",
       "      <td>&lt;0.005</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table><br><div>\n",
       "<style scoped>\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Concordance</th>\n",
       "      <td>0.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Partial AIC</th>\n",
       "      <td>499723.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log-likelihood ratio test</th>\n",
       "      <td>1595.27 on 1 df</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-log2(p) of ll-ratio test</th>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/latex": [
       "\\begin{tabular}{lrrrrrrrrrr}\n",
       "\\toprule\n",
       "{} &  coef &  exp(coef) &  se(coef) &  coef lower 95\\% &  coef upper 95\\% &  exp(coef) lower 95\\% &  exp(coef) upper 95\\% &      z &    p &  -log2(p) \\\\\n",
       "covariate &       &            &           &                 &                 &                      &                      &        &      &           \\\\\n",
       "\\midrule\n",
       "X2        & -0.02 &       0.98 &      0.00 &           -0.02 &           -0.02 &                 0.98 &                 0.98 & -42.21 & 0.00 &       inf \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "<lifelines.CoxPHFitter: fitted with 124826 total observations, 100754 right-censored observations>\n",
       "             duration col = 'duree'\n",
       "                event col = 'deces'\n",
       "      baseline estimation = breslow\n",
       "   number of observations = 124826\n",
       "number of events observed = 24072\n",
       "   partial log-likelihood = -249860.73\n",
       "         time fit was run = 2021-02-24 23:48:59 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         -0.02       0.98       0.00            -0.02            -0.02                 0.98                 0.98\n",
       "\n",
       "               z      p   -log2(p)\n",
       "covariate                         \n",
       "X2        -42.21 <0.005        inf\n",
       "---\n",
       "Concordance = 0.69\n",
       "Partial AIC = 499723.45\n",
       "log-likelihood ratio test = 1595.27 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": 12,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.035640</td>\n",
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       "      <td>2.183341</td>\n",
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       "      <th>217.0</th>\n",
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       "      <td>2.295356</td>\n",
       "      <td>2.260952</td>\n",
       "      <td>2.307199</td>\n",
       "      <td>2.292237</td>\n",
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       "[165 rows x 5 columns]"
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     "execution_count": 13,
     "metadata": {},
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   "source": [
    "cox.predict_cumulative_hazard(data_test[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.099540</td>\n",
       "      <td>0.101040</td>\n",
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     "execution_count": 14,
     "metadata": {},
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    }
   ],
   "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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