From 25a937cd0a86894e08ded2e4da8cac21952435bd Mon Sep 17 00:00:00 2001 From: "A.Changenet" Date: Mon, 5 Apr 2021 17:44:44 +0100 Subject: [PATCH] Exo 3 commit pdf et html --- module3/exo1/analyse-syndrome-grippal.Rmd | 4 +- module3/exo1/analyse-syndrome-grippal.html | 422 +++++ module3/exo2/incidence-PAY-7.csv | 1584 +++++++++++++++++ module3/exo3/Simpson_paradox_A.Changenet.html | 445 +++++ module3/exo3/exercice_fr.Rmd | 256 ++- module3/exo3/exercice_fr.html | 601 +++++++ module3/exo3/exercice_fr.pdf | Bin 0 -> 302022 bytes ...le3_Practical_session_Subject6_smoking.csv | 1315 ++++++++++++++ 8 files changed, 4609 insertions(+), 18 deletions(-) create mode 100644 module3/exo1/analyse-syndrome-grippal.html create mode 100644 module3/exo2/incidence-PAY-7.csv create mode 100644 module3/exo3/Simpson_paradox_A.Changenet.html create mode 100644 module3/exo3/exercice_fr.html create mode 100644 module3/exo3/exercice_fr.pdf create mode 100644 module3/exo3/module3_Practical_session_Subject6_smoking.csv diff --git a/module3/exo1/analyse-syndrome-grippal.Rmd b/module3/exo1/analyse-syndrome-grippal.Rmd index a32be87..7e13e3a 100644 --- a/module3/exo1/analyse-syndrome-grippal.Rmd +++ b/module3/exo1/analyse-syndrome-grippal.Rmd @@ -3,11 +3,11 @@ title: "Analyse de l'incidence du syndrôme grippal" author: "Alexandre Changenet" date: "02/04/2021" output: - pdf_document: - toc: true html_document: toc: true theme: journal + pdf_document: + toc: true documentclass: article classoption: a4paper header-includes: diff --git a/module3/exo1/analyse-syndrome-grippal.html b/module3/exo1/analyse-syndrome-grippal.html new file mode 100644 index 0000000..f9d5ef2 --- /dev/null +++ b/module3/exo1/analyse-syndrome-grippal.html @@ -0,0 +1,422 @@ + + + + + + + + + + + + + + + +Analyse de l’incidence du syndrôme grippal + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + +
+

Préparation des données

+

Les données de l’incidence du syndrome grippal sont disponibles du site Web du Réseau Sentinelles. Nous les récupérons sous forme d’un fichier en format CSV dont chaque ligne correspond à une semaine de la période demandée. Nous téléchargeons toujours le jeu de données complet, qui commence en 1984 et se termine avec une semaine récente. L’URL est:

+
data_url = "http://www.sentiweb.fr/datasets/incidence-PAY-3.csv"
+

Voici l’explication des colonnes donnée sur le sur le site d’origine:

+ ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Nom de colonneLibellé de colonne
weekSemaine calendaire (ISO 8601)
indicatorCode de l’indicateur de surveillance
incEstimation de l’incidence de consultations en nombre de cas
inc_lowEstimation de la borne inférieure de l’IC95% du nombre de cas de consultation
inc_upEstimation de la borne supérieure de l’IC95% du nombre de cas de consultation
inc100Estimation du taux d’incidence du nombre de cas de consultation (en cas pour 100,000 habitants)
inc100_lowEstimation de la borne inférieure de l’IC95% du taux d’incidence du nombre de cas de consultation (en cas pour 100,000 habitants)
inc100_upEstimation de la borne supérieure de l’IC95% du taux d’incidence du nombre de cas de consultation (en cas pour 100,000 habitants)
geo_inseeCode de la zone géographique concernée (Code INSEE) http://www.insee.fr/fr/methodes/nomenclatures/cog/
geo_nameLibellé de la zone géographique (ce libellé peut être modifié sans préavis)
+

La première ligne du fichier CSV est un commentaire, que nous ignorons en précisant skip=1. ### Téléchargement la ligne suivante n’est pas exécuté

+
data = read.csv(data_url, skip=1)
+

Afin que l’analyse soit complètement reproductible, plutot que de télécharger les données à chaque fois, nous chargeons le fichier téléchargé en local (pour être sur qu’il ne change pas, ou pour que l’on puisse s’assurer qu’il a changer ou pas.)

+
data <- read.csv("~/Google Drive/Cours/mooc-rr/module3/incidence-PAY-3.csv", comment.char="#")
+

Regardons ce que nous avons obtenu:

+
head(data)
+
##     week indicator   inc inc_low inc_up inc100 inc100_low inc100_up geo_insee
+## 1 202112         3 36542   30199  42885     55         45        65        FR
+## 2 202111         3 25206   20860  29552     38         31        45        FR
+## 3 202110         3 19539   15951  23127     30         25        35        FR
+## 4 202109         3 17572   13926  21218     27         21        33        FR
+## 5 202108         3 20882   16907  24857     32         26        38        FR
+## 6 202107         3 22393   18303  26483     34         28        40        FR
+##   geo_name
+## 1   France
+## 2   France
+## 3   France
+## 4   France
+## 5   France
+## 6   France
+
tail(data)
+
##        week indicator    inc inc_low inc_up inc100 inc100_low inc100_up
+## 1895 198449         3 101073   81684 120462    184        149       219
+## 1896 198448         3  78620   60634  96606    143        110       176
+## 1897 198447         3  72029   54274  89784    131         99       163
+## 1898 198446         3  87330   67686 106974    159        123       195
+## 1899 198445         3 135223  101414 169032    246        184       308
+## 1900 198444         3  68422   20056 116788    125         37       213
+##      geo_insee geo_name
+## 1895        FR   France
+## 1896        FR   France
+## 1897        FR   France
+## 1898        FR   France
+## 1899        FR   France
+## 1900        FR   France
+

Y a-t-il des points manquants dans nos données ?

+
na_records = apply(data, 1, function (x) any(is.na(x)))
+data[na_records,]
+
##        week indicator inc inc_low inc_up inc100 inc100_low inc100_up geo_insee
+## 1664 198919         3   0      NA     NA      0         NA        NA        FR
+##      geo_name
+## 1664   France
+

Les deux colonnes qui nous intéressent sont week et inc. Vérifions leurs classes:

+
class(data$week)
+
## [1] "integer"
+
class(data$inc)
+
## [1] "integer"
+

Ce sont des entiers, tout va bien !

+
+

Conversion des numéros de semaine

+

La gestion des dates est toujours un sujet délicat. Il y a un grand nombre de conventions différentes qu’il ne faut pas confondre. Notre jeux de données utilise un format que peu de logiciels savent traiter: les semaines en format ISO-8601. En R, il est géré par la bibliothèque parsedate:

+
library(parsedate)
+

Pour faciliter le traitement suivant, nous remplaçons ces semaines par les dates qui correspondent aux lundis. Voici une petite fonction qui fait la conversion pour une seule valeur:

+
convert_week = function(w) {
+    ws = paste(w)
+    iso = paste0(substring(ws, 1, 4), "-W", substring(ws, 5, 6))
+    as.character(parse_iso_8601(iso))
+}
+

Nous appliquons cette fonction à tous les points, créant une nouvelle colonne date dans notre jeu de données:

+
data$date = as.Date(convert_week(data$week))
+

Vérifions qu’elle est de classe Date:

+
class(data$date)
+
## [1] "Date"
+

Les points sont dans l’ordre chronologique inverse, il est donc utile de les trier:

+
data = data[order(data$date),]
+

C’est l’occasion pour faire une vérification: nos dates doivent être séparées d’exactement sept jours:

+
all(diff(data$date) == 7)
+
## [1] TRUE
+
+
+

Inspection

+

Regardons enfin à quoi ressemblent nos données !

