{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sujet 6 : Autour du Paradoxe de Simpson\n",
    "## Contexte\n",
    "*En 1972-1974, à Whickham, une ville du nord-est de l'Angleterre, située à environ 6,5 kilomètres au sud-ouest de Newcastle upon Tyne, un sondage d'un sixième des électeurs a été effectué afin d'éclairer des travaux sur les maladies thyroïdiennes et cardiaques (Tunbridge et al. 1977). Une suite de cette étude a été menée vingt ans plus tard (Vanderpump et al. 1995). Certains des résultats avaient trait au tabagisme et cherchaient à savoir si les individus étaient toujours en vie lors de la seconde étude. Par simplicité, nous nous restreindrons aux femmes et parmi celles-ci aux 1314 qui ont été catégorisées comme \"fumant actuellement\" ou \"n'ayant jamais fumé\". Il y avait relativement peu de femmes dans le sondage initial ayant fumé et ayant arrêté depuis (162) et très peu pour lesquelles l'information n'était pas disponible (18). La survie à 20 ans a été déterminée pour l'ensemble des femmes du premier sondage.*\n",
    "\n",
    "## Importation des données\n",
    "Nous travaillons avec la version 6.0.3 du Notebook Jupyter en langage R version 3.4.1 (2017-06-30).\n",
    "\n",
    "La librairie ggplot2 est nécessaire pour la question 3.\n",
    "\n",
    "Les données sont mises à disposition sur Github. Pour nous protéger contre une éventuelle disparition ou modification du jeux de données, nous faisons une copie locale de ce jeux de données que nous préservons avec notre analyse. Il est inutile et même risquée de télécharger les données à chaque exécution, car dans le cas d'une panne nous pourrions remplacer nos données par un fichier défectueux. Pour cette raison, nous téléchargeons les données seulement si la copie locale n'existe pas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Smoker</th><th scope=col>Status</th><th scope=col>Age</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Yes  </td><td>Alive</td><td>21.0 </td></tr>\n",
       "\t<tr><td>Yes  </td><td>Alive</td><td>19.3 </td></tr>\n",
       "\t<tr><td>No   </td><td>Dead </td><td>57.5 </td></tr>\n",
       "\t<tr><td>No   </td><td>Alive</td><td>47.1 </td></tr>\n",
       "\t<tr><td>Yes  </td><td>Alive</td><td>81.4 </td></tr>\n",
       "\t<tr><td>No   </td><td>Alive</td><td>36.8 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " Smoker & Status & Age\\\\\n",
       "\\hline\n",
       "\t Yes   & Alive & 21.0 \\\\\n",
       "\t Yes   & Alive & 19.3 \\\\\n",
       "\t No    & Dead  & 57.5 \\\\\n",
       "\t No    & Alive & 47.1 \\\\\n",
       "\t Yes   & Alive & 81.4 \\\\\n",
       "\t No    & Alive & 36.8 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Smoker | Status | Age | \n",
       "|---|---|---|---|---|---|\n",
       "| Yes   | Alive | 21.0  | \n",
       "| Yes   | Alive | 19.3  | \n",
       "| No    | Dead  | 57.5  | \n",
       "| No    | Alive | 47.1  | \n",
       "| Yes   | Alive | 81.4  | \n",
       "| No    | Alive | 36.8  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Smoker Status Age \n",
       "1 Yes    Alive  21.0\n",
       "2 Yes    Alive  19.3\n",
       "3 No     Dead   57.5\n",
       "4 No     Alive  47.1\n",
       "5 Yes    Alive  81.4\n",
       "6 No     Alive  36.8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_url = \"https://gitlab.inria.fr/learninglab/mooc-rr/mooc-rr-ressources/-/raw/master/module3/Practical_session/Subject6_smoking.csv?inline=false\"\n",
    "data_file = \"Subject6_smoking.csv\"\n",
    "\n",
    "if (!file.exists(data_file))\n",
    "    download.file(data_url, data_file, method=\"auto\")\n",
    "    \n",
    "data = read.csv(data_file)\n",
    "head(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 1\n",
    "### Enoncé\n",
    "*Représentez dans un tableau le nombre total de femmes vivantes et décédées sur la période en fonction de leur habitude de tabagisme. Calculez dans chaque groupe (fumeuses / non fumeuses) le taux de mortalité (le rapport entre le nombre de femmes décédées dans un groupe et le nombre total de femmes dans ce groupe). Vous pourrez proposer une représentation graphique de ces données et calculer des intervalles de confiance si vous le souhaitez. En quoi ce résultat est-il surprenant ?*\n",
