Commit de l'exercice 3 du module 3

module3/exo3/exercice_fr.Rmd

 ---
-title: "Exercice paradox de Simpson"
+title: "Exercice paradoxe de Simpson"
 author: "Hugues de Courson"
 date: "La date du jour"
-output: pdf_document
+output:
+  pdf_document:
+    df_print: paged
 ---
 
 
@@ -12,10 +14,12 @@ knitr::opts_chunk$set(echo = TRUE)
 
 ### Début: chargement des packages pouvant être utiles
 
-```{r package, include=F, echo=FALSE}
+```{r package,message=F, warning=F}
 library(epiDisplay)
 library(epiR)
 library(prettyR)
+library(knitr)
+library(kableExtra)
 ```
 
 
@@ -38,5 +42,313 @@ str(data)
 
 Tout semble ok.
 
+### Mission 1
 
+## Creation du tableau :
 
+L'objectif est de créer un tableau avec le nombre total de femme vivantes ou décédées sur la période en fonction des habitudes de tabagisme. 
+
+```{r tableau 1}
+vivantes_fum <- sum(data$Status[data$Smoker=="Yes"]=="Alive")
+vivantes_nonfum <- sum(data$Status[data$Smoker=="No"]=="Alive")
+
+decedees_fum <- sum(data$Status[data$Smoker=="Yes"]=="Dead")
+decedees_nonfum  <- sum(data$Status[data$Smoker=="No"]=="Dead")
+tab_1 <- data.frame(Vivantes = c(vivantes_fum,vivantes_nonfum), Decedees = c(decedees_fum,decedees_nonfum), row.names = c("Fumeuses","Non fumeuses"))
+kable(tab_1,align = 'l')
+```
+
+
+## Calcul des taux de mortalité :
+# Creation d'un tableau de contigence
+```{r taux mortalite}
+
+mort_fum <- sum(data$Status[data$Smoker=="Yes"]=="Dead")
+mort_nonfum <- sum(data$Status[data$Smoker=="No"]=="Dead")
+vivant_fum <-sum(data$Status[data$Smoker=="Yes"]=="Alive")
+vivant_nonfum <- sum(data$Status[data$Smoker=="No"]=="Alive")
+nb_fum <- sum(data$Smoker=="Yes")
+nb_nonfum <- sum(data$Smoker=="No")
+nb_viv <- sum(data$Status=="Alive")
+nb_deces <-sum(data$Status=="Dead")
+tot <- sum(data$Status=="Alive"|data$Status=="Dead")
+
+tab_2 <- data.frame(cbind(rbind(mort_fum, vivant_fum, nb_fum)), rbind(mort_nonfum,vivant_nonfum, nb_nonfum),rbind(nb_deces,nb_viv,tot))
+row.names(tab_2) <- c("Decedees", "Vivantes","Total")
+names(tab_2) <- c("Fumeuses", "Non Fumeuses", "Total")
+
+kable(tab_2,align = "c")
+```
+
+# Representation graphique
+Ceci passe par la création d'un tableau avec les pourcentages de mortalité
+```{r representation graphique taux de mortalite}
+tab_3 <- data.frame(cbind(rbind((sum(data$Status[data$Smoker=="Yes"]=="Dead")/sum(data$Smoker=="Yes"))*100,(sum(data$Status[data$Smoker=="Yes"]=="Alive")/sum(data$Smoker=="Yes"))*100)), 
+                    rbind((sum(data$Status[data$Smoker=="No"]=="Dead")/sum(data$Smoker=="No"))*100,(sum(data$Status[data$Smoker=="No"]=="Alive")/sum(data$Smoker=="No"))*100))
+                                
+names(tab_3) <- c("Fumeuses", "Non fumeuses")
+row.names(tab_3) <- c("Decedees", "Vivantes")
+
+kable(tab_3, align = "c")
+
+barplot(as.matrix(tab_3), col = c("black","gray"), space = 1.5,width = 0.5) 
+legend("center",xpd=NA, legend = c("Decedees", "Vivantes"), fill = c("black","gray"))
+```
+
+# Calcul des intervalles de confiance des proportions
+```{r intervalle de confiance}
+
+#  creation de la fonction :
+
+IC = function(x) {
+  y <- x/100
+  inf = y-(1.96*sqrt((y*(1-y))/n))
+  sup = y+(1.96*sqrt((y*(1-y))/n))
+  print(c(x,inf*100,sup*100))
+}
+
+```
+Chez les fumeuses : 
+```{r IC fumeuses}
+
+x <- tab_3[1,1]
+n <- as.numeric(tab_2[3,1])
+
+IC(x)
+```
+Chez les non fumeuses :
+```{r IC non fumeuses}
+x <- tab_3[1,2]
+n <- tab_2[3,2]
+
+IC(x)
+
+```
+
