From 5eb6ca4eeeed5ad434c42d0613d22173a84f0aa8 Mon Sep 17 00:00:00 2001 From: x0s Date: Fri, 24 Apr 2020 10:14:13 +0200 Subject: [PATCH] Ajout sujet 6 paradoxe simpson export dysfonctionnel --- module3/sujet6/html_dysfunc/backup.html | 1492 +++++++++++++++++ .../captures_dysfunc/plot_dysfunc_code.png | Bin 0 -> 78940 bytes .../plot_dysfunc_first_export.png | Bin 0 -> 70693 bytes .../table_dysfunc_second_export.png | Bin 0 -> 14783 bytes .../table_ok_first_export.png | Bin 0 -> 24473 bytes .../html_dysfunc/data_as_stacked_bar_plot.png | Bin 0 -> 10776 bytes .../data_as_stacked_bar_plot_agecut.png | Bin 0 -> 27679 bytes module3/sujet6/html_dysfunc/roc.png | Bin 0 -> 50026 bytes .../html_dysfunc/smoker_survival_logistic.png | Bin 0 -> 103058 bytes .../smoker_survival_logistic_custom.png | Bin 0 -> 29977 bytes .../html_dysfunc/smoker_survival_violin.png | Bin 0 -> 46355 bytes module3/sujet6/paradoxe_simpson_dysfunc.org | 623 +++++++ 12 files changed, 2115 insertions(+) create mode 100644 module3/sujet6/html_dysfunc/backup.html create mode 100644 module3/sujet6/html_dysfunc/captures_dysfunc/plot_dysfunc_code.png create mode 100644 module3/sujet6/html_dysfunc/captures_dysfunc/plot_dysfunc_first_export.png create mode 100644 module3/sujet6/html_dysfunc/captures_dysfunc/table_dysfunc_second_export.png create mode 100644 module3/sujet6/html_dysfunc/captures_dysfunc/table_ok_first_export.png create mode 100644 module3/sujet6/html_dysfunc/data_as_stacked_bar_plot.png create mode 100644 module3/sujet6/html_dysfunc/data_as_stacked_bar_plot_agecut.png create mode 100644 module3/sujet6/html_dysfunc/roc.png create mode 100644 module3/sujet6/html_dysfunc/smoker_survival_logistic.png create mode 100644 module3/sujet6/html_dysfunc/smoker_survival_logistic_custom.png create mode 100644 module3/sujet6/html_dysfunc/smoker_survival_violin.png create mode 100644 module3/sujet6/paradoxe_simpson_dysfunc.org diff --git a/module3/sujet6/html_dysfunc/backup.html b/module3/sujet6/html_dysfunc/backup.html new file mode 100644 index 0000000..250b346 --- /dev/null +++ b/module3/sujet6/html_dysfunc/backup.html @@ -0,0 +1,1492 @@ + + + + + + + +Sujet 6: Autour du Paradoxe de Simpson + + + + + + + + + + + + + + +
+

Sujet 6: Autour du Paradoxe de Simpson

+ + +
+

1 Introduction

+
+

+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. +

+ +

+Vous trouverez sur chaque ligne si la personne fume ou non, si elle est vivante ou décédée au moment de la seconde étude, et son âge lors du premier sondage. +(source) +

+
+
+
+

2 Mission

+
+
+
+

2.1 Relation entre tabagisme et décès

+
+

+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 ? +

+ +

+Tout d'abord Chargons le jeu de données dans une dataframe pandas pour +faciliter la manipulation de données +

+
+
from pathlib import Path
+import matplotlib.pyplot as plt
+import pandas as pd
+
+# set floating precision to 1 (ie: 97.244->97.2) 
+pd.set_option("display.precision", 1)
+
+data_url = "http://gitlab.inria.fr/learninglab/mooc-rr/mooc-rr-ressources/blob/master/module3/Practical_session/Subject6_smoking.csv"
+data_file = Path("Subject6_smoking.csv")
+
+if not data_file.exists():
+    raise IOError(f"Jeu de données introuvable, merci de le télécharger à nouveau via ce lien {data_url}")
+
+data = pd.read_csv(data_file, dtype={'Smoker': 'category', 'Status': 'category'})
+data
+
+
+ + + + +++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + +
210.929390020.916447940.897696840.81438290.766931060.73277370.686885250.637020140.593905030.523096130.467373120.422379030.354184280.215202880
+ +
+
data.describe(include='all')
+
+
+ + + + +++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + +
210.929390020.916447940.897696840.81438290.766931060.73277370.686885250.637020140.593905030.523096130.467373120.422379030.354184280.215202880
+ +

+On a bien deux valeurs possibles pour les variables catégorielles: +

+
    +
  • Fumeuse(Smoker): Yes/No +
      +
    • Indique si la personne est fumeuse au moment de la seconde étude +(20 ans après la première)
    • +
  • +
  • Etat(Status) : Alive/Dead +
      +
    • Indique si la personne est vivante au moment de la seconde étude
    • +
  • +
+ +

+Au moment de la première étude, les 1314 femmes sollicitées étaient majeures. La moitié avait moins de 44,8 ans et +la doyenne était agée de 89,9 ans. +

+ +

+Etudions le lien entre tabagisme et décès via ce tableau de +contingence sur les variables Smoker et Status: +

+
+
pd.crosstab(data.Smoker, data.Status, margins=True)
+
+
+ + + + +++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + +
210.929390020.916447940.897696840.81438290.766931060.73277370.686885250.637020140.593905030.523096130.467373120.422379030.354184280.215202880
+ +

+Depuis la première étude, 369 personnes sont décédées(\(39\%=\frac{369}{1314}\)). On observe +aussi que le nombre de non fumeuses est sensiblement plus élévé(\(+26\%=\frac{732}{582}\)) +que le nombre de fumeuses. Ainsi, on peut s'attendre à avoir une +distortion sur le nombre de morts. C'est effectivement le cas, mais +bien plus qu'on ne le supposerait car les non-fumeuses sont décédées +en bien plus grand nombre (\(+65%\%=\frac{230}{139}\)) que les fumeuses! +