    "\n",
    "### Analyse descriptive des données"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t1314 obs. of  3 variables:\n",
      " $ Smoker: Factor w/ 2 levels \"No\",\"Yes\": 2 2 1 1 2 1 1 2 2 2 ...\n",
      " $ Status: Factor w/ 2 levels \"Alive\",\"Dead\": 1 1 2 1 1 1 1 2 1 1 ...\n",
      " $ Age   : num  21 19.3 57.5 47.1 81.4 36.8 23.8 57.5 24.8 49.5 ...\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       " Smoker      Status         Age       \n",
       " No :732   Alive:945   Min.   :18.00  \n",
       " Yes:582   Dead :369   1st Qu.:31.30  \n",
       "                       Median :44.80  \n",
       "                       Mean   :47.36  \n",
       "                       3rd Qu.:60.60  \n",
       "                       Max.   :89.90  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "str(data)\n",
    "summary(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le jeux de données contient 1314 observations. Il regroupe 3 variables : le tabagisme (oui/non), le statut de santé (vivante/morte) et l'âge des femmes au moment de la première étude.\n",
    "\n",
    "Première analyse descriptive :\n",
    "\n",
    "- L'âge moyen au moment de la première étude est de 47 ans (min : 18 ans et max : 89 ans). \n",
    "- Presque la moitié de la population étudiée fumait lors de la première étude.\n",
    "- Environ 1/4 des femmes sont décédées au moment de la deuxième étude. \n",
    "\n",
    "### Calcul de l'effectif et du taux de mortalité"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Alive</th><th scope=col>Dead</th><th scope=col>Sum</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>No</th><td>502 </td><td>230 </td><td> 732</td></tr>\n",
       "\t<tr><th scope=row>Yes</th><td>443 </td><td>139 </td><td> 582</td></tr>\n",
       "\t<tr><th scope=row>Sum</th><td>945 </td><td>369 </td><td>1314</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & Alive & Dead & Sum\\\\\n",
       "\\hline\n",
       "\tNo & 502  & 230  &  732\\\\\n",
       "\tYes & 443  & 139  &  582\\\\\n",
       "\tSum & 945  & 369  & 1314\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Alive | Dead | Sum | \n",
       "|---|---|---|\n",
       "| No | 502  | 230  |  732 | \n",
       "| Yes | 443  | 139  |  582 | \n",
       "| Sum | 945  | 369  | 1314 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "     \n",
       "      Alive Dead Sum \n",
       "  No  502   230   732\n",
       "  Yes 443   139   582\n",
       "  Sum 945   369  1314"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "global <- table(data$Smoker,data$Status) #tableau de fréquence\n",
    "addmargins(global)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous avons un tableau de fréquence décrivant le nombre de femmes vivantes/décedées selon leur tabagisme.\n",
    "\n",
    "Calculons maintenant le taux de mortalité."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     \n",
       "          Alive      Dead\n",
       "  No  0.6857923 0.3142077\n",
       "  Yes 0.7611684 0.2388316"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mortality <- prop.table(global, margin=1)\n",
    "mortality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le taux de mortalité des fumeuses est de 31% et celui des non fumeuses de 24%. Ce résultat est surprenant car le tabagisme est un facteur de risque pour de nombreuses maladies cardio-vasculaires et respiratoires donc nous aurions pu penser que la mortalité des fumeuses soit plus élevée.\n",
    "\n",
    "### Représentation graphique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Smoker Alive Dead Mortality_rate\n",
      "1      1   443  139      0.3142077\n",
      "2      0   502  230      0.2388316\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAC91BMVEUAAAABAQECAgIDAwME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\nAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Smoker <- c(1,0)\n",