+Au vu de l'ensemble des résultats, on fait le constat suivant :
+  Il semblerait que le taux de mortalité est plus important chez les non-fumeuses...
+  Ceci va à l'encontre des connaissances sur le tabac, on pourrait s'attendre à ce que les non fumeuses décèdent moins. 
+  
+### Mission 2
+
+Il s'agit de reprendre les données, cette fois-ci en fonction de la classe d'âge
+
+## Première étape : création de la variable classe d'âge
+
+```{r var classe dage}
+
+data$cl_age <- as.factor(ifelse(data$Age>=18&data$Age<35,"[18;34]",
+                                ifelse(data$Age>=35&data$Age<54,"[35;54]",
+                                       ifelse(data$Age>=55&data$Age<65,"[55;64]","[65;["))))
+
+tab1(data$cl_age)
+
+```
+
+## Deuxième étape on refait les tableaux de contingence mais cette fois-ci de manière plus optimisée
+
+Pour cela on utilise [ce lien](http://olivier.godechot.free.fr/hoparticle.php?id_art=465) pour connaître la méthode. 
+Et [ce lien](https://haozhu233.github.io/kableExtra/awesome_table_in_pdf.pdf) pour la réalisation de beaux tableaux.
+
+```{r table contingence}
+
+tab_5 <- ftable(data[,c(1,2,4)])
+tab_5 <- round(prop.table(tab_5,2)*100,1)
+tab_5 <- rbind(tab_5, tab1(data$cl_age)$output.table[,1])
+tab_5 <- as.table(tab_5)
+row.names(tab_5) <- c("Non fumeuses vivantes ", "Non fumeuses decedees", "Fumeuses vivantes", "Fumeuses decedees" ,"Effectifs")
+colnames(tab_5) <- c("[18;34]", "[35;54]", "[55;64]", "[65;[")
+
+kable(tab_5,"latex", align = "c") %>% kable_styling(latex_options = "striped", stripe_index = c(1,2))
+```
+
+## Et maintenant on trace les barplots
+
+Super [lien](http://zoonek2.free.fr/UNIX/48_R/04.html) pour les paramètres graphiques.
+Et autre [lien](https://sites.google.com/site/rgraphiques/realiser-des-graphiques-avec-le-logiciel-r/diagrammes-en-barres) pour les diagrammes en barre.
+
+```{r deuxieme barplot}
+
+par(mar = c(5,5,5,13))
+barplot(tab_5[c(1:4),], col = c("gray","black","gray","black"), density = c(30,30,40,100),angle = c(70,70,0,0))
+xmin <- par("usr")[1]
+xmax <- par("usr")[2]
+ymin <- par("usr")[3]
+ymax <- par("usr")[4]
+par(xpd=TRUE)
+lambda <- 0.025
+legend(((1 + lambda) * par("usr")[2] - lambda * par("usr")[1]),50, legend = c("Non fumeuses vivantes", "Non fumeuses decedees", "Fumeuses vivantes", "Fumeuses decedees"), fill = c("gray","black","gray","black"),density = c(30,30,40,100),angle = (c(70,70,0,0)))
+
+
+```
+
+**NB** : dans le code précédent :
+
+```{r explication par mar}
+par(mar = c(5,5,5,15))
+```
+On définit les paramètres de marge, dans l'ordre c(bas,gauche,haut,droite)
+
+```{r explication lsite usr}
+xmin <- par("usr")[1]
+xmax <- par("usr")[2]
+ymin <- par("usr")[3]
+ymax <- par("usr")[4]
+```
+On récupère les valeurs min et max du plot précédent
+
+
+## Et maintenant on peut obtenir les intervalles de confiance
+<!--# Pour le premier groupe d'age non fumeuses decedees-->
+```{r IC premier groupe dage non fum, include=FALSE}
+
+x <- tab_5[2,1]
+n <- tab_5[5,1]
+
+IC1<- round(IC(x),1)
+IC1 <- paste(c(IC1[1],"[",IC1[2],"-",IC1[3],"]"),collapse = "")
+
+```
+<!--# Pour le premier groupe d'age fumeuses decedees-->
+```{r IC premier groupe dage fum, include=FALSE}
+
+x <- tab_5[4,1]
+n <- tab_5[5,1]
+
+IC2 <- round(IC(x),1)
+IC2 <- paste(c(IC2[1],"[",IC2[2],"-",IC2[3],"]"), collapse = "")
+```
+
+<!--# Pour le deuxième groupe d'age non fum-->
+```{r IC deuxieme groupe dage non fum, include=FALSE}
+