+ +

+Regardons maintenant les mêmes données sous forme de ratios par +rapport à toute la population. Par exemple, 10,6% des femmes de +l'étude étaient fumeuses avant de décéder. +

+
+
pd.crosstab(data.Smoker, data.Status, margins=True, normalize='all')*100
+
+
+ + + + +++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + +
210.929390020.916447940.897696840.81438290.766931060.73277370.686885250.637020140.593905030.523096130.467373120.422379030.354184280.215202880
+ +

+Les ratios confirment ce que nous avons vu précédemment: les femmes +sont inégalement réparties selon la modalité fumeuse(44,3%)/non fumeuse(55,7%) +

+ +

+Déterminons maintenant les taux de mortalités pour chaque groupe +(fumeuse/ non fumeuse): +

+
+
pd.crosstab(data.Smoker, data.Status, margins=True, normalize='index')*100
+
+
+ + + + +++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + +
210.929390020.916447940.897696840.81438290.766931060.73277370.686885250.637020140.593905030.523096130.467373120.422379030.354184280.215202880
+ +

+Contre-intuitivement, nous observons que proportionnellement le taux +de mortalité est bien plus élevé chez les non-fumeuses que chez les +fumeuses(31,4% contre 23,9%) +

+ +

+Observons ce résultat surprenant sous forme graphique: +

+ +
+
pd.crosstab(data.Smoker, data.Status).plot.barh(stacked=True)
+
+figure_path = "data_as_stacked_bar_plot.png"
+plt.savefig(figure_path)
+figure_path
+
+
+ +

+[[file:[2. 1. 0.92939002 0.91644794 0.89769684 0.8143829 + 0.76693106 0.7327737 0.68688525 0.63702014 0.59390503 0.52309613 + 0.46737312 0.42237903 0.35418428 0.21520288 0. ]]] +

+ +

+Qu'est-ce qui pourrait justifier que la surmortalité chez les +non-fumeuses ? +Existerait-il une autre variable qui +influencerait ces résultats ? Une autre comorbidité par exemple ? +Ou alors fumeraient-elle des MELL-O-WELL comme le recommande ce +médecin sur une publicité de 1930 ?! +

+ +

+176.jpg +(source) +

+
+
+ +
+

2.2 Partitionnement selon la classe d'âge

+
+

+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, +34-54ans, 55-64 ans, plus de 65 ans.En quoi ce résultat est-il +surprenant ? Arrivez-vous à expliquer ceparadoxe ? De même, +vous pourrez proposer une représentationgraphique de ces +données pour étayer vos explications. +

+ + +

+Comme suggéré, groupons par tranches d'age les femmes de l'études: +

+
+
# On choisit 17 ans en borne inférieur pour être sûr d'inclure le minimum (18)
+data['AgeCut'] = pd.cut(data.Age, bins=[17, 34, 54, 64, data.Age.max()], labels=["18-34 ans", "34-54 ans", "55-64 ans", "+ de 65 ans"])
+data.AgeCut
+
+
+ + + + +++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + +
210.929390020.916447940.897696840.81438290.766931060.73277370.686885250.637020140.593905030.523096130.467373120.422379030.354184280.215202880
+ +

+Remarquons que le choix des tranches d'age est ici arbitraire. On +aurait pu choisir ces 4 tranches de manière homogènes en regroupant par +quartile: +

+
+
print("Avec Quartiles:", *pd.qcut(data.Age, 4, retbins=True)[1].astype(int), sep='|')
+print("Sans Quartiles:", *[18, 34, 54, 64, 89], sep='|')
+
+
+ +
+Avec Quartiles:|18|31|44|60|89
+Sans Quartiles:|18|34|54|64|89
+
+
+ +

+Dénombrons les femmes ayant survécu/décédé selon leur tranche d'age +et si elles fumaient ou non: +

+
+
pd.crosstab([data.Smoker, data.AgeCut], data.Status, margins=True)
+
+
+ + + + +++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + +
210.929390020.916447940.897696840.81438290.766931060.73277370.686885250.637020140.593905030.523096130.467373120.422379030.354184280.215202880
+ +

+Si on regarde maintenant les ratios, on se rend compte qu'il y avait +sensiblement moins de fumeuses de plus de 65 ans que de fumeuses (3,7% +contre 14,7%) lors de la première étude. +

+ +

+Aussi, la mortalité semble plus élevée chez les fumeuses des tranches de +34 à 54 ans(3,1% contre 1,4%) +et de 55 à 64 ans(3,9% contre 3,0%). +Même si on a vu que la classe fumeuse/non fumeuse est déséquilibrée, +c'est étrange que cette tendance s'inverse sévèrement en passant +dans la tranche des plus de 65 ans(3,2% contre 12,6%) +Faudrait-il fumer toute sa vie pour enfin voir des effets positifs sur sa +santé ?! +

+ +
+
pd.crosstab([data.AgeCut, data.Smoker], data.Status, margins=True, normalize='all')*100
+
+
+ + + + +++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + +
210.929390020.916447940.897696840.81438290.766931060.73277370.686885250.637020140.593905030.523096130.467373120.422379030.354184280.215202880
+ +

+L'observation précédente n'est pas tout à fait exacte car elle compare +les tendances sur le ratio de la population globale. Si on se concentre sur les groupes +(fumeuse/non-fumeuse, tranche d'age) on se rend compte que les taux de +mortalités n'augmentent pas si on est fumeur pour les plus jeunes(~3%) mais +aussi pour les plus agés!(~85%) +Comme précédemment, au milieu de la vie, on observe une mortalité signficativement plus +élévée chez les fumeuses: 17,3% contre 9,5% chez les 34-54 ans et +44,3% contre 33,1% chez les 55-64 ans) +Au delà de 65 ans, cette surmortalité semble disparaître. Y aurait-il +une autre variable influençant les résultats ? +

+ +
+
pd.crosstab([data.AgeCut, data.Smoker], data.Status, margins=True, normalize='index')*100
+
+
+ + + + +++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + +
210.929390020.916447940.897696840.81438290.766931060.73277370.686885250.637020140.593905030.523096130.467373120.422379030.354184280.215202880
+ +