    "Alive <- c(global[2,1], global[1,1])\n",
    "Dead <- c(global[2,2], global[1,2])\n",
    "Mortality_rate <- c(mortality[1,2], mortality[2,2])\n",
    "\n",
    "data_exo1 <- data.frame(Smoker, Alive, Dead, Mortality_rate)\n",
    "print(data_exo1)\n",
    "\n",
    "plot (x=data_exo1$Smoker, y=data_exo1$Mortality_rate, ylim=c(0,0.5), type='h')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2\n",
    "### Enoncé\n",
    "*Reprenez la question 1 (effectifs et taux de mortalité) en rajoutant une nouvelle catégorie liée à la classe d'âge. On considérera par exemple les classes suivantes : 18-34 ans, 34-54 ans, 55-64 ans, plus de 65 ans. En quoi ce résultat est-il surprenant ? Arrivez-vous à expliquer ce paradoxe ? De même, vous pourrez proposer une représentation graphique de ces données pour étayer vos explications.*\n",
    "\n",
    "### Calcul de l'effectif et du taux de mortalité selon l'âge\n",
    "#### Groupe des fumeuses\n",
    "\n",
    "Nous étudions dans un premier temps le taux de mortalité des fumeuses selon leur âge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Alive</th><th scope=col>Dead</th><th scope=col>Sum</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>[18,34]</th><td>176</td><td>  5</td><td>181</td></tr>\n",
       "\t<tr><th scope=row>(34,54]</th><td>196</td><td> 41</td><td>237</td></tr>\n",
       "\t<tr><th scope=row>(54,64]</th><td> 64</td><td> 51</td><td>115</td></tr>\n",
       "\t<tr><th scope=row>(64,100]</th><td>  7</td><td> 42</td><td> 49</td></tr>\n",
       "\t<tr><th scope=row>Sum</th><td>443</td><td>139</td><td>582</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & Alive & Dead & Sum\\\\\n",
       "\\hline\n",
       "\t{[}18,34{]} & 176 &   5 & 181\\\\\n",
       "\t(34,54{]} & 196 &  41 & 237\\\\\n",
       "\t(54,64{]} &  64 &  51 & 115\\\\\n",
       "\t(64,100{]} &   7 &  42 &  49\\\\\n",
       "\tSum & 443 & 139 & 582\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Alive | Dead | Sum | \n",
       "|---|---|---|---|---|\n",
       "| [18,34] | 176 |   5 | 181 | \n",
       "| (34,54] | 196 |  41 | 237 | \n",
       "| (54,64] |  64 |  51 | 115 | \n",
       "| (64,100] |   7 |  42 |  49 | \n",
       "| Sum | 443 | 139 | 582 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "                \n",
       "smoker_age_group Alive Dead Sum\n",
       "        [18,34]  176     5  181\n",
       "        (34,54]  196    41  237\n",
       "        (54,64]   64    51  115\n",
       "        (64,100]   7    42   49\n",
       "        Sum      443   139  582"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "smoker_age <- subset(data, Smoker==\"Yes\", select=c(Smoker, Status, Age))\n",
    "smoker_age_group <- cut(smoker_age$Age, c(18,34,54,64,100),vright=FALSE, include.lowest=TRUE)\n",
    "smoker_age_prop <- table(smoker_age_group,smoker_age$Status)\n",
    "addmargins(smoker_age_prop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                \n",
       "smoker_age_group      Alive       Dead\n",
       "        [18,34)  0.97206704 0.02793296\n",
       "        [34,54)  0.82845188 0.17154812\n",
       "        [54,64)  0.55652174 0.44347826\n",
       "        [64,100] 0.14285714 0.85714286"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mortality_smoker <-prop.table(smoker_age_prop, margin=1)\n",
    "mortality_smoker"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Groupe des non fumeuses\n",
    "\n",
    "Nous étudions dans un second temps le taux de mortalité des non fumeuses selon leur groupe d'âge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Alive</th><th scope=col>Dead</th><th scope=col>Sum</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>[18,34)</th><td>213</td><td>  6</td><td>219</td></tr>\n",
       "\t<tr><th scope=row>[34,54)</th><td>180</td><td> 19</td><td>199</td></tr>\n",
       "\t<tr><th scope=row>[54,64)</th><td> 80</td><td> 39</td><td>119</td></tr>\n",
       "\t<tr><th scope=row>[64,100]</th><td> 29</td><td>166</td><td>195</td></tr>\n",