+
plot(data$date, data$inc, type="l", xlab="Date", ylab="Incidence hebdomadaire")
+

+

Un zoom sur les dernières années montre mieux la localisation des pics en hiver. Le creux des incidences se trouve en été.

+
with(tail(data, 200), plot(date, inc, type="l", xlab="Date", ylab="Incidence hebdomadaire"))
+

+
+
+
+

L’incidence annuelle

+
+

Calcul

+

Étant donné que le pic de l’épidémie se situe en hiver, à cheval entre deux années civiles, nous définissons la période de référence entre deux minima de l’incidence, du 1er août de l’année \(N\) au 1er août de l’année \(N+1\). Nous mettons l’année \(N+1\) comme étiquette sur cette année décalée, car le pic de l’épidémie est toujours au début de l’année \(N+1\). Comme l’incidence de syndrome grippal est très faible en été, cette modification ne risque pas de fausser nos conclusions. L’argument na.rm=True dans la sommation précise qu’il faut supprimer les points manquants. Ce choix est raisonnable car il n’y a qu’un seul point manquant, dont l’impact ne peut pas être très fort.

+
pic_annuel = function(annee) {
+      debut = paste0(annee-1,"-08-01")
+      fin = paste0(annee,"-08-01")
+      semaines = data$date > debut & data$date <= fin
+      sum(data$inc[semaines], na.rm=TRUE)
+      }
+

Nous devons aussi faire attention aux premières et dernières années de notre jeux de données. Les données commencent en octobre 1984, ce qui ne permet pas de quantifier complètement le pic attribué à 1985. Nous l’enlevons donc de notre analyse. Par contre, pour une exécution en octobre 2018, les données se terminent après le 1er août 2018, ce qui nous permet d’inclure cette année.

+
annees = 1986:2020
+

Nous créons un nouveau jeu de données pour l’incidence annuelle, en applicant la fonction pic_annuel à chaque année:

+
inc_annuelle = data.frame(annee = annees,
+                          incidence = sapply(annees, pic_annuel))
+head(inc_annuelle)
+
##   annee incidence
+## 1  1986   5100540
+## 2  1987   2861556
+## 3  1988   2766142
+## 4  1989   5460155
+## 5  1990   5233987
+## 6  1991   1660832
+
+
+

Inspection

+

Voici les incidences annuelles en graphique:

+
plot(inc_annuelle, type="p", xlab="Année", ylab="Incidence annuelle")
+

+
+
+

Identification des épidémies les plus fortes

+

Une liste triée par ordre décroissant d’incidence annuelle permet de plus facilement repérer les valeurs les plus élevées:

+
head(inc_annuelle[order(-inc_annuelle$incidence),])
+
##    annee incidence
+## 4   1989   5460155
+## 5   1990   5233987
+## 1   1986   5100540
+## 28  2013   4182265
+## 25  2010   4085126
+## 14  1999   3897443
+

Enfin, un histogramme montre bien que les épidémies fortes, qui touchent environ 10% de la population française, sont assez rares: il y en eu trois au cours des 35 dernières années.

+
hist(inc_annuelle$incidence, breaks=10, xlab="Incidence annuelle", ylab="Nb d'observations", main="")
+

+
+
+ + + + +
+ + + + + + + + + + + + + + + diff --git a/module3/exo2/incidence-PAY-7.csv b/module3/exo2/incidence-PAY-7.csv new file mode 100644 index 0000000..e634b32 --- /dev/null +++ b/module3/exo2/incidence-PAY-7.csv @@ -0,0 +1,1584 @@ +# @source="rseau Sentinelles, INSERM, Sorbonne Universit, http://www.sentiweb.fr", @meta={"period":[199049,202112],"geo":["PAY","1"],"geo_ref":"insee","indicator":"7","type":"all","conf_int":true,"compact":false}, @date=2021-04-02T12:44:58+02:00 +week,indicator,inc,inc_low,inc_up,inc100,inc100_low,inc100_up,geo_insee,geo_name +202112,7,14023,9841,18205,21,15,27,FR,France +202111,7,9501,6752,12250,14,10,18,FR,France +202110,7,9056,6452,11660,14,10,18,FR,France +202109,7,10988,7938,14038,17,12,22,FR,France +202108,7,11281,8361,14201,17,13,21,FR,France +202107,7,13561,10315,16807,21,16,26,FR,France +202106,7,13401,9810,16992,20,15,25,FR,France +202105,7,12210,8988,15432,18,13,23,FR,France +202104,7,12026,8826,15226,18,13,23,FR,France 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+199101,7,15565,10271,20859,27,18,36,FR,France +199052,7,19375,13295,25455,34,23,45,FR,France +199051,7,19080,13807,24353,34,25,43,FR,France +199050,7,11079,6660,15498,20,12,28,FR,France +199049,7,1143,0,2610,2,0,5,FR,France diff --git a/module3/exo3/Simpson_paradox_A.Changenet.html b/module3/exo3/Simpson_paradox_A.Changenet.html new file mode 100644 index 0000000..1b07aca --- /dev/null +++ b/module3/exo3/Simpson_paradox_A.Changenet.html @@ -0,0 +1,445 @@ + + + + + + + + + + + + + + + +Exercice 3: Simson paradox + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + +

On commence par importer les données depuis le repertoire local:

+
data <- read.csv("~/Google Drive/Cours/mooc-rr/module3/exo3/module3_Practical_session_Subject6_smoking.csv")
+

Puis on représente dans un tableau le nombre total de femmes vivantes et décédées sur la période en fonction de leur habitude de tabagisme:

+
data.table <- table(data$Smoker, data$Status)
+data.table
+
##      
+##       Alive Dead
+##   No    502  230
+##   Yes   443  139
+

On calcule 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). L’argument margin permets de calculer les proportions relativement aux sommes des lignes (donc par statut de fumeuse ou non)

+
data.table.prop <- prop.table(data.table, margin=1)*100
+data.table.prop
+
##      
+##          Alive     Dead
+##   No  68.57923 31.42077
+##   Yes 76.11684 23.88316
+

Pour vérifier que notre calcul est bon, on ajoute la, porportion de vivant à la proportion de personne morte. On s’attends à avoir 100% dans les deux cas.

+
apply(data.table.prop,1,sum)
+
##  No Yes 
+## 100 100
+

On a bien 100% pour les deux catégories.

+

Maintenant on fait un graphique de la proportion de mort en fonction du statut de smoker:

+
dataf <- as.data.frame(data.table.prop)
+Mort_rate <- dataf[dataf$Var2=="Dead",]
+barplot(Mort_rate$Freq~Mort_rate$Var1,main = "Mortality rate VS smoking statuts",xlab = "Smoker",ylab = "proportion of dead")
+

+

On constate avec surprise que le taux de mortalité est plus elevé chez les non fumeuse que chez les fumeuse alors que l’on pourrait s’attendre à l’inverse.

