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module3/exo3/exercice.ipynb
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{
"cells": [],
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Sujet 6 : Autour du Paradoxe de Simpson"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 89,
"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>Smoker</th>\n",
" <th>Status</th>\n",
" <th>Age</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>21.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>19.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>No</td>\n",
" <td>Dead</td>\n",
" <td>57.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>47.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>81.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>36.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>23.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>Yes</td>\n",
" <td>Dead</td>\n",
" <td>57.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>24.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>49.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>30.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>No</td>\n",
" <td>Dead</td>\n",
" <td>66.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>49.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>58.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>No</td>\n",
" <td>Dead</td>\n",
" <td>60.6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>25.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>43.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>27.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>58.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>65.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>No</td>\n",
" <td>Dead</td>\n",
" <td>73.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>21</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>38.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>33.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>23</th>\n",
" <td>Yes</td>\n",
" <td>Dead</td>\n",
" <td>62.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>24</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>18.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>56.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>26</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>59.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>27</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>25.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>28</th>\n",
" <td>No</td>\n",
" <td>Dead</td>\n",
" <td>36.9</td>\n",
" </tr>\n",
" <tr>\n",
" <th>29</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>20.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1284</th>\n",
" <td>Yes</td>\n",
" <td>Dead</td>\n",
" <td>36.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1285</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>48.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1286</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>63.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1287</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>60.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1288</th>\n",
" <td>Yes</td>\n",
" <td>Dead</td>\n",
" <td>39.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1289</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>36.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1290</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>63.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1291</th>\n",
" <td>No</td>\n",
" <td>Dead</td>\n",
" <td>71.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1292</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>57.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1293</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>63.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1294</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>46.6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1295</th>\n",
" <td>Yes</td>\n",
" <td>Dead</td>\n",
" <td>82.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1296</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>38.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1297</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>32.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1298</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>39.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1299</th>\n",