+Visuallement, c'est plus parlant: +

+ +
+
pd.crosstab([data.AgeCut, data.Smoker], data.Status).plot.barh(stacked=True)
+
+figure_path = "data_as_stacked_bar_plot_agecut.png"
+plt.savefig(figure_path, bbox_inches='tight')
+figure_path
+
+
+ +

+[[file:[2. 1. 0.92939002 0.91644794 0.89769684 0.8143829 + 0.76693106 0.7327737 0.68688525 0.63702014 0.59390503 0.52309613 + 0.46737312 0.42237903 0.35418428 0.21520288 0. ]]] +Même si le taux de mortalité semble être le même chez les femmes les plus +agées, le nombre d'individus est considérablement plus élévé chez les +non-fumeuses. Difficile de comparer correctement si les groupes ne sont pas homogènes. +

+ +

+On peut supposer que la mortalité plus élevée chez les fumeuses au +cours de leur vie se poursuit au delà de 65 ans mais que d'autres +causes de mortalité viennent s'ajouter. Ce qui paraît intuitif en fin +de vie. +

+ +

+Au Royaume-Uni, l'espérance de vie à la naissance en 1974 était de 72,5 ans +(source). Ainsi, lors de la première étude(de 1972 à 1974), les femmes de +plus de 65 ans pouvaient espérer vivre en moyenne 7,5ans. Ce chiffre +serait inférieur si on avait pris leur espérance de vie aux naissance +des femmes (avant 1910). +On peut naturellement attendre que 20 ans après la première étude, un +grand nombre de femmes aient décédées pour de multiples raisons, le +tabagisme n'étant que l'une des possibilités. +

+
+
+ +
+

2.3 Modélisation de la probabilité de décès en fonction de l'âge

+
+

+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). +

+ +

+Nous avons vu précédemment que le regroupement en tranches d'age +arbitraire pouvait surréprésenter certaines modalités(fumeuse/non +fumeuse) et amener à des conclusions innattendues(les fumeuses agées +décèdent moins que les non fumeuses agées). +

+ +

+En effet, nous pouvons voir sur le diagramme en violon ci-dessous que la +mortalité est plus faible chez les non fumeuses agées(+65 ans), mais +ne serait-pas parce qu'une majorité des fumeuses décèdent autour de 60 +ans ? +

+ +
+
import seaborn as sns
+plt.figure(figsize=(9, 7))
+sns.violinplot(x='Smoker', y='Age', hue='Status', data=data, split=True, inner='quartile')
+sns.despine()
+figure_path = "smoker_survival_violin.png"
+plt.savefig(figure_path, bbox_inches='tight')
+figure_path
+
+
+ +

+[[file:[2. 1. 0.92939002 0.91644794 0.89769684 0.8143829 + 0.76693106 0.7327737 0.68688525 0.63702014 0.59390503 0.52309613 + 0.46737312 0.42237903 0.35418428 0.21520288 0. ]]] +

+ +

+Comme conseillé, nous créeons une variable Death à partir de la +variable Status. Il s'agit simplement de faire correspondre 'Alive' à +0 et 'Dead' à 1: +

+
+
# On définit une variable Death(0 si survie, 1 si décès)
+data['Death'] = data.Status.cat.codes
+data[['Status', 'Death']]
+
+
+ + + + +++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + + + + + + + + + + + + + + + + + + + + + +
210.929390020.916447940.897696840.81438290.766931060.73277370.686885250.637020140.593905030.523096130.467373120.422379030.354184280.215202880
+ + +

+Observons rapidement ce qu'une modélisation avec une régression +logistique sur chaque groupe fumeuse/non fumeuse pourrait donner: +

+
+
plt.close()
+plt.figure(figsize=(12, 15))
+sns.lmplot(x="Age", y="Death", data=data, logistic=True, hue='Smoker', y_jitter=.03, aspect=1.5, markers=['o', 'x']);
+
+sns.despine()
+figure_path = "smoker_survival_logistic.png"
+plt.savefig(figure_path, bbox_inches='tight')
+figure_path
+
+
+ +

+[[file:[2. 1. 0.92939002 0.91644794 0.89769684 0.8143829 + 0.76693106 0.7327737 0.68688525 0.63702014 0.59390503 0.52309613 + 0.46737312 0.42237903 0.35418428 0.21520288 0. ]]] +

+ +

+Plusieurs remarques intéressantes: +

+
    +
  • La modélisation en sigmoïde(logistique) chez les non-fumeuses semble +mieux coller aux observations que chez les fumeuses. Vers les 60 +ans, on observe une courbure tendant vers un point d'inflexion(ce +qui va dans le sens de la régression logistique). En revanche, dans +cette même zône, on observe une courbure linéaire chez les +fumeuses.
  • +
  • Plus l'age des fumeuses augmente, plus l'intervalle de confiance est +large. Cela révèle une fois de plus le manque de données concernant +les personnes agées chez les fumeuses
  • +
  • L'intervalle de confiance semble plus étroit et plus stable selon +les ages chez les non-fumeuses. Cela est cohérent avec la forme +sigmoïdale déjà repérée sur le diagramme en violon.
  • +
+ +

+Cette analyse est à prendre avec des pincettes, c'est surtout pour +avoir un premier aperçu avant d'aller étudier et affiner les modèles +entraînés. C'est hélas la seule chose que nous permet la librairie +Seaborn puisque l'accès aux paramètres +ne +sera jamais permis! +

+ +

+Construisons alors un modèle de classification binaire pour +chaque sous-groupe fumeuse/non fumeuse afin d'essayer d'évaluer +l'impact de la cigarette sur la capacité à avoir survécu pendant les +20 ans séparant les deux études: +