+

On commence par importer les données depuis le repertoire local:

+
data <- read.csv("~/Google Drive/Cours/mooc-rr/module3/exo3/module3_Practical_session_Subject6_smoking.csv")
+

Dans un premier temps, on s’assure que l’âge minimum n’est pas en dessous de 18 ans.

+
summary(data$Age)
+
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
+##   18.00   31.30   44.80   47.36   60.60   89.90
+

C’est bien le cas, donc on peut ajouter une variable liée à la classe d’âge. On considérera ici les classes suivantes : 18-34 ans, 34-54 ans, 55-64 ans, plus de 65 ans

+
data$Ageclass <- cut(data$Age,breaks = c(18,34,54,64,Inf))
+

Puis on représente dans un tableau le nombre total de femmes vivantes et décédées sur la période en fonction de leur habitude de tabagisme, et de leur classe d’âge:

+
data.table <- table(data$Smoker, data$Status,data$Ageclass)
+data.table
+
## , ,  = (18,34]
+## 
+##      
+##       Alive Dead
+##   No    212    6
+##   Yes   172    5
+## 
+## , ,  = (34,54]
+## 
+##      
+##       Alive Dead
+##   No    180   19
+##   Yes   196   41
+## 
+## , ,  = (54,64]
+## 
+##      
+##       Alive Dead
+##   No     81   40
+##   Yes    64   51
+## 
+## , ,  = (64,Inf]
+## 
+##      
+##       Alive Dead
+##   No     28  165
+##   Yes     7   42
+

On calcule dans chaque groupe (fumeuses / non fumeuses) de chaque classe d’âge, le taux de mortalité (le rapport entre le nombre de femmes décédées dans un groupe et le nombre total de femmes dans ce groupe). L’argument margin permets de calculer les proportions relativement aux sommes des lignes (donc par statut de fumeuse ou non = 1), au sein de chaque catégorie d’âge (3).

+
data.table.prop <- prop.table(data.table, c(1,3))*100
+data.table.prop
+
## , ,  = (18,34]
+## 
+##      
+##           Alive      Dead
+##   No  97.247706  2.752294
+##   Yes 97.175141  2.824859
+## 
+## , ,  = (34,54]
+## 
+##      
+##           Alive      Dead
+##   No  90.452261  9.547739
+##   Yes 82.700422 17.299578
+## 
+## , ,  = (54,64]
+## 
+##      
+##           Alive      Dead
+##   No  66.942149 33.057851
+##   Yes 55.652174 44.347826
+## 
+## , ,  = (64,Inf]
+## 
+##      
+##           Alive      Dead
+##   No  14.507772 85.492228
+##   Yes 14.285714 85.714286
+

Maintenant on fait un graphique de la proportion de mort en fonction du statut de smoker:

+
dataf <- as.data.frame(data.table.prop)
+Mort_rate <- dataf[dataf$Var2=="Dead",]
+barplot(Mort_rate$Freq~Mort_rate$Var1+Mort_rate$Var3,beside=T,main = "Mortality rate VS smoking statuts in different age classes",xlab = "Age",ylab = "proportion of dead",legend=T,args.legend=list(title="Smoker"))
+

+

On constate que cette fois, la proportion de mort est plus élevé chez les fumeurs quelque soit la tranche d’âge. C’est paradoxal avec le résultat précédent, ou on observait un taux de mortalité plus faible chez les fumeurs.

+

Deux explications possibles: L’âge que nous n’avons pas pris en compte dans la première analyse est un paramètre important (et à priori il est important car on s’attends globalement a ce que les plus jeune meurt moins (fumeurs ou pas), et que les plus vieux meurent plus (fumeurs ou pas). Cet effet de sénescence est pris en compte dans le second temps.

+

Seconde explication: Le déséquilibre dans les effectifs (globaux, et au sein de chaque classes): * On remarque dans un premier temps le déséquilibre au sein

+
summary(as.factor(data$Smoker))
+
##  No Yes 
+## 732 582
+
summary(as.factor(data$Status))
+
## Alive  Dead 
+##   945   369
+
table(data$Smoker, data$Status)
+
##      
+##       Alive Dead
+##   No    502  230
+##   Yes   443  139
+

Les classes d’âge ot l’air homogènes en revanche classe d’âge en revanche:

+
summary(as.factor(data$Ageclass))
+
##  (18,34]  (34,54]  (54,64] (64,Inf]     NA's 
+##      395      436      236      242        5
+

Quand on regarde les statuts et conditions en fonction de ces tranches d’âge en revanche, on remarque un total déséquilibre:

+
data.table <- table(data$Smoker, data$Status,data$Ageclass)
+data.table
+
## , ,  = (18,34]
+## 
+##      
+##       Alive Dead
+##   No    212    6
+##   Yes   172    5
+## 
+## , ,  = (34,54]
+## 
+##      
+##       Alive Dead
+##   No    180   19
+##   Yes   196   41
+## 
+## , ,  = (54,64]
+## 
+##      
+##       Alive Dead
+##   No     81   40
+##   Yes    64   51
+## 
+## , ,  = (64,Inf]
+## 
+##      
+##       Alive Dead
+##   No     28  165
+##   Yes     7   42
+

En particulier, dans la tranche d’âge la plus élevé, les fumeurs sont compltement sous représentés en nombre par rapport aux non fumeurs. Comme c’est dans cette tranche dâge que l’on trouve le taux de mortalité le plus élevé (sénéscence) quelque soit le statut de fumeur ou non, c’est cette tranche d’âge qui biaise totalement nos résultats puisque même si la proportion de mort chez les fumeurs est aussi élevé que chez les non fumeurs, le nombre de mort lui est bien plus faible (42 contre 165), impactant la dynamique générale. Il est donc important de prendre en compte la variable âge.

+

Pour s’n rendre compte on peut aussi visualiser les données:

+
dataf <- as.data.frame(data.table)
+Mort_rate <- dataf[dataf$Var2=="Dead",]
+Live_rate <- dataf[dataf$Var2=="Alive",]
+
+par(mfrow=c(1,2))
+barplot(Mort_rate$Freq~Mort_rate$Var1+Mort_rate$Var3,beside=T,main = "Mortality count VS smoking statuts in different age classes",xlab = "Age",ylab = "Number of dead",legend=T,args.legend=list(title="Smoker","right"))
+barplot(Live_rate$Freq~Mort_rate$Var1+Mort_rate$Var3,beside=T,main = "Living count VS smoking statuts in different age classes",xlab = "Age",ylab = "Number of living",legend=T,args.legend=list(title="Smoker","topright"))
+

On voit ici le déséquilibre flagrant entre tranche d’âge pour les vivants comme pour les morts. Dans la tranche d’âge la plus élevée on voit clairement que les non fumeurs morts sont surreprésentés en nombre (alors qu’ils représentent une proportion semblables chez les fumeurs).

+
+

Modele binomial:

+

Dans un premier temps on recode la variable Status en “Death” avec 0 indiquant la survie, et 1 un évènement de mortalité

+
data$Death <- "0"
+data[data$Status=="Dead","Death"] <- 1
+data$Death <- as.numeric(data$Death)
+

Dans un second temps, on étudie 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.