       "\t<tr><th scope=row>Sum</th><td>502</td><td>230</td><td>732</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & Alive & Dead & Sum\\\\\n",
       "\\hline\n",
       "\t{[}18,34) & 213 &   6 & 219\\\\\n",
       "\t{[}34,54) & 180 &  19 & 199\\\\\n",
       "\t{[}54,64) &  80 &  39 & 119\\\\\n",
       "\t{[}64,100{]} &  29 & 166 & 195\\\\\n",
       "\tSum & 502 & 230 & 732\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Alive | Dead | Sum | \n",
       "|---|---|---|---|---|\n",
       "| [18,34) | 213 |   6 | 219 | \n",
       "| [34,54) | 180 |  19 | 199 | \n",
       "| [54,64) |  80 |  39 | 119 | \n",
       "| [64,100] |  29 | 166 | 195 | \n",
       "| Sum | 502 | 230 | 732 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "                   \n",
       "no_smoker_age_group Alive Dead Sum\n",
       "           [18,34)  213     6  219\n",
       "           [34,54)  180    19  199\n",
       "           [54,64)   80    39  119\n",
       "           [64,100]  29   166  195\n",
       "           Sum      502   230  732"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "no_smoker_age <- subset(data, Smoker==\"No\", select=c(Smoker, Status, Age))\n",
    "no_smoker_age_group <- cut(no_smoker_age$Age, c(18,34,54,64,100), right=FALSE, include.lowest=TRUE)\n",
    "no_smoker_age_prop <- table(no_smoker_age_group,no_smoker_age$Status)\n",
    "addmargins(no_smoker_age_prop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                   \n",
       "no_smoker_age_group      Alive       Dead\n",
       "           [18,34)  0.97260274 0.02739726\n",
       "           [34,54)  0.90452261 0.09547739\n",
       "           [54,64)  0.67226891 0.32773109\n",
       "           [64,100] 0.14871795 0.85128205"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mortality_no_smoker <-prop.table(no_smoker_age_prop, margin=1)\n",
    "mortality_no_smoker"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparons maintenant les taux de mortalité des fumeuses et non fumeuses selon leur âge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "$Fumeuses\n",
       "                \n",
       "smoker_age_group      Alive       Dead\n",
       "        [18,34)  0.97206704 0.02793296\n",
       "        [34,54)  0.82845188 0.17154812\n",
       "        [54,64)  0.55652174 0.44347826\n",
       "        [64,100] 0.14285714 0.85714286\n",
       "\n",
       "$`Non fumeuses`\n",
       "                   \n",
       "no_smoker_age_group      Alive       Dead\n",
       "           [18,34)  0.97260274 0.02739726\n",
       "           [34,54)  0.90452261 0.09547739\n",
       "           [54,64)  0.67226891 0.32773109\n",
       "           [64,100] 0.14871795 0.85128205\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mortality_smoking_age <- list(mortality_smoker,mortality_no_smoker)\n",
    "names(mortality_smoking_age) <-c (\"Fumeuses\",\"Non fumeuses\")\n",
    "mortality_smoking_age"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous remarquons que le taux de mortalité est supérieur pour les fumeuses que pour les non fumeuses pour chaque groupe d'âge. Ces résultats sont surprenants car ils sont en contradiction avec ceux de la première question (sans prendre en compte les groupes d'âge).\n",
    "\n",
    "Représentons ces résultats dans un graphique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAC/VBMVEUAAAABAQECAgIDAwME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\n",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#regroupement des données dans un tableau\n",
    "smoker_mortality <- c(mortality_smoker[1,2],mortality_smoker[2,2],mortality_smoker[3,2],mortality_smoker[4,2])\n",
    "no_smoker_mortality <- c(mortality_no_smoker[1,2],mortality_no_smoker[2,2],mortality_no_smoker[3,2],mortality_no_smoker[4,2])\n",
    "group_age <- c(\"[18-34)\",\"[34-54)\",\" [54-64)\",\"[>64]\")\n",
    "mortality_age <- c(smoker_mortality,no_smoker_mortality)\n",
    "\n",
    "#transformation en matrice pour le graphique\n",