+
+
from sklearn.model_selection import cross_val_score, cross_validate
+from sklearn.model_selection import RepeatedStratifiedKFold
+
+def train(model, model_name, data):
+    """Entraine un modèle pour chaque partition(Fumeuse/Non Fumeuse).
+    Ajoute également 2 colonnes à data contenant les prédictions du modèles ainsi que les probabilités"""
+    
+    # On stocke les classifieurs pour chaque groupe (fumeuse/non fumeuse)
+    clf = dict(Yes=None, No=None, name=model_name)
+    
+    for is_smoker in ['Yes', 'No']:
+        # Définition des jeux de données pour la validation croisée
+        cv = RepeatedStratifiedKFold(n_splits=6, n_repeats=3, random_state=1)
+        X = data[data.Smoker == is_smoker]['Age'].to_frame()
+        targets = data[data.Smoker == is_smoker]['Death']
+        
+        # Entrainement
+        scores = cross_validate(model, X, targets, scoring='roc_auc', cv=cv, n_jobs=-1, return_estimator=True)
+        # On récupère le meilleur classifieur
+        clf.update({is_smoker: scores['estimator'][scores['test_score'].argmax()]})
+        
+        # Ajout des prédictions et probabilités du modèle entrainé pour la partition en cours(fumeuse ou non fumeuse)
+        # Les probabilités retournées sont [P(Death = 0), P(Death = 1)]. On stocke donc le deuxième élément.
+        # Visualiser ordre des classes{0,1} dans clf[is_smoker].classes_ pour retrouver cette information
+        data.loc[data.Smoker == is_smoker, f'DeathProba{model_name}'] = clf[is_smoker].predict_proba(data[data.Smoker == is_smoker]['Age'].to_frame())[:,1]
+    return clf
+
+
+ +

+Nous allons également entraîner un modèle d'arbre de décision, qui +peut se retrouver assez performant pour la classification binaire. +

+ +
+
from sklearn.linear_model import LogisticRegression
+from sklearn.tree import DecisionTreeClassifier
+
+# train models
+model = LogisticRegression(solver='lbfgs', class_weight='balanced', C=0.1)
+clf_LR = train(model, "LR", data)
+
+model = DecisionTreeClassifier(class_weight='balanced', min_samples_leaf=5)
+clf_tree = train(model, "Tree", data)
+
+
+ +

+Observons les résultats +

+ +
+
import numpy as np
+from scipy.special import expit
+
+plt.clf()
+colors = dict(Yes='green', No='Red')
+
+for is_smoker in ['Yes', 'No']:
+    clf = clf_LR[is_smoker]
+    age, death = data[data.Smoker == is_smoker][['Age', 'Death']].T.values
+    
+    # Prepare for drawing logistic curve estimate
+    age_values = np.linspace(-0, 100, 300)
+    logit = expit(age_values * clf.coef_ + clf.intercept_).ravel()
+    
+    # Draw
+    plt.scatter(age, death, color=colors[is_smoker], marker='+')
+    plt.plot(age_values, logit, color=colors[is_smoker], linewidth=2)
+
+figure_path = 'smoker_survival_logistic_custom.png'
+plt.savefig(figure_path)
+figure_path
+
+
+ +

+[[file:[2. 1. 0.92939002 0.91644794 0.89769684 0.8143829 + 0.76693106 0.7327737 0.68688525 0.63702014 0.59390503 0.52309613 + 0.46737312 0.42237903 0.35418428 0.21520288 0. ]]] +On a le même type de courbe que précèdemment. C'est encore +contre-intuitif puisque les non-fumeuses(en vert) semblent se +précipiter plus vite que les fumeuses (en rouge) vers la mort (passer de 0 à 1). +

+ +

+Regardons quelques métriques usuelles +

+ +
+
from sklearn import metrics
+
+metrics_dict = dict(accuracy=metrics.accuracy_score,
+                    precision=metrics.precision_score,
+                    recall=metrics.recall_score)
+
+for clf in [clf_LR, clf_tree]:
+    print(f"<<<clf is {clf['Yes'].__class__.__name__}>>>")
+    for is_smoker in ['Yes', 'No']:
+        print(f"------Smoker is {is_smoker}------")
+        y_true = data[data.Smoker == is_smoker]['Death']
+        y_pred = clf[is_smoker].predict(data[data.Smoker == is_smoker]['Age'].to_frame())
+        for metric,score in metrics_dict.items():
+            print(f"{metric:>10} : {score(y_true, y_pred):.3}")
+        #print(metrics.confusion_matrix(y_true, y_pred)))
+
+
+
+ +
+<<<clf is LogisticRegression>>>
+------Smoker is Yes------
+  accuracy : 0.722
+ precision : 0.448
+    recall : 0.712
+------Smoker is No------
+  accuracy : 0.832
+ precision : 0.683
+    recall : 0.87
+<<<clf is DecisionTreeClassifier>>>
+------Smoker is Yes------
+  accuracy : 0.789
+ precision : 0.537
+    recall : 0.827
+------Smoker is No------
+  accuracy : 0.851
+ precision : 0.711
+    recall : 0.887
+
+ + +
+
from itertools import product
+plt.clf()
+
+for clf,is_smoker in product([clf_LR, clf_tree], ['Yes', 'No']):
+    y_true = data[data.Smoker == is_smoker]['Death']
+    y_pred_proba = data[data.Smoker == is_smoker][f"DeathProba{clf['name']}"]
+    
+    fpr, tpr, _ = metrics.roc_curve(y_true,  y_pred_proba)
+    auc = metrics.roc_auc_score(y_true, y_pred_proba)
+    plt.plot(fpr,tpr,label=f"{clf['name']}(Smoker={is_smoker}), auc={auc:.2}")
+    plt.legend(loc=4)
+
+plt.xlabel('Taux de faux positifs')
+plt.ylabel('Taux de vrais positifs')
+plt.title('Courbe ROC')
+figure_path = "roc.png"
+plt.savefig(figure_path, bbox_inches='tight');
+plt.close()
+return figure_path
+
+
+ +

+[[file:[2. 1. 0.92939002 0.91644794 0.89769684 0.8143829 + 0.76693106 0.7327737 0.68688525 0.63702014 0.59390503 0.52309613 + 0.46737312 0.42237903 0.35418428 0.21520288 0. ]]] +[[file:[2. 1. 0.92939002 0.91644794 0.89769684 0.8143829 + 0.76693106 0.7327737 0.68688525 0.63702014 0.59390503 0.52309613 + 0.46737312 0.42237903 0.35418428 0.21520288 0. ]]] +