+

Le plus simple est d’inclure un effet âge et un effet “fumeur” dans notre modèle:

+
M1 <- glm(Death ~ Smoker+Age, data = data, family = binomial(logit))
+

On regarde les sorties de notre modèle:

+
summary(M1)
+
## 
+## Call:
+## glm(formula = Death ~ Smoker + Age, family = binomial(logit), 
+##     data = data)
+## 
+## Deviance Residuals: 
+##     Min       1Q   Median       3Q      Max  
+## -2.3129  -0.5947  -0.2830   0.4570   2.9490  
+## 
+## Coefficients:
+##              Estimate Std. Error z value Pr(>|z|)    
+## (Intercept) -6.351874   0.360121 -17.638   <2e-16 ***
+## SmokerYes    0.278654   0.164981   1.689   0.0912 .  
+## Age          0.099837   0.005774  17.291   <2e-16 ***
+## ---
+## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+## 
+## (Dispersion parameter for binomial family taken to be 1)
+## 
+##     Null deviance: 1560.3  on 1313  degrees of freedom
+## Residual deviance: 1001.9  on 1311  degrees of freedom
+## AIC: 1007.9
+## 
+## Number of Fisher Scoring iterations: 5
+

On constate que l’effet $age est significatif mais que l’effet “smoker” ne l’est pas. Voyons de plus prêt:

+
cowplot::plot_grid(plotlist = plot(ggeffects::ggeffect(M1)))
+

On remarque que les fumeurs ont une probbailité plus grande de mort que les non fumeurs. On remarque aussi que la probabilité de mort augmente drastiquement avec l’âge (c’est la sénéscence).

+

On peut égalament regarder la même courbe pour les deux groupes. Pour se faire, on définit une plage d’âge pour laquelle on veut des prédictions, disons 18 à 100 ans, pour un groupe de fumeur et un groupe de non fumeurs. On transforme ces vecteurs en un data frame pour pouvoir faire nos prédictions:

+
Age <- seq(18,100,1)
+SmokerYes <- rep("Yes",length(Age))
+SmokerNo <- rep("No",length(Age))
+newdata <- as.data.frame(cbind(Age,SmokerYes,SmokerNo))
+

On prédit successivement les réponses (en terme de mortalité), pour le groupe des fumeur de 18 à 100 ans et celui des non fumeur de 18 à 100 ans. On précise que l’on veut aussi récupérer l’intervalle de confiance.

+
Pred.Yes <- predict(M1,list(Smoker=SmokerYes,Age=Age),se.fit = T,type="response")
+Pred.No <- predict(M1,list(Smoker=SmokerNo,Age=Age),se.fit = T,type="response")
+

On plot nos points observés. Puis on ajoute successivement le groupe des fumeurs avec l’intervalle de confiance, et celui des non fumeurs, avaec la légende adequat.

+
plot(data$Death~data$Age,pch = 16, xlab = "Age", ylab = "Death probability")
+polygon(x=c(newdata$Age,rev(newdata$Age)),y=c(Pred.Yes$fit-Pred.Yes$se.fit,rev(Pred.Yes$fit+Pred.Yes$se.fit)),col=adjustcolor("blue",alpha.f=0.1)
+,border=NA)
+lines(Pred.Yes$fit~newdata$Age,col="blue")
+
+polygon(x=c(newdata$Age,rev(newdata$Age)),y=c(Pred.No$fit-Pred.No$se.fit,rev(Pred.No$fit+Pred.No$se.fit)),col=adjustcolor("red",alpha.f=0.1)
+,border=NA)
+lines(Pred.No$fit~newdata$Age,col="red")
+
+legend("left",title="Smoker",c("Yes","No"),col=c("blue","red"),fill=c("blue","red"))
+

+

On constate bien qu’on prédit, à âge égale, moins de mortalité chez les non fumeurs que chez les fumeurs, quelquesoit l’âge.