    "mortality_age <- matrix(mortality_age,nc=4,nr=2,byrow=T)\n",
    "colnames(mortality_age)=group_age\n",
    "\n",
    "#graphique\n",
    "barplot(mortality_age,beside=T,xlab=\"Groupe d'âge\", ylab=\"Taux de Mortalité\", legend.text=c(\"Fumeuses\", \"Non fumeuses\"), ylim=c(0,1.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avec le graphique ci-dessus nous voyons bien que pour chaque groupe d'âge, les fumeuses ont un taux de mortalité plus élevé que les non fumeuses.\n",
    "\n",
    "En étudiant les résultats des tableaux de fréquence nous remarquons que l'effectif des personnes âgées est plus important chez les non fumeuses que les fumeuses : il y a plus de personnes âgées non fumeuses que fumeuses. Cette différence peut expliquer les résultats contradictoires que nous observons (question 1 et question 2).\n",
    "\n",
    "## Question 3\n",
    "### Enoncé\n",
    "*Afin d'éviter un biais induit par des regroupements en tranches d'âges arbitraires et non régulières, il est envisageable d'essayer de réaliser une régression logistique. Si on introduit une variable Death valant 1 ou 0 pour indiquer si l'individu est décédé durant la période de 20 ans, on peut étudier le modèle Death ~ Age pour étudier la probabilité de décès en fonction de l'âge selon que l'on considère le groupe des fumeuses ou des non fumeuses. Ces régressions vous permettent-elles de conclure sur la nocivité du tabagisme ? Vous pourrez proposer une représentation graphique de ces régressions (en n'omettant pas les régions de confiance).*\n",
    "\n",
    "### Introduction de la nouvelle variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Smoker</th><th scope=col>Status</th><th scope=col>Age</th><th scope=col>Death</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>Yes  </td><td>Alive</td><td>21.0 </td><td>0    </td></tr>\n",
       "\t<tr><td>Yes  </td><td>Alive</td><td>19.3 </td><td>0    </td></tr>\n",
       "\t<tr><td>No   </td><td>Dead </td><td>57.5 </td><td>1    </td></tr>\n",
       "\t<tr><td>No   </td><td>Alive</td><td>47.1 </td><td>0    </td></tr>\n",
       "\t<tr><td>Yes  </td><td>Alive</td><td>81.4 </td><td>0    </td></tr>\n",
       "\t<tr><td>No   </td><td>Alive</td><td>36.8 </td><td>0    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       " Smoker & Status & Age & Death\\\\\n",
       "\\hline\n",
       "\t Yes   & Alive & 21.0  & 0    \\\\\n",
       "\t Yes   & Alive & 19.3  & 0    \\\\\n",
       "\t No    & Dead  & 57.5  & 1    \\\\\n",
       "\t No    & Alive & 47.1  & 0    \\\\\n",
       "\t Yes   & Alive & 81.4  & 0    \\\\\n",
       "\t No    & Alive & 36.8  & 0    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Smoker | Status | Age | Death | \n",
       "|---|---|---|---|---|---|\n",
       "| Yes   | Alive | 21.0  | 0     | \n",
       "| Yes   | Alive | 19.3  | 0     | \n",
       "| No    | Dead  | 57.5  | 1     | \n",
       "| No    | Alive | 47.1  | 0     | \n",
       "| Yes   | Alive | 81.4  | 0     | \n",
       "| No    | Alive | 36.8  | 0     | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Smoker Status Age  Death\n",
       "1 Yes    Alive  21.0 0    \n",
       "2 Yes    Alive  19.3 0    \n",
       "3 No     Dead   57.5 1    \n",
       "4 No     Alive  47.1 0    \n",
       "5 Yes    Alive  81.4 0    \n",
       "6 No     Alive  36.8 0    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data$Death <- ifelse(data$Status=='Dead',1,0)\n",
    "head(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Régression linéaire : groupe des fumeuses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "glm(formula = Death ~ Age, family = binomial(logit), data = death_smoker)\n",
       "\n",
       "Deviance Residuals: \n",
       "    Min       1Q   Median       3Q      Max  \n",
       "-2.0745  -0.6464  -0.3756  -0.2013   2.6560  \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) -5.508106   0.466221  -11.81   <2e-16 ***\n",
       "Age          0.088977   0.008721   10.20   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "(Dispersion parameter for binomial family taken to be 1)\n",