+x <- tab_5[2,2]
+n <- tab_5[5,2]
+
+IC3 <- round(IC(x),1)
+IC3 <- paste(c(IC3[1],"[",IC3[2],"-",IC3[3],"]"),collapse = "")
+
+```
+<!--# Pour le deuxième groupe d'age fum-->
+```{r IC deuxieme groupe dage fum, include=FALSE}
+
+x <- tab_5[4,2]
+n <- tab_5[5,2]
+
+IC4 <- round(IC(x),1)
+IC4 <- paste(c(IC4[1],"[",IC4[2],"-",IC4[3],"]"),collapse = "")
+
+```
+<!--# Pour le troisieme groupe d'age non fum-->
+```{r IC troisieme groupe dage non fum, include=FALSE}
+
+x <- tab_5[2,3]
+n <- tab_5[5,3]
+
+IC5 <- round(IC(x),1)
+IC5 <- paste(c(IC5[1],"[",IC5[2],"-",IC5[3],"]"),collapse = "")
+
+```
+<!--# Pour le troisieme groupe d'age  fum-->
+```{r IC troisieme groupe dage  fum, include=FALSE}
+
+x <- tab_5[4,3]
+n <- tab_5[5,3]
+
+IC6 <- round(IC(x),1)
+IC6 <- paste(c(IC6[1],"[",IC6[2],"-",IC6[3],"]"),collapse = "")
+```
+<!--# Pour le quatrieme groupe d'age non fum-->
+```{r IC quatrieme groupe dage non fum, include=FALSE}
+
+x <- tab_5[2,4]
+n <- tab_5[5,4]
+
+IC7<- round(IC(x),1)
+IC7 <- paste(c(IC7[1],"[",IC7[2],"-",IC7[3],"]"),collapse = "")
+
+```
+
+<!--# Pour le quatrieme groupe d'age fum-->
+```{r IC quatrieme groupe dage fum, include=FALSE}
+
+x <- tab_5[4,4]
+n <- tab_5[5,4]
+
+IC8<- round(IC(x),1)
+IC8 <- paste(c(IC8[1],"[",IC8[2],"-",IC8[3],"]"), collapse = "")
+
+```
+
+Sous forme d'un tableau :
+```{r, message=FALSE}
+
+tab_6 <- cbind(rbind(IC1,IC2), rbind(IC3,IC4), rbind(IC5,IC6), rbind(IC7,IC8))
+colnames(tab_6) <- colnames(tab_5)
+row.names(tab_6) <- c("Non Fumeuses", "Fumeuses")
+kable(tab_6,align = "c")
+
+```
+
+Une fois de plus à la vue de ces résultats on est étonnés ! En effet, autant c'est cohérent chez les non fumeurs mais chez les fumeurs il y a une discordance car ce ne sont pas les personnes les plus agées qui décèdent le plus. Il y a probablement une interaction entre l'âge et le fait d'être fumeur, où alors les catégories sont mal faites...
+
+### Mission 3
+Il s'agit maintenant de faire une régression logistique pour utiliser l'âge en continu et ainsi ne pas perdre d'information.
+
+## On commence par bien coder la variable décès
+
+```{r recodage deces}
+
+data$deces <- as.factor(ifelse(data$Status=="Alive",0,1))
+
+```
+
+## Ensuite on fait la regression logistique, d'abord univariable.
+
+#Pour le tabac :
+
+```{r univar tabac}
+
+regunita <- glm(deces~Smoker, family = binomial, data = data)
+
+# pour obtenir les OR
+
+logistic.display(regunita)
+
+```
+
+#Pour l'âge :
+
+```{r uni age}
+
+reguniage <- glm(deces~Age, family = binomial(), data = data)
+
+logistic.display(reguniage)
+
+```
+
+La subtilité pour l'âge est qu'il faut vérifier l'hypothèse de linéarité du Logit car variable quantitative et hypothèse sous-jacente d'un modèle de régression logistique.
+Pour cela on introduit un polynome fractionnaire dans le modèle de régression.
+
+```{r linearite logit}
+
+library(mfp)
+
+reguniage2 <- mfp(deces~fp(Age, df =4, select = 1, scale = T), family = binomial, data = data)
+
+summary(reguniage2)
+```
+
+En lisant le summary, le meilleur polynome est de degrès 1 donc l'hypothèse de linéarité est respectée.
+
+## Modèle multivariable
+
+```{r modele multi}
+
+regtot <- glm(deces~Age+Smoker, family = binomial, data = data)
+
+logistic.display(regtot)
+```
+
+
+Et là on constate une inversion de l'odds ratio associé au tabac lorsque l'on ajuste sur l'âge...
\ No newline at end of file

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