+
+ + + + +
+ + + + + + + + + + + + + + + diff --git a/module3/exo3/exercice_fr.Rmd b/module3/exo3/exercice_fr.Rmd index 7eece5e..98c01c1 100644 --- a/module3/exo3/exercice_fr.Rmd +++ b/module3/exo3/exercice_fr.Rmd @@ -1,33 +1,257 @@ --- -title: "Votre titre" -author: "Votre nom" -date: "La date du jour" -output: html_document +title: 'Exercice 3: Simson paradox' +author: "A.Changenet" +date: "02/04/2021" +output: + pdf_document: + pandoc_args: --listings + toc: true + html_document: + toc: true + theme: journal +documentclass: article +classoption: a4paper +header-includes: +- \hypersetup{colorlinks=true,pagebackref=true} +- \lstset{breaklines=true,basicstyle=\ttfamily} --- - ```{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE) ``` -## Quelques explications -Ceci est un document R markdown que vous pouvez aisément exporter au format HTML, PDF, et MS Word. Pour plus de détails sur R Markdown consultez . +# Question 1 + +On commence par importer les données depuis le repertoire local: +```{r} +data <- +read.csv("~/Google Drive/Cours/mooc-rr/module3/exo3/module3_Practical_session_Subject6_smoking.csv") + +``` + +Puis on représente dans un tableau le nombre total de femmes vivantes et décédées sur la période en fonction de leur habitude de tabagisme: + +```{r} +data.table <- table(data$Smoker, data$Status) +data.table + +``` + +On calcule dans chaque groupe (fumeuses / non fumeuses) le taux de mortalité (le rapport entre le nombre de femmes décédées dans un groupe et le nombre total de femmes dans ce groupe). L'argument margin permets de calculer les proportions relativement aux sommes des lignes (donc par statut de fumeuse ou non). Multiplier par 100 permets d'avoir un pourcentage. +```{r} +data.table.prop <- prop.table(data.table, margin=1)*100 +data.table.prop +``` + +Pour vérifier que notre calcul est bon, on ajoute la, porportion de vivant à la proportion de personne morte. On s'attends à avoir 100% dans les deux cas. + +```{r} +apply(data.table.prop,1,sum) +``` +On a bien 100% pour les deux catégories. + + +Maintenant on fait un graphique de la proportion de mort en fonction du statut de smoker: + +```{r} +dataf <- as.data.frame(data.table.prop) +Mort_rate <- dataf[dataf$Var2=="Dead",] +barplot(Mort_rate$Freq~Mort_rate$Var1,main = "Mortality rate VS smoking statuts", + xlab = "Smoker",ylab = "proportion of dead") +``` + +On constate avec surprise que le taux de mortalité est plus elevé chez les non fumeuse que chez les fumeuse alors que l'on pourrait s'attendre à l'inverse. + + +# Question 2 + +On commence par importer les données depuis le repertoire local: +```{r} +data <- +read.csv("~/Google Drive/Cours/mooc-rr/module3/exo3/module3_Practical_session_Subject6_smoking.csv") + +``` + +Dans un premier temps, on s'assure que l'âge minimum n'est pas en dessous de 18 ans. +```{r} +summary(data$Age) +``` + +C'est bien le cas (min = 18) donc on peut ajouter une variable liée à la classe d'âge. On considérera ici les classes suivantes : 18-34 ans, 34-54 ans, 55-64 ans, plus de 65 ans + +```{r} +data$Ageclass <- cut(data$Age,breaks = c(18,34,54,64,Inf)) +``` + + +Puis on représente dans un tableau le nombre total de femmes vivantes et décédées sur la période en fonction de leur habitude de tabagisme, et de leur classe d'âge: +```{r} +data.table <- table(data$Smoker, data$Status,data$Ageclass) +data.table +``` + + +On calcule dans chaque groupe (fumeuses / non fumeuses) de chaque classe d'âge, le taux de mortalité (le rapport entre le nombre de femmes décédées dans un groupe et le nombre total de femmes dans ce groupe). L'argument margin permets de calculer les proportions relativement aux sommes des lignes (donc par statut de fumeuse ou non = 1), au sein de chaque catégorie d'âge (3). -Lorsque vous cliquerez sur le bouton **Knit** ce document sera compilé afin de ré-exécuter le code R et d'inclure les résultats dans un document final. Comme nous vous l'avons montré dans la vidéo, on inclue du code R de la façon suivante: +```{r} +data.table.prop <- prop.table(data.table, c(1,3))*100 +data.table.prop +``` + + +Maintenant on fait un graphique de la proportion de mort en fonction du statut de smoker: + +```{r} +dataf <- as.data.frame(data.table.prop) +Mort_rate <- dataf[dataf$Var2=="Dead",] +barplot(Mort_rate$Freq~Mort_rate$Var1+Mort_rate$Var3,beside=T, + main = "Mortality rate VS smoking statuts in different age classes", + xlab = "Age",ylab = "proportion of dead",legend=T,args.legend=list(title="Smoker")) -```{r cars} -summary(cars) ``` -Et on peut aussi aisément inclure des figures. Par exemple: +On constate que cette fois, la proportion de mort est plus élevé chez les fumeurs quelque soit la tranche d'âge. +C'est paradoxal avec le résultat précédent, ou on observait un taux de mortalité plus faible chez les fumeurs. C'est ce que l'on appelle le [paradoxe de Simpson](https://fr.wikipedia.org/wiki/Paradoxe_de_Simpson). + +Deux explications possibles: +* L'âge que nous n'avons pas pris en compte dans la première analyse est un paramètre important (et à priori il est important car on s'attends globalement a ce que les plus jeune meurt moins (fumeurs ou pas), et que les plus vieux meurent plus (fumeurs ou pas). Cet effet de sénescence est pris en compte dans le second temps. + +Seconde explication: +* Le déséquilibre dans les effectifs (globaux, et au sein de chaque classes) pourrait être responsable de ces conclusions trompeuses. + + +## Visualisation graphique: + + +```{r} +summary(as.factor(data$Smoker)) +summary(as.factor(data$Status)) +table(data$Smoker, data$Status) -```{r pressure, echo=FALSE} -plot(pressure) ``` +* On remarque dans un premier temps ci dessus, le déséquilibre au sein des variables qualitatives "Smoker" et "Status". En revanche: + +```{r} +summary(as.factor(data$Ageclass)) -Vous remarquerez le paramètre `echo = FALSE` qui indique que le code ne doit pas apparaître dans la version finale du document. Nous vous recommandons dans le cadre de ce MOOC de ne pas utiliser ce paramètre car l'objectif est que vos analyses de données soient parfaitement transparentes pour être reproductibles. +``` +Les classes d'âge ont l'air homogènes. Poursuivons en regardant les effectifs en fonction de plusieurs variables: + +```{r} +data.table <- table(data$Smoker, data$Status,data$Ageclass) +data.table +``` +Quand on regarde les statuts et conditions en fonction de ces tranches d'âge en revanche, on remarque un total déséquilibre. + +En particulier, dans la tranche d'âge la plus élevée, les fumeurs sont compltement sous représentés en nombre par rapport aux non fumeurs. +Comme c'est dans cette tranche dâge que l'on trouve le taux de mortalité le plus élevé (sénéscence) quelque soit le statut de fumeur ou non, c'est cette tranche d'âge qui biaise totalement nos résultats puisque même si la proportion de mort chez les fumeurs est aussi élevé que chez les non fumeurs, le **nombre** de mort lui est bien plus faible (42 contre 165), impactant fortement nos conclusions générale sur la dynamique globale qui ne reposent que sur les proportions totale ! +Il est donc important de prendre en compte la variable âge. + + +* Pour s'en rendre compte on peut aussi visualiser les données: + +```{r,fig.height=7} +dataf <- as.data.frame(data.table) +Mort_rate <- dataf[dataf$Var2=="Dead",] +Live_rate <- dataf[dataf$Var2=="Alive",] + +par(mfrow=c(1,2)) +barplot(Mort_rate$Freq~Mort_rate$Var1+Mort_rate$Var3,beside=T, + main = "Mortality count\n VS smoking statuts\n in different age classes", + xlab = "Age",ylab = "Number of dead",legend=T, + args.legend=list(x="topleft",title="Smoker")) +barplot(Live_rate$Freq~Mort_rate$Var1+Mort_rate$Var3,beside=T, + main = "Living count\n VS smoking statuts\n in different age classes", + xlab = "Age",ylab = "Number of living",legend=T, + args.legend=list(title="Smoker","topright")) +``` +On voit ici le déséquilibre flagrant entre tranche d'âge pour les vivants comme pour les morts. Dans la tranche d'âge la plus élevée on voit clairement que les non fumeurs morts sont surreprésentés en nombre (alors qu'ils représentent une proportion semblables chez les fumeurs). + + +# Question 3: modèle binomial: + +Dans un premier temps on recode la variable "Status" en "Death" avec 0 indiquant la survie, et 1 un évènement de mortalité +```{r} +data$Death <- "0" +data[data$Status=="Dead","Death"] <- 1 +data$Death <- as.numeric(data$Death) +``` + + +Dans un second temps, on étudie 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. + +Le plus simple est d'inclure un effet âge et un effet "fumeur" dans notre modèle: + +```{r} +M1 <- glm(Death ~ Smoker+Age, data = data, family = binomial(logit)) +``` + + +On regarde les sorties de notre modèle: +```{r} +summary(M1) +``` +On constate que l'effet $age est significatif mais que l'effet "smoker" ne l'est pas. Voyons de plus prêt à l'aide des packages 'cowplot' et 'ggeffects' que l'on pourra installer grace aux commandes: `install.packages(c("cowplot","ggeffects"))` + + +```{r} +cowplot::plot_grid(plotlist = plot(ggeffects::ggeffect(M1))) +``` +On remarque que les fumeurs ont une probbailité plus grande de mort que les non fumeurs. On remarque aussi que la probabilité de mort augmente drastiquement avec l'âge (c'est la sénéscence). + + +On peut égalament regarder la même courbe pour les deux groupes. +Pour se faire, on définit une plage d'âge pour laquelle on veut des prédictions, disons 18 à 100 ans, pour un groupe de fumeur et un groupe de non fumeurs. On transforme ces vecteurs en un data frame pour pouvoir faire nos prédictions: + +```{r} +Age <- seq(18,100,1) +SmokerYes <- rep("Yes",length(Age)) +SmokerNo <- rep("No",length(Age)) +newdata <- as.data.frame(cbind(Age,SmokerYes,SmokerNo)) + +``` + +Ici on vérifie qu'on a bien la structure attendue: +```{r} +newdata +``` + +On prédit successivement les réponses (en terme de mortalité), pour le groupe des fumeurs de 18 à 100 ans et celui des non fumeur de 18 à 100 ans. On précise que l'on veut aussi récupérer l'intervalle de confiance grace a l'argument `se.fit = T` et on récupère le tout dans deux nouveaaux objects. +```{r} +Pred.Yes <- predict(M1,list(Smoker=SmokerYes,Age=Age),se.fit = T,type="response") +Pred.No <- predict(M1,list(Smoker=SmokerNo,Age=Age),se.fit = T,type="response") +``` + + +On représente nos points observés d'abord. Puis on ajoute successivement le groupe des fumeurs avec l'intervalle de confiance, et celui des non fumeurs, avec la légende adequat. +La commande `lines`permet d'ajouter la ligne que l'on souhaite (ici la réponse en terme de mortalité des fumeurs ou des non fumeurs). Dans un second temps on ajoute les intervalles de confiance grace à la commande `polygon`. + +```{r} +plot(data$Death~data$Age,pch = 16, xlab = "Age", ylab = "Death probability") +polygon(x=c(newdata$Age,rev(newdata$Age)), + y=c(Pred.Yes$fit-Pred.Yes$se.fit, + rev(Pred.Yes$fit+Pred.Yes$se.fit)), + col=adjustcolor("blue",alpha.f=0.1), + border=NA) +lines(Pred.Yes$fit~newdata$Age,col="blue") + +polygon(x=c(newdata$Age,rev(newdata$Age)), + y=c(Pred.No$fit-Pred.No$se.fit, + rev(Pred.No$fit+Pred.No$se.fit)), + col=adjustcolor("red",alpha.f=0.1), + border=NA) +lines(Pred.No$fit~newdata$Age,col="red") + +legend("left",title="Smoker",c("Yes","No"),col=c("blue","red"),fill=c("blue","red")) +``` + +On constate bien qu'on prédit, à âge égale, moins de mortalité chez les non fumeurs que chez les fumeurs, quelquesoit l'âge. Le tabac semble donc nocif, au regard de ces données. + + +Toutes les analyses ont été réalisé sur R +```{r} +sessionInfo() +``` -Comme les résultats ne sont pas stockés dans les fichiers Rmd, pour faciliter la relecture de vos analyses par d'autres personnes, vous aurez donc intérêt à générer un HTML ou un PDF et à le commiter. -Maintenant, à vous de jouer! Vous pouvez effacer toutes ces informations et les remplacer par votre document computationnel. diff --git a/module3/exo3/exercice_fr.html b/module3/exo3/exercice_fr.html new file mode 100644 index 0000000..b13e662 --- /dev/null +++ b/module3/exo3/exercice_fr.html @@ -0,0 +1,601 @@ + + + + + + + + + + + + + + + +Exercice 3: Simson paradox + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + +
+