       "\n",
       "    Null deviance: 639.89  on 581  degrees of freedom\n",
       "Residual deviance: 480.41  on 580  degrees of freedom\n",
       "AIC: 484.41\n",
       "\n",
       "Number of Fisher Scoring iterations: 5\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "death_smoker <- subset(data,Smoker==\"Yes\")\n",
    "reg_smoker <- glm(data=death_smoker, Death ~ Age,family=binomial(logit))\n",
    "summary(reg_smoker)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'âge influe positivement sur le risque de décès pour les fumeuses car la p_value<2e-16 et l'estimation du paramètre Age vaut 0.088977."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Régression linéaire : groupe des non fumeuses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "glm(formula = Death ~ Age, family = binomial(logit), data = death_no_smoker)\n",
       "\n",
       "Deviance Residuals: \n",
       "    Min       1Q   Median       3Q      Max  \n",
       "-2.4019  -0.5179  -0.2003   0.4728   3.0457  \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) -6.795507   0.479430  -14.17   <2e-16 ***\n",
       "Age          0.107275   0.007806   13.74   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "(Dispersion parameter for binomial family taken to be 1)\n",
       "\n",
       "    Null deviance: 911.23  on 731  degrees of freedom\n",
       "Residual deviance: 519.08  on 730  degrees of freedom\n",
       "AIC: 523.08\n",
       "\n",
       "Number of Fisher Scoring iterations: 6\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "death_no_smoker <- subset(data,Smoker==\"No\")\n",
    "reg_no_smoker <- glm(data=death_no_smoker, Death ~ Age,family=binomial(logit))\n",
    "summary(reg_no_smoker)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'âge influe positivement sur le risque de décès pour les non fumeuses car la p_value<2e-16 et l'estimation du paramètre Age vaut 0.107275."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Représentation des régressions linéaires"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAACXBIWXMAABJ0AAASdAHeZh94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\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# création d'un ggplot vide à remplir avec les deux ggplot (fumeuses, non fumeuses)\n",
    "p <- ggplot() +\n",
    "labs(x = \"Age\", y = \"Death\",\n",
    "title = \"Régression logistique Death/Age selon le tabagisme\") +\n",
    "theme_minimal()\n",
    "\n",
    "# ajout des infos sur le tabagisme pour différencier les deux graphiques\n",
    "death_smoker$tabac <- 'Smoker'\n",
    "death_no_smoker$tabac <- 'Non-Smoker'\n",
    "\n",
    "# ajout des fumeuses\n",
    "p <- p + geom_point(data = death_smoker, aes(x = Age, y = Death, color = tabac)) +\n",
    "stat_smooth(data = death_smoker, aes(x = Age, y = Death, color = tabac),\n",
    "method = \"glm\", method.args = list(family = \"binomial\"),\n",
    "formula = y ~ x, geom = \"smooth\")\n",
    "\n",
    "# ajout des non  fumeuses\n",
    "p <- p + geom_point(data = death_no_smoker, aes(x = Age, y = Death, color = tabac)) +\n",
    "stat_smooth(data = death_no_smoker, aes(x = Age, y = Death, color = tabac),\n",
    "method = \"glm\", method.args = list(family = \"binomial\"),\n",
    "formula = y ~ x, geom = \"smooth\")\n",
    "\n",
    "# customisation des légendes\n",
    "p <- p + scale_color_manual(name = \"Tabagisme\",\n",
    "values = c(\"Smoker\" = \"red\", \"Non-Smoker\" = \"blue\"),\n",
    "labels = c(\"Smoker\" = \"Smoker\", \"Non-Smoker\" = \"Non-Smoker\"))\n",
    "# Print the plot\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous remarquons que le risque est plus important pour les fumeuses que les non fumeuses jusque 70 ans. Pour les femmes plus âgées la tendance est inversée, néanmoins comme nous avons peu de données pour ces âges les résultats sont à prendre avec des pincettes. Nous pouvons donc conclure quant à l'association entre le tabagisme et le risque de décès."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}