+ + + +

+On se rend compte qu'il y a une différence non négligeable de +performance entre les modèles des fumeuses et ceux des non +fumeuses. Cette différence est visible même en changeant la nature du +modèle(Arbre de décision contre Régression logistique) +Avant de tirer des conclusions sur la nocivité du tabagisme, il +faudrait avoir des modèles ayant des performances similaires qui +disposeraient donc de capacité prédictives similaires. +

+ +

+En conclusion, il faudrait plus de données pour avoir des +distributions plus représentatives de la réalité. Aussi, ajouter de +l'expertise métier(information a priori) aux modèles pourrait aider +avoir une bonne capacité prédictive et sortir du Paradox de Simpson. On imagine créer d'autres +variables, comme l'écart à l'espérance de vie par exemple. +

+
+
+
+
+
+

Date: 2020-04-21

+

Auteur: Guillaume

+

Created: 2020-04-24 ven. 09:51

+

Validate

+
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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. + +Vous trouverez sur chaque ligne si la personne fume ou non, si elle est vivante ou décédée au moment de la seconde étude, et son âge lors du premier sondage. +([[https://gitlab.inria.fr/learninglab/mooc-rr/mooc-rr-ressources/blob/master//module3/Practical_session/Subject6_fr.md][source]]) +* Mission +** Relation entre tabagisme et décès + 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 ? + +Tout d'abord Chargons le jeu de données dans une dataframe pandas pour +faciliter la manipulation de données +#+begin_src python :results value :exports both +from pathlib import Path +import matplotlib.pyplot as plt +import pandas as pd + +# set floating precision to 1 (ie: 97.244->97.2) +pd.set_option("display.precision", 1) + +data_url = "http://gitlab.inria.fr/learninglab/mooc-rr/mooc-rr-ressources/blob/master/module3/Practical_session/Subject6_smoking.csv" +data_file = Path("Subject6_smoking.csv") + +if not data_file.exists(): + raise IOError(f"Jeu de données introuvable, merci de le télécharger à nouveau via ce lien {data_url}") + +data = pd.read_csv(data_file, dtype={'Smoker': 'category', 'Status': 'category'}) +data +#+end_src + +#+RESULTS: +#+begin_example + Smoker Status Age +0 Yes Alive 21.0 +1 Yes Alive 19.3 +2 No Dead 57.5 +3 No Alive 47.1 +4 Yes Alive 81.4 +... ... ... ... +1309 Yes Alive 35.9 +1310 No Alive 22.3 +1311 Yes Dead 62.1 +1312 No Dead 88.6 +1313 No Alive 39.1 + +[1314 rows x 3 columns] +#+end_example + +#+begin_src python :results value :exports both +data.describe(include='all') +#+end_src + + #+RESULTS: + #+begin_example + Smoker Status Age + count 1314 1314 1314.0 + unique 2 2 NaN + top No Alive NaN + freq 732 945 NaN + mean NaN NaN 47.4 + std NaN NaN 19.2 + min NaN NaN 18.0 + 25% NaN NaN 31.3 + 50% NaN NaN 44.8 + 75% NaN NaN 60.6 + max NaN NaN 89.9 + #+end_example + +On a bien deux valeurs possibles pour les variables catégorielles: + - Fumeuse(Smoker): Yes/No + - Indique si la personne est fumeuse *au moment de la seconde étude* + (20 ans après la première) + - Etat(Status) : Alive/Dead + - Indique si la personne est vivante *au moment de la seconde étude* + +*Au moment de la première étude*, les 1314 femmes sollicitées étaient majeures. La moitié avait moins de 44,8 ans et +la doyenne était agée de 89,9 ans. + +Etudions le lien entre tabagisme et décès via ce tableau de +contingence sur les variables Smoker et Status: +#+begin_src python :results value :exports both +pd.crosstab(data.Smoker, data.Status, margins=True) +#+end_src + +#+RESULTS: +: Status Alive Dead All +: Smoker +: No 502 230 732 +: Yes 443 139 582 +: All 945 369 1314 + +Depuis la première étude, 369 personnes sont décédées($39\%=\frac{369}{1314}$). On observe +aussi que le nombre de non fumeuses est sensiblement plus élévé($+26\%=\frac{732}{582}$) +que le nombre de fumeuses. Ainsi, on peut s'attendre à avoir une +distortion sur le nombre de morts. C'est effectivement le cas, mais +bien plus qu'on ne le supposerait car les non-fumeuses sont décédées +en bien plus grand nombre ($+65%\%=\frac{230}{139}$) que les fumeuses! + +Regardons maintenant les mêmes données sous forme de ratios par +rapport à *toute la population*. Par exemple, 10,6% des femmes de +l'étude étaient fumeuses avant de décéder. +#+begin_src python :results value :exports both +pd.crosstab(data.Smoker, data.Status, margins=True, normalize='all')*100 +#+end_src + +#+RESULTS: +: Status Alive Dead All +: Smoker +: No 38.2 17.5 55.7 +: Yes 33.7 10.6 44.3 +: All 71.9 28.1 100.0 + +Les ratios confirment ce que nous avons vu précédemment: les femmes +sont inégalement réparties selon la modalité fumeuse(44,3%)/non fumeuse(55,7%) + +Déterminons maintenant les taux de mortalités pour chaque groupe +(fumeuse/ non fumeuse): +#+begin_src python :results value :exports both +pd.crosstab(data.Smoker, data.Status, margins=True, normalize='index')*100 +#+end_src + +#+RESULTS: +: Status Alive Dead +: Smoker +: No 68.6 31.4 +: Yes 76.1 23.9 +: All 71.9 28.1 + +Contre-intuitivement, nous observons que proportionnellement le taux +de mortalité est bien plus élevé chez les non-fumeuses que chez les +fumeuses(31,4% contre 23,9%) + +Observons ce résultat surprenant sous forme graphique: + +#+begin_src python :results