Question 1

+

On commence par importer les données depuis le repertoire local:

+
data <- 
+read.csv("~/Google Drive/Cours/mooc-rr/module3/exo3/module3_Practical_session_Subject6_smoking.csv")
+

Puis on représente dans un tableau le nombre total de femmes vivantes et décédées sur la période en fonction de leur habitude de tabagisme:

+
data.table <- table(data$Smoker, data$Status)
+data.table
+
##      
+##       Alive Dead
+##   No    502  230
+##   Yes   443  139
+

On calcule 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). L’argument margin permets de calculer les proportions relativement aux sommes des lignes (donc par statut de fumeuse ou non). Multiplier par 100 permets d’avoir un pourcentage.

+
data.table.prop <- prop.table(data.table, margin=1)*100
+data.table.prop
+
##      
+##          Alive     Dead
+##   No  68.57923 31.42077
+##   Yes 76.11684 23.88316
+

Pour vérifier que notre calcul est bon, on ajoute la, porportion de vivant à la proportion de personne morte. On s’attends à avoir 100% dans les deux cas.

+
apply(data.table.prop,1,sum)
+
##  No Yes 
+## 100 100
+

On a bien 100% pour les deux catégories.

+

Maintenant on fait un graphique de la proportion de mort en fonction du statut de smoker:

+
dataf <- as.data.frame(data.table.prop)
+Mort_rate <- dataf[dataf$Var2=="Dead",]
+barplot(Mort_rate$Freq~Mort_rate$Var1,main = "Mortality rate VS smoking statuts",
+        xlab = "Smoker",ylab = "proportion of dead")
+

+

On constate avec surprise que le taux de mortalité est plus elevé chez les non fumeuse que chez les fumeuse alors que l’on pourrait s’attendre à l’inverse.

+
+
+

Question 2

+

On commence par importer les données depuis le repertoire local:

+
data <- 
+read.csv("~/Google Drive/Cours/mooc-rr/module3/exo3/module3_Practical_session_Subject6_smoking.csv")
+

Dans un premier temps, on s’assure que l’âge minimum n’est pas en dessous de 18 ans.

+
summary(data$Age)
+
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
+##   18.00   31.30   44.80   47.36   60.60   89.90
+

C’est bien le cas (min = 18) donc on peut ajouter une variable liée à la classe d’âge. On considérera ici les classes suivantes : 18-34 ans, 34-54 ans, 55-64 ans, plus de 65 ans

+
data$Ageclass <- cut(data$Age,breaks = c(18,34,54,64,Inf))
+

Puis on représente dans un tableau le nombre total de femmes vivantes et décédées sur la période en fonction de leur habitude de tabagisme, et de leur classe d’âge:

+
data.table <- table(data$Smoker, data$Status,data$Ageclass)
+data.table
+
## , ,  = (18,34]
+## 
+##      
+##       Alive Dead
+##   No    212    6
+##   Yes   172    5
+## 
+## , ,  = (34,54]
+## 
+##      
+##       Alive Dead
+##   No    180   19
+##   Yes   196   41
+## 
+## , ,  = (54,64]
+## 
+##      
+##       Alive Dead
+##   No     81   40
+##   Yes    64   51
+## 
+## , ,  = (64,Inf]
+## 
+##      
+##       Alive Dead
+##   No     28  165
+##   Yes     7   42
+

On calcule dans chaque groupe (fumeuses / non fumeuses) de chaque classe d’âge, le taux de mortalité (le rapport entre le nombre de femmes décédées dans un groupe et le nombre total de femmes dans ce groupe). L’argument margin permets de calculer les proportions relativement aux sommes des lignes (donc par statut de fumeuse ou non = 1), au sein de chaque catégorie d’âge (3).

+
data.table.prop <- prop.table(data.table, c(1,3))*100
+data.table.prop
+
## , ,  = (18,34]
+## 
+##      
+##           Alive      Dead
+##   No  97.247706  2.752294
+##   Yes 97.175141  2.824859
+## 
+## , ,  = (34,54]
+## 
+##      
+##           Alive      Dead
+##   No  90.452261  9.547739
+##   Yes 82.700422 17.299578
+## 
+## , ,  = (54,64]
+## 
+##      
+##           Alive      Dead
+##   No  66.942149 33.057851
+##   Yes 55.652174 44.347826
+## 
+## , ,  = (64,Inf]
+## 
+##      
+##           Alive      Dead
+##   No  14.507772 85.492228
+##   Yes 14.285714 85.714286
+

Maintenant on fait un graphique de la proportion de mort en fonction du statut de smoker:

+
dataf <- as.data.frame(data.table.prop)
+Mort_rate <- dataf[dataf$Var2=="Dead",]
+barplot(Mort_rate$Freq~Mort_rate$Var1+Mort_rate$Var3,beside=T,
+        main = "Mortality rate VS smoking statuts in different age classes",
+        xlab = "Age",ylab = "proportion of dead",legend=T,args.legend=list(title="Smoker"))
+

+

On constate que cette fois, la proportion de mort est plus élevé chez les fumeurs quelque soit la tranche d’âge. C’est paradoxal avec le résultat précédent, ou on observait un taux de mortalité plus faible chez les fumeurs. C’est ce que l’on appelle le paradoxe de Simpson.