" <td>Yes</td>\n",
" <td>Dead</td>\n",
" <td>60.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1300</th>\n",
" <td>No</td>\n",
" <td>Dead</td>\n",
" <td>71.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1301</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>20.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1302</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>44.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1303</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>31.2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1304</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>47.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1305</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>60.9</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1306</th>\n",
" <td>No</td>\n",
" <td>Dead</td>\n",
" <td>61.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1307</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>43.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1308</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>42.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1309</th>\n",
" <td>Yes</td>\n",
" <td>Alive</td>\n",
" <td>35.9</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1310</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>22.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1311</th>\n",
" <td>Yes</td>\n",
" <td>Dead</td>\n",
" <td>62.1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1312</th>\n",
" <td>No</td>\n",
" <td>Dead</td>\n",
" <td>88.6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1313</th>\n",
" <td>No</td>\n",
" <td>Alive</td>\n",
" <td>39.1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>1314 rows × 3 columns</p>\n",
"</div>"
],
"text/plain": [
" Smoker Status Age\n",
"0 Yes Alive 21.0\n",
"1 Yes Alive 19.3\n",
"2 No Dead 57.5\n",
"3 No Alive 47.1\n",
"4 Yes Alive 81.4\n",
"5 No Alive 36.8\n",
"6 No Alive 23.8\n",
"7 Yes Dead 57.5\n",
"8 Yes Alive 24.8\n",
"9 Yes Alive 49.5\n",
"10 Yes Alive 30.0\n",
"11 No Dead 66.0\n",
"12 Yes Alive 49.2\n",
"13 No Alive 58.4\n",
"14 No Dead 60.6\n",
"15 No Alive 25.1\n",
"16 No Alive 43.5\n",
"17 No Alive 27.1\n",
"18 No Alive 58.3\n",
"19 Yes Alive 65.7\n",
"20 No Dead 73.2\n",
"21 Yes Alive 38.3\n",
"22 No Alive 33.4\n",
"23 Yes Dead 62.3\n",
"24 No Alive 18.0\n",
"25 No Alive 56.2\n",
"26 Yes Alive 59.2\n",
"27 No Alive 25.8\n",
"28 No Dead 36.9\n",
"29 No Alive 20.2\n",
"... ... ... ...\n",
"1284 Yes Dead 36.0\n",
"1285 Yes Alive 48.3\n",
"1286 No Alive 63.1\n",
"1287 No Alive 60.8\n",
"1288 Yes Dead 39.3\n",
"1289 No Alive 36.7\n",
"1290 No Alive 63.8\n",
"1291 No Dead 71.3\n",
"1292 No Alive 57.7\n",
"1293 No Alive 63.2\n",
"1294 No Alive 46.6\n",
"1295 Yes Dead 82.4\n",
"1296 Yes Alive 38.3\n",
"1297 Yes Alive 32.7\n",
"1298 No Alive 39.7\n",
"1299 Yes Dead 60.0\n",
"1300 No Dead 71.0\n",
"1301 No Alive 20.5\n",
"1302 No Alive 44.4\n",
"1303 Yes Alive 31.2\n",
"1304 Yes Alive 47.8\n",
"1305 Yes Alive 60.9\n",
"1306 No Dead 61.4\n",
"1307 Yes Alive 43.0\n",
"1308 No Alive 42.1\n",
"1309 Yes Alive 35.9\n",
"1310 No Alive 22.3\n",
"1311 Yes Dead 62.1\n",
"1312 No Dead 88.6\n",
"1313 No Alive 39.1\n",
"\n",
"[1314 rows x 3 columns]"
]
},
"execution_count": 89,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# get data\n",
"data_url = \"https://gitlab.inria.fr/learninglab/mooc-rr/mooc-rr-ressources/-/raw/master/module3/Practical_session/Subject6_smoking.csv\"\n",
"\n",
"raw_data = pd.read_csv(data_url)\n",
"raw_data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. taux de mortalité en fonction de leur habitude de tabagisme"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
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" <th></th>\n",
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" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>taux de décès parmi les non-fumeurs (%)</th>\n",
" <td>31.420765</td>\n",
" </tr>\n",
" <tr>\n",
" <th>taux de décès parmi les fumeurs (%)</th>\n",
" <td>23.883162</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" \n",
"taux de décès parmi les non-fumeurs (%) 31.420765\n",
"taux de décès parmi les fumeurs (%) 23.883162"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# data[i] i=0: non-smoker, i=1 smoker\n",
"# data[i][j] j=0: alive, j=1 dead\n",
"data = [[0, 0], [0, 0]]\n",