file :exports both +pd.crosstab(data.Smoker, data.Status).plot.barh(stacked=True) + +figure_path = "data_as_stacked_bar_plot.png" +plt.savefig(figure_path) +figure_path +#+end_src + +#+RESULTS: +[[file:data_as_stacked_bar_plot.png]] + +Qu'est-ce qui pourrait justifier que la surmortalité chez les +non-fumeuses ? +Existerait-il une autre variable qui +influencerait ces résultats ? Une autre comorbidité par exemple ? +Ou alors fumeraient-elle des /MELL-O-WELL/ comme le recommande ce +médecin sur une publicité de 1930 ?! + +[[https://www.vivelapub.fr/wp-content/uploads/2012/08/clop/176.jpg]] +([[https://tobacco.stanford.edu/tobacco_main/][source]]) + +** Partitionnement selon la classe d'âge + 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, + 34-54ans, 55-64 ans, plus de 65 ans.En quoi ce résultat est-il + surprenant ? Arrivez-vous à expliquer ceparadoxe ? De même, + vous pourrez proposer une représentationgraphique de ces + données pour étayer vos explications. + + +Comme suggéré, groupons par tranches d'age les femmes de l'études: +#+begin_src python :results value :exports both +# On choisit 17 ans en borne inférieur pour être sûr d'inclure le minimum (18) +data['AgeCut'] = pd.cut(data.Age, bins=[17, 34, 54, 64, data.Age.max()], labels=["18-34 ans", "34-54 ans", "55-64 ans", "+ de 65 ans"]) +data.AgeCut +#+end_src + +#+RESULTS: +#+begin_example +0 18-34 ans +1 18-34 ans +2 55-64 ans +3 34-54 ans +4 + de 65 ans + ... +1309 34-54 ans +1310 18-34 ans +1311 55-64 ans +1312 + de 65 ans +1313 34-54 ans +Name: AgeCut, Length: 1314, dtype: category +Categories (4, object): [18-34 ans < 34-54 ans < 55-64 ans < + de 65 ans] +#+end_example + +Remarquons que le choix des tranches d'age est ici arbitraire. On +aurait pu choisir ces 4 tranches de manière homogènes en regroupant par +quartile: +#+begin_src python :results output :exports both +print("Avec Quartiles:", *pd.qcut(data.Age, 4, retbins=True)[1].astype(int), sep='|') +print("Sans Quartiles:", *[18, 34, 54, 64, 89], sep='|') +#+end_src + +#+RESULTS: +: Avec Quartiles:|18|31|44|60|89 +: Sans Quartiles:|18|34|54|64|89 + +Dénombrons les femmes ayant survécu/décédé selon leur tranche d'age +et si elles fumaient ou non: +#+begin_src python :results value :exports both +pd.crosstab([data.Smoker, data.AgeCut], data.Status, margins=True) +#+end_src + +#+RESULTS: +#+begin_example +Status Alive Dead All +Smoker AgeCut +No 18-34 ans 213 6 219 + 34-54 ans 180 19 199 + 55-64 ans 81 40 121 + + de 65 ans 28 165 193 +Yes 18-34 ans 176 5 181 + 34-54 ans 196 41 237 + 55-64 ans 64 51 115 + + de 65 ans 7 42 49 +All 945 369 1314 +#+end_example + +Si on regarde maintenant les ratios, on se rend compte qu'il y avait +sensiblement moins de fumeuses de plus de 65 ans que de fumeuses (3,7% +contre 14,7%) *lors de la première étude*. + +Aussi, la mortalité semble plus élevée chez les fumeuses des tranches de +34 à 54 ans(3,1% contre 1,4%) +et de 55 à 64 ans(3,9% contre 3,0%). +Même si on a vu que la classe fumeuse/non fumeuse est déséquilibrée, +c'est étrange que cette tendance s'inverse sévèrement en passant +dans la tranche des plus de 65 ans(3,2% contre 12,6%) +Faudrait-il fumer toute sa vie pour enfin voir des effets positifs sur sa +santé ?! + +#+begin_src python :results value :exports both +pd.crosstab([data.AgeCut, data.Smoker], data.Status, margins=True, normalize='all')*100 +#+end_src + +#+RESULTS: +#+begin_example +Status Alive Dead All +AgeCut Smoker +18-34 ans No 16.2 0.5 16.7 + Yes 13.4 0.4 13.8 +34-54 ans No 13.7 1.4 15.1 + Yes 14.9 3.1 18.0 +55-64 ans No 6.2 3.0 9.2 + Yes 4.9 3.9 8.8 ++ de 65 ans No 2.1 12.6 14.7 + Yes 0.5 3.2 3.7 +All 71.9 28.1 100.0 +#+end_example + +L'observation précédente n'est pas tout à fait exacte car elle compare +les tendances sur le ratio de la population globale. Si on se concentre sur les groupes +(fumeuse/non-fumeuse, tranche d'age) on se rend compte que les taux de +mortalités n'augmentent pas si on est fumeur pour les plus jeunes(~3%) mais +*aussi pour les plus agés*!(~85%) +Comme précédemment, au milieu de la vie, on observe une mortalité signficativement plus +élévée chez les fumeuses: 17,3% contre 9,5% chez les 34-54 ans et +44,3% contre 33,1% chez les 55-64 ans) +Au delà de 65 ans, cette surmortalité semble disparaître. Y aurait-il +une autre variable influençant les résultats ? + +#+begin_src python :results value :exports both +pd.crosstab([data.AgeCut, data.Smoker], data.Status, margins=True, normalize='index')*100 +#+end_src + +#+RESULTS: +#+begin_example +Status Alive Dead +AgeCut Smoker +18-34 ans No 97.3 2.7 + Yes 97.2 2.8 +34-54 ans No 90.5 9.5 + Yes 82.7 17.3 +55-64 ans No 66.9 33.1 + Yes 55.7 44.3 ++ de 65 ans No 14.5 85.5 + Yes 14.3 85.7 +All 71.9 28.1 +#+end_example + +Visuallement, c'est plus parlant: + +#+begin_src python :results file :exports both +pd.crosstab([data.AgeCut, data.Smoker], data.Status).plot.barh(stacked=True) + +figure_path = "data_as_stacked_bar_plot_agecut.png" +plt.savefig(figure_path, bbox_inches='tight') +figure_path +#+end_src + +#+RESULTS: +[[file:data_as_stacked_bar_plot_agecut.png]] +Même si le taux de mortalité semble être le même chez les femmes les plus +agées, le nombre d'individus est considérablement plus élévé chez les +non-fumeuses. Difficile de comparer correctement si les groupes ne sont pas homogènes. + +On peut supposer que la mortalité plus élevée chez les fumeuses au +cours de leur vie se poursuit au delà de 65 ans mais que d'autres +causes de mortalité viennent s'ajouter. Ce qui paraît intuitif en fin +de vie. + +Au Royaume-Uni, l'espérance de vie à la naissance en 1974 était de 72,5 ans +([[https://donnees.banquemondiale.org/indicateur/SP.DYN.LE00.IN?locations=GB][source]]). Ainsi, lors de la première étude(de 1972 à 1974), les femmes de +plus de 65 ans pouvaient espérer vivre en moyenne 7,5ans. Ce chiffre +serait inférieur si on avait pris leur espérance de vie aux naissance +des femmes (avant 1910). +On peut naturellement attendre que 20 ans après la première étude, un +grand nombre de femmes aient décédées pour de multiples raisons, le +tabagisme n'étant que l'une des possibilités. + +** Modélisation de la probabilité de décès en fonction de l'âge + 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). + +Nous avons vu précédemment que le regroupement en tranches d'age +arbitraire pouvait surréprésenter certaines modalités(fumeuse/non +fumeuse) et amener à des conclusions innattendues(les fumeuses agées +décèdent moins que les non fumeuses agées). + +En effet, nous pouvons voir sur le diagramme en violon ci-dessous que la +mortalité est plus faible chez les non fumeuses agées(+65 ans), mais +ne serait-pas parce qu'une majorité des fumeuses décèdent autour de 60 +ans ? + +#+begin_src python :results file :exports both +import seaborn as sns +plt.figure(figsize=(9, 7)) +sns.violinplot(x='Smoker', y='Age', hue='Status', data=data, split=True, inner='quartile') +sns.despine() +figure_path = "smoker_survival_violin.png" +plt.savefig(figure_path, bbox_inches='tight') +figure_path +#+end_src + +#+RESULTS: +[[file:smoker_survival_violin.png]] + +Comme conseillé, nous créeons une variable Death à partir de la +variable Status. Il s'agit simplement de faire correspondre 'Alive' à +0 et 'Dead' à 1: +#+begin_src python :results value :exports both +# On définit une variable Death(0 si survie, 1 si décès) +data['Death'] = data.Status.cat.codes +data[['Status', 'Death']] +#+end_src + +#+RESULTS: +#+begin_example + Status Death +0 Alive 0 +1 Alive 0 +2 Dead 1 +3 Alive 0 +4 Alive 0 +... ... ... +1309 Alive 0 +1310 Alive 0 +1311 Dead 1 +1312 Dead 1 +1313 Alive 0 + +[1314 rows x 2 columns] +#+end_example + + +Observons rapidement ce qu'une modélisation avec une régression +logistique sur chaque groupe fumeuse/non fumeuse pourrait donner: +#+begin_src python :results file :exports both +plt.close() +plt.figure(figsize=(12, 15)) +sns.lmplot(x="Age", y="Death", data=data, logistic=True, hue='Smoker', y_jitter=.03, aspect=1.5, markers=['o', 'x']); + +sns.despine() +figure_path = "smoker_survival_logistic.png" +plt.savefig(figure_path, bbox_inches='tight') +figure_path +#+end_src + +#+RESULTS: +[[file:smoker_survival_logistic.png]] + +Plusieurs remarques intéressantes: +- La modélisation en sigmoïde(logistique) chez les non-fumeuses semble + mieux coller aux observations que chez les fumeuses. Vers les 60 + ans, on observe une courbure tendant vers un point d'inflexion(ce + qui va dans le sens de la régression logistique). En revanche, dans + cette même zône, on observe une courbure linéaire chez les + fumeuses. +- Plus l'age des fumeuses augmente, plus l'intervalle de confiance est + large. Cela révèle une fois de plus le manque de données concernant + les personnes agées chez les fumeuses +- L'intervalle de confiance semble plus étroit et plus stable selon + les ages chez les non-fumeuses. Cela est cohérent avec la forme + sigmoïdale déjà repérée sur le diagramme en violon. + +Cette analyse est à prendre avec des pincettes, c'est surtout pour +avoir un premier aperçu avant d'aller étudier et affiner les modèles +entraînés. C'est hélas la seule chose que nous permet la librairie +Seaborn puisque l'accès aux paramètres +[[https://github.com/mwaskom/seaborn/issues/655#issuecomment-125073496][ne +sera jamais permis!]] + +Construisons alors un modèle de classification binaire pour +chaque sous-groupe fumeuse/non fumeuse afin d'essayer d'évaluer +l'impact de la cigarette sur la capacité à avoir survécu pendant les +20 ans séparant les deux études: +#+begin_src python :results silent :exports both +from sklearn.model_selection import cross_val_score, cross_validate +from sklearn.model_selection import RepeatedStratifiedKFold + +def train(model, model_name, data): + """Entraine un modèle pour chaque partition(Fumeuse/Non Fumeuse). + Ajoute également 2 colonnes à data contenant les prédictions du modèles ainsi que les probabilités""" + + # On stocke les classifieurs pour chaque groupe (fumeuse/non fumeuse) + clf = dict(Yes=None, No=None, name=model_name) + + for is_smoker in ['Yes', 'No']: + # Définition des jeux de données pour la validation croisée + cv = RepeatedStratifiedKFold(n_splits=6, n_repeats=3, random_state=1) + X = data[data.Smoker == is_smoker]['Age'].to_frame() + targets = data[data.Smoker == is_smoker]['Death'] + + # Entrainement + scores = cross_validate(model, X, targets, scoring='roc_auc', cv=cv, n_jobs=-1, return_estimator=True) + # On récupère le meilleur classifieur + clf.update({is_smoker: scores['estimator'][scores['test_score'].argmax()]}) + + # Ajout des prédictions et probabilités du modèle entrainé pour la partition en cours(fumeuse ou non fumeuse) + # Les probabilités retournées sont [P(Death = 0), P(Death = 1)]. On stocke donc le deuxième élément. + # Visualiser ordre des classes{0,1} dans clf[is_smoker].classes_ pour retrouver cette information + data.loc[data.Smoker == is_smoker, f'DeathProba{model_name}'] = clf[is_smoker].predict_proba(data[data.Smoker == is_smoker]['Age'].to_frame())[:,1] + return clf +#+end_src + +#+RESULTS: + +Nous allons également entraîner un modèle d'arbre de décision, qui +peut se retrouver assez performant pour la classification binaire. + +#+begin_src python :results output :exports both +from sklearn.linear_model import LogisticRegression +from sklearn.tree import DecisionTreeClassifier + +# train models +model = LogisticRegression(solver='lbfgs', class_weight='balanced', C=0.1) +clf_LR = train(model, "LR", data) + +model = DecisionTreeClassifier(class_weight='balanced', min_samples_leaf=5) +clf_tree = train(model, "Tree", data) +#+end_src + +#+RESULTS: + +Observons les résultats + +#+begin_src python :results silent :exports none +"""from sklearn.tree import plot_tree +plt.close() +plt.figure(figsize=(4,3), dpi=400) +plot_tree(clf_tree['No'], filled=True, feature_names=['Age']) +plt.tight_layout() +plt.show()""" +#+end_src + +#+RESULTS: + +#+begin_src python :results file :exports both +import numpy as np +from scipy.special import expit + +plt.clf() +colors = dict(Yes='green', No='Red') + +for is_smoker in ['Yes', 'No']: + clf = clf_LR[is_smoker] + age, death = data[data.Smoker == is_smoker][['Age', 'Death']].T.values + + # Prepare for drawing logistic curve estimate + age_values = np.linspace(-0, 100, 300) + logit = expit(age_values * clf.coef_ + clf.intercept_).ravel() + + # Draw + plt.scatter(age, death, color=colors[is_smoker], marker='+') + plt.plot(age_values, logit, color=colors[is_smoker], linewidth=2) + +figure_path = 'smoker_survival_logistic_custom.png' +plt.savefig(figure_path) +figure_path +#+end_src + +#+RESULTS: +[[file:smoker_survival_logistic_custom.png]] +On a le même type de courbe que précèdemment. C'est encore +contre-intuitif puisque les non-fumeuses(en vert) semblent se +précipiter plus vite que les fumeuses (en rouge) vers la mort (passer de 0 à 1). + +Regardons quelques métriques usuelles + +#+RESULTS: + +#+begin_src python :results output :exports both +from sklearn import metrics + +metrics_dict = dict(accuracy=metrics.accuracy_score, + precision=metrics.precision_score, + recall=metrics.recall_score) + +for clf in [clf_LR, clf_tree]: + print(f"<<>>") + for is_smoker in ['Yes', 'No']: + print(f"------Smoker is {is_smoker}------") + y_true = data[data.Smoker == is_smoker]['Death'] + y_pred = clf[is_smoker].predict(data[data.Smoker == is_smoker]['Age'].to_frame()) + for metric,score in metrics_dict.items(): + print(f"{metric:>10} : {score(y_true, y_pred):.3}") + #print(metrics.confusion_matrix(y_true, y_pred))) + +#+end_src + +#+RESULTS: +#+begin_example +<<>> +------Smoker is Yes------ + accuracy : 0.722 + precision : 0.448 + recall : 0.712 +------Smoker is No------ + accuracy : 0.832 + precision : 0.683 + recall : 0.87 +<<>> +------Smoker is Yes------ + accuracy : 0.789 + precision : 0.537 + recall : 0.827 +------Smoker is No------ + accuracy : 0.851 + precision : 0.711 + recall : 0.887 +#+end_example + + +#+begin_src python :results file :exports both +from itertools import product +plt.clf() + +for clf,is_smoker in product([clf_LR, clf_tree], ['Yes', 'No']): + y_true = data[data.Smoker == is_smoker]['Death'] + y_pred_proba = data[data.Smoker == is_smoker][f"DeathProba{clf['name']}"] + + fpr, tpr, _ = metrics.roc_curve(y_true, y_pred_proba) + auc = metrics.roc_auc_score(y_true, y_pred_proba) + plt.plot(fpr,tpr,label=f"{clf['name']}(Smoker={is_smoker}), auc={auc:.2}") + plt.legend(loc=4) + +plt.xlabel('Taux de faux positifs') +plt.ylabel('Taux de vrais positifs') +plt.title('Courbe ROC') +figure_path = "roc.png" +plt.savefig(figure_path, bbox_inches='tight'); +plt.close() +return figure_path +#+end_src + +#+RESULTS: +[[file:[2. 1. 0.92939002 0.91644794 0.89769684 0.8143829 + 0.76693106 0.7327737 0.68688525 0.63702014 0.59390503 0.52309613 + 0.46737312 0.42237903 0.35418428 0.21520288 0. ]]] + + + +On se rend compte qu'il y a une différence non négligeable de +performance entre les modèles des fumeuses et ceux des non +fumeuses. Cette différence est visible même en changeant la nature du +modèle(Arbre de décision contre Régression logistique) +Avant de tirer des conclusions sur la nocivité du tabagisme, il +faudrait avoir des modèles ayant des performances similaires qui +disposeraient donc de capacité prédictives similaires. + +En conclusion, il faudrait plus de données pour avoir des +distributions plus représentatives de la réalité. Aussi, ajouter de +l'expertise métier(information a priori) aux modèles pourrait aider +avoir une bonne capacité prédictive et sortir du Paradox de Simpson. On imagine créer d'autres +variables, comme l'écart à l'espérance de vie par exemple. + + -- 2.18.1

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