+

Deux explications possibles: * L’âge que nous n’avons pas pris en compte dans la première analyse est un paramètre important (et à priori il est important car on s’attends globalement a ce que les plus jeune meurt moins (fumeurs ou pas), et que les plus vieux meurent plus (fumeurs ou pas). Cet effet de sénescence est pris en compte dans le second temps.

+

Seconde explication: * Le déséquilibre dans les effectifs (globaux, et au sein de chaque classes) pourrait être responsable de ces conclusions trompeuses.

+
+

Visualisation graphique:

+
summary(as.factor(data$Smoker))
+
##  No Yes 
+## 732 582
+
summary(as.factor(data$Status))
+
## Alive  Dead 
+##   945   369
+
table(data$Smoker, data$Status)
+
##      
+##       Alive Dead
+##   No    502  230
+##   Yes   443  139
+
    +
  • On remarque dans un premier temps ci dessus, le déséquilibre au sein des variables qualitatives “Smoker” et “Status”. En revanche:
    • +
+
summary(as.factor(data$Ageclass))
+
##  (18,34]  (34,54]  (54,64] (64,Inf]     NA's 
+##      395      436      236      242        5
+

Les classes d’âge ont l’air homogènes. Poursuivons en regardant les effectifs en fonction de plusieurs variables:

+
data.table <- table(data$Smoker, data$Status,data$Ageclass)
+data.table
+
## , ,  = (18,34]
+## 
+##      
+##       Alive Dead
+##   No    212    6
+##   Yes   172    5
+## 
+## , ,  = (34,54]
+## 
+##      
+##       Alive Dead
+##   No    180   19
+##   Yes   196   41
+## 
+## , ,  = (54,64]
+## 
+##      
+##       Alive Dead
+##   No     81   40
+##   Yes    64   51
+## 
+## , ,  = (64,Inf]
+## 
+##      
+##       Alive Dead
+##   No     28  165
+##   Yes     7   42
+

Quand on regarde les statuts et conditions en fonction de ces tranches d’âge en revanche, on remarque un total déséquilibre.

+

En particulier, dans la tranche d’âge la plus élevée, les fumeurs sont compltement sous représentés en nombre par rapport aux non fumeurs. Comme c’est dans cette tranche dâge que l’on trouve le taux de mortalité le plus élevé (sénéscence) quelque soit le statut de fumeur ou non, c’est cette tranche d’âge qui biaise totalement nos résultats puisque même si la proportion de mort chez les fumeurs est aussi élevé que chez les non fumeurs, le nombre de mort lui est bien plus faible (42 contre 165), impactant fortement nos conclusions générale sur la dynamique globale qui ne reposent que sur les proportions totale ! Il est donc important de prendre en compte la variable âge.

+
    +
  • Pour s’en rendre compte on peut aussi visualiser les données:
    • +
+
dataf <- as.data.frame(data.table)
+Mort_rate <- dataf[dataf$Var2=="Dead",]
+Live_rate <- dataf[dataf$Var2=="Alive",]
+
+par(mfrow=c(1,2))
+barplot(Mort_rate$Freq~Mort_rate$Var1+Mort_rate$Var3,beside=T,
+        main = "Mortality count\n VS smoking statuts\n in different age classes",
+        xlab = "Age",ylab = "Number of dead",legend=T,
+        args.legend=list(x="topleft",title="Smoker"))
+barplot(Live_rate$Freq~Mort_rate$Var1+Mort_rate$Var3,beside=T,
+        main = "Living count\n VS smoking statuts\n in different age classes",
+        xlab = "Age",ylab = "Number of living",legend=T,
+        args.legend=list(title="Smoker","topright"))
+

On voit ici le déséquilibre flagrant entre tranche d’âge pour les vivants comme pour les morts. Dans la tranche d’âge la plus élevée on voit clairement que les non fumeurs morts sont surreprésentés en nombre (alors qu’ils représentent une proportion semblables chez les fumeurs).

+
+
+
+

Question 3: modèle binomial:

+

Dans un premier temps on recode la variable “Status” en “Death” avec 0 indiquant la survie, et 1 un évènement de mortalité

+
data$Death <- "0"
+data[data$Status=="Dead","Death"] <- 1
+data$Death <- as.numeric(data$Death)
+

Dans un second temps, on étudie 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.

+

Le plus simple est d’inclure un effet âge et un effet “fumeur” dans notre modèle:

+
M1 <- glm(Death ~ Smoker+Age, data = data, family = binomial(logit))
+

On regarde les sorties de notre modèle:

+
summary(M1)
+
## 
+## Call:
+## glm(formula = Death ~ Smoker + Age, family = binomial(logit), 
+##     data = data)
+## 
+## Deviance Residuals: 
+##     Min       1Q   Median       3Q      Max  
+## -2.3129  -0.5947  -0.2830   0.4570   2.9490  
+## 
+## Coefficients:
+##              Estimate Std. Error z value Pr(>|z|)    
+## (Intercept) -6.351874   0.360121 -17.638   <2e-16 ***
+## SmokerYes    0.278654   0.164981   1.689   0.0912 .  
+## Age          0.099837   0.005774  17.291   <2e-16 ***
+## ---
+## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+## 
+## (Dispersion parameter for binomial family taken to be 1)
+## 
+##     Null deviance: 1560.3  on 1313  degrees of freedom
+## Residual deviance: 1001.9  on 1311  degrees of freedom
+## AIC: 1007.9
+## 
+## Number of Fisher Scoring iterations: 5
+

On constate que l’effet $age est significatif mais que l’effet “smoker” ne l’est pas. Voyons de plus prêt à l’aide des packages ‘cowplot’ et ‘ggeffects’ que l’on pourra installer grace aux commandes: install.packages(c("cowplot","ggeffects"))

+
cowplot::plot_grid(plotlist = plot(ggeffects::ggeffect(M1)))
+

On remarque que les fumeurs ont une probbailité plus grande de mort que les non fumeurs. On remarque aussi que la probabilité de mort augmente drastiquement avec l’âge (c’est la sénéscence).