"NONSMOKER, SMOKER = (0, 1)\n",
"ALIVE, DEAD = (0, 1)\n",
"\n",
"for _, e in raw_data.iterrows(): \n",
" data[e[\"Smoker\"]==\"Yes\"][e[\"Status\"]==\"Dead\"] += 1\n",
"\n",
"# mortality_rate = (%dead among non-smokers), (%dead among smokers)\n",
"mortality_rate = [\n",
" data[NONSMOKER][DEAD]/sum(data[NONSMOKER])*100,\n",
" data[SMOKER][DEAD]/sum(data[SMOKER])*100\n",
"]\n",
"\n",
"pd.DataFrame(mortality_rate, columns=[\"\"], index=[\"taux de décès parmi les non-fumeurs (%)\", \"taux de décès parmi les fumeurs (%)\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Conclusion: Il y a plus de morts parmi les non-fumeurs. Ne pas fumer serait dangereux ?\n",
" \n",
"## 2. taux de mortalité en fonction de l'age et l'habitude de tabagisme"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
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" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>taux de décès parmi les non-fumeurs (%)</th>\n",
" <th>taux de décès parmi les fumeurs (%)</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>18-34 ans</th>\n",
" <td>2.739726</td>\n",
" <td>3.296703</td>\n",
" </tr>\n",
" <tr>\n",
" <th>34-54 ans</th>\n",
" <td>9.547739</td>\n",
" <td>17.299578</td>\n",
" </tr>\n",
" <tr>\n",
" <th>55-64 ans</th>\n",
" <td>33.057851</td>\n",
" <td>43.859649</td>\n",
" </tr>\n",
" <tr>\n",
" <th>65+ ans</th>\n",
" <td>85.492228</td>\n",
" <td>85.714286</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" taux de décès parmi les non-fumeurs (%) \\\n",
"18-34 ans 2.739726 \n",
"34-54 ans 9.547739 \n",
"55-64 ans 33.057851 \n",
"65+ ans 85.492228 \n",
"\n",
" taux de décès parmi les fumeurs (%) \n",
"18-34 ans 3.296703 \n",
"34-54 ans 17.299578 \n",
"55-64 ans 43.859649 \n",
"65+ ans 85.714286 "
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"age_categories = [\"18-34 ans\", \"34-54 ans\", \"55-64 ans\", \"65+ ans\"]\n",
"# data[age][is smoking][is dead] = nb people\n",
"data = [ [[0, 0], [0, 0]] for a in age_categories ]\n",
"\n",
"for _, e in raw_data.iterrows():\n",
" age = 0\n",
" if e[\"Age\"] > 34 and e[\"Age\"] <= 54:\n",
" age = 1\n",
" elif e[\"Age\"] > 55 and e[\"Age\"] <= 64:\n",
" age = 2\n",
" elif e[\"Age\"] > 64:\n",
" age = 3\n",
" data[age][e[\"Smoker\"]==\"Yes\"][e[\"Status\"]==\"Dead\"] += 1\n",
"\n",
"mortality_rate = [[\n",
" e[NONSMOKER][DEAD]/sum(e[NONSMOKER])*100,\n",
" e[SMOKER][DEAD]/sum(e[SMOKER])*100\n",
"] for e in data]\n",
" \n",
"pd.DataFrame(mortality_rate, index=age_categories, columns=[\"taux de décès parmi les non-fumeurs (%)\", \"taux de décès parmi les fumeurs (%)\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Conclusion: il y a moins de décès chez les non-fumeurs indépendament de leur catégorie d'age.\n",
"\n",
"Ce qui semble contredire le résultat précédent ? Pas forcément. Pour y voir plus clair, étudions le nombre de fumeurs en fonction de leur catégorie d'age.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
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"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>nb non-fumeurs</th>\n",
" <th>nb fumeurs</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>18-34 ans</th>\n",
" <td>219</td>\n",
" <td>182</td>\n",
" </tr>\n",
" <tr>\n",
" <th>34-54 ans</th>\n",
" <td>199</td>\n",
" <td>237</td>\n",
" </tr>\n",
" <tr>\n",
" <th>55-64 ans</th>\n",
" <td>121</td>\n",
" <td>114</td>\n",
" </tr>\n",
" <tr>\n",
" <th>65+ ans</th>\n",
" <td>193</td>\n",
" <td>49</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" nb non-fumeurs nb fumeurs\n",
"18-34 ans 219 182\n",
"34-54 ans 199 237\n",
"55-64 ans 121 114\n",
"65+ ans 193 49"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nb = [[\n",
" sum(e[NONSMOKER]), sum(e[SMOKER])\n",
"] for e in data]\n",
"\n",
"pd.DataFrame(nb, index=age_categories, columns=[\"nb non-fumeurs\", \"nb fumeurs\"])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On remarque le piège ! La plupart des personnes de 65+ ans ne fument pas (~75%) ! Mais ont le plus grand taux de décès, indépendament du fait qu'elles fument. En aggrégant les catégories d'age, elles font remonter énormément le nombre de décès parmi les non-fumeurs et peu parmi les non-fumeurs. D'où le fait qu'on observe un taux de décès parmi les non-fumeurs plus important."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
......@@ -16,10 +796,9 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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