+

On peut égalament regarder la même courbe pour les deux groupes. Pour se faire, on définit une plage d’âge pour laquelle on veut des prédictions, disons 18 à 100 ans, pour un groupe de fumeur et un groupe de non fumeurs. On transforme ces vecteurs en un data frame pour pouvoir faire nos prédictions:

+
Age <- seq(18,100,1)
+SmokerYes <- rep("Yes",length(Age))
+SmokerNo <- rep("No",length(Age))
+newdata <- as.data.frame(cbind(Age,SmokerYes,SmokerNo))
+

Ici on vérifie qu’on a bien la structure attendue:

+
newdata
+
##    Age SmokerYes SmokerNo
+## 1   18       Yes       No
+## 2   19       Yes       No
+## 3   20       Yes       No
+## 4   21       Yes       No
+## 5   22       Yes       No
+## 6   23       Yes       No
+## 7   24       Yes       No
+## 8   25       Yes       No
+## 9   26       Yes       No
+## 10  27       Yes       No
+## 11  28       Yes       No
+## 12  29       Yes       No
+## 13  30       Yes       No
+## 14  31       Yes       No
+## 15  32       Yes       No
+## 16  33       Yes       No
+## 17  34       Yes       No
+## 18  35       Yes       No
+## 19  36       Yes       No
+## 20  37       Yes       No
+## 21  38       Yes       No
+## 22  39       Yes       No
+## 23  40       Yes       No
+## 24  41       Yes       No
+## 25  42       Yes       No
+## 26  43       Yes       No
+## 27  44       Yes       No
+## 28  45       Yes       No
+## 29  46       Yes       No
+## 30  47       Yes       No
+## 31  48       Yes       No
+## 32  49       Yes       No
+## 33  50       Yes       No
+## 34  51       Yes       No
+## 35  52       Yes       No
+## 36  53       Yes       No
+## 37  54       Yes       No
+## 38  55       Yes       No
+## 39  56       Yes       No
+## 40  57       Yes       No
+## 41  58       Yes       No
+## 42  59       Yes       No
+## 43  60       Yes       No
+## 44  61       Yes       No
+## 45  62       Yes       No
+## 46  63       Yes       No
+## 47  64       Yes       No
+## 48  65       Yes       No
+## 49  66       Yes       No
+## 50  67       Yes       No
+## 51  68       Yes       No
+## 52  69       Yes       No
+## 53  70       Yes       No
+## 54  71       Yes       No
+## 55  72       Yes       No
+## 56  73       Yes       No
+## 57  74       Yes       No
+## 58  75       Yes       No
+## 59  76       Yes       No
+## 60  77       Yes       No
+## 61  78       Yes       No
+## 62  79       Yes       No
+## 63  80       Yes       No
+## 64  81       Yes       No
+## 65  82       Yes       No
+## 66  83       Yes       No
+## 67  84       Yes       No
+## 68  85       Yes       No
+## 69  86       Yes       No
+## 70  87       Yes       No
+## 71  88       Yes       No
+## 72  89       Yes       No
+## 73  90       Yes       No
+## 74  91       Yes       No
+## 75  92       Yes       No
+## 76  93       Yes       No
+## 77  94       Yes       No
+## 78  95       Yes       No
+## 79  96       Yes       No
+## 80  97       Yes       No
+## 81  98       Yes       No
+## 82  99       Yes       No
+## 83 100       Yes       No
+

On prédit successivement les réponses (en terme de mortalité), pour le groupe des fumeurs de 18 à 100 ans et celui des non fumeur de 18 à 100 ans. On précise que l’on veut aussi récupérer l’intervalle de confiance grace a l’argument se.fit = T et on récupère le tout dans deux nouveaaux objects.

+
Pred.Yes <- predict(M1,list(Smoker=SmokerYes,Age=Age),se.fit = T,type="response")
+Pred.No <- predict(M1,list(Smoker=SmokerNo,Age=Age),se.fit = T,type="response")
+

On représente nos points observés d’abord. Puis on ajoute successivement le groupe des fumeurs avec l’intervalle de confiance, et celui des non fumeurs, avec la légende adequat. La commande linespermet d’ajouter la ligne que l’on souhaite (ici la réponse en terme de mortalité des fumeurs ou des non fumeurs). Dans un second temps on ajoute les intervalles de confiance grace à la commande polygon.

+
plot(data$Death~data$Age,pch = 16, xlab = "Age", ylab = "Death probability")
+polygon(x=c(newdata$Age,rev(newdata$Age)),
+        y=c(Pred.Yes$fit-Pred.Yes$se.fit,
+            rev(Pred.Yes$fit+Pred.Yes$se.fit)),
+        col=adjustcolor("blue",alpha.f=0.1),
+        border=NA)
+lines(Pred.Yes$fit~newdata$Age,col="blue")
+
+polygon(x=c(newdata$Age,rev(newdata$Age)),
+        y=c(Pred.No$fit-Pred.No$se.fit,
+            rev(Pred.No$fit+Pred.No$se.fit)),
+        col=adjustcolor("red",alpha.f=0.1),
+        border=NA)
+lines(Pred.No$fit~newdata$Age,col="red")
+
+legend("left",title="Smoker",c("Yes","No"),col=c("blue","red"),fill=c("blue","red"))
+

+

On constate bien qu’on prédit, à âge égale, moins de mortalité chez les non fumeurs que chez les fumeurs, quelquesoit l’âge. Le tabac semble donc nocif, au regard de ces données.

+

Toutes les analyses ont été réalisé sur R

+
sessionInfo()
+
## R version 4.0.4 (2021-02-15)
+## Platform: x86_64-apple-darwin17.0 (64-bit)
+## Running under: macOS High Sierra 10.13.6
+## 
+## Matrix products: default
+## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
+## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
+## 
+## locale:
+## [1] fr_FR.UTF-8/fr_FR.UTF-8/fr_FR.UTF-8/C/fr_FR.UTF-8/fr_FR.UTF-8
+## 
+## attached base packages:
+## [1] stats     graphics  grDevices utils     datasets  methods   base     
+## 
+## loaded via a namespace (and not attached):
+##  [1] statmod_1.4.35    tidyselect_1.1.0  sjlabelled_1.1.7  xfun_0.22        
+##  [5] bslib_0.2.4       mitools_2.4       purrr_0.3.4       splines_4.0.4    
+##  [9] lattice_0.20-41   carData_3.0-4     colorspace_2.0-0  vctrs_0.3.7      
+## [13] generics_0.1.0    htmltools_0.5.1.1 yaml_2.2.1        survival_3.2-10  
+## [17] utf8_1.2.1        rlang_0.4.10      jquerylib_0.1.3   pillar_1.5.1     
+## [21] nloptr_1.2.2.2    glue_1.4.2        DBI_1.1.1         lifecycle_1.0.0  
+## [25] stringr_1.4.0     effects_4.2-0     munsell_0.5.0     gtable_0.3.0     
+## [29] evaluate_0.14     labeling_0.4.2    knitr_1.31        fansi_0.4.2      
+## [33] highr_0.8         Rcpp_1.0.6        scales_1.1.1      ggeffects_1.0.2  
+## [37] jsonlite_1.7.2    farver_2.1.0      lme4_1.1-26       ggplot2_3.3.3    
+## [41] digest_0.6.27     stringi_1.5.3     insight_0.13.1    dplyr_1.0.5      
+## [45] survey_4.0        cowplot_1.1.1     grid_4.0.4        tools_4.0.4      
+## [49] magrittr_2.0.1    sass_0.3.1        tibble_3.1.0      crayon_1.4.1     
+## [53] pkgconfig_2.0.3   ellipsis_0.3.1    MASS_7.3-53.1     Matrix_1.3-2     
+## [57] estimability_1.3  assertthat_0.2.1  minqa_1.2.4       rmarkdown_2.7    
+## [61] R6_2.5.0          boot_1.3-27       nnet_7.3-15       nlme_3.1-152     
+## [65] compiler_4.0.4
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