Simulation of data
We simulate a data set with 3 groups of 80 observations each. All of the group follow a Weibull distribution but with different shape and scale parameters. We simulate as well 3 continuous variables \(x_1\), \(x_2\) and \(x_3\) and 2 binaries variables \(z_1\) and \(z_2\).
set.seed(0)
simulated_data<-
data.frame(label=rep(c("A","B","C"),c(80,80,80)))%>%
mutate(
time=case_when(
label=="A"~rweibull(n(),shape=2,scale=2),
label=="B"~rweibull(n(),shape=2,scale=5),
label=="C"~rweibull(n(),shape=2,scale=3)),
survtime=pmin(time,10),
survevent=time<10)%>%
select(-time)%>%
mutate(
x1=case_when(
label=="A"~rnorm(n(),0),
label=="B"~rnorm(n(),3),
label=="C"~rnorm(n(),3)),
x2=case_when(
label=="A"~rnorm(n(),3),
label=="B"~rnorm(n(),0),
label=="C"~rnorm(n(),3)),
x3=case_when(
label=="A"~rnorm(n(),0),
label=="B"~rnorm(n(),0),
label=="C"~rnorm(n(),2)),
z1=case_when(
label=="A"~sample(c("F1","F2"),n(),replace=T,prob=c(0.8,0.2)),
label=="B"~sample(c("F1","F2"),n(),replace=T,prob=c(0.5,0.5)),
label=="C"~sample(c("F1","F2"),n(),replace=T,prob=c(0.2,0.8))),
z2=case_when(
label=="A"~sample(c("G1","G2"),n(),replace=T,prob=c(0.7,0.3)),
label=="B"~sample(c("G1","G2"),n(),replace=T,prob=c(0.1,0.9)),
label=="C"~sample(c("G2","G2"),n(),replace=T,prob=c(0.4,0.6))))First, we fit a set of trees with the survival_forest function.
a_survival_forest<-
survival_forest(
survival_outcome=Surv(survtime,survevent)~1,
numeric_predictor=~x1+x2+x3,
factor_predictor=~z1+z2,
data=simulated_data,
nboot=100,
min_weights=20)We then compute the distance between the observation using the predict_distance_forest function.
a_distance<-predict_distance_forest(
a_survival_forest,
numeric_predictor=~x1+x2+x3,
factor_predictor=~z1+z2,
data=simulated_data)Once the distances have been computed, it is possible to explore how the observatins are related to each other. In this example it appears that there are 3 large clusters which different strongly from each others.
a_dist<-as.dist(a_distance$mean_distance)
a_cmdscale_fit<-cmdscale(a_dist)
a_hclust<-hclust(a_dist,method="average")
a_dendrogram<-as.dendrogram(a_hclust)
plot(a_dendrogram)
Dendrogram
It is possible to identify the optimum number of clusters by identifying the cut off with the largest ASWw.
a_clustrange<-as.clustrange(a_hclust,diss=a_dist,ncluster=10)
df_ASWw<-data.frame(nclus=2:10,ASWw=a_clustrange$stats[,"ASWw"])
ggplot(df_ASWw,aes(x=nclus,y=ASWw))+geom_line()+geom_vline(xintercept=3,lty=2)+theme_bw()
Dendrogram
Finaly, it is possible to identify how the observations are similar and how does the clustering model performs.
result_data<-data.frame(
x=a_cmdscale_fit[,1],
y=a_cmdscale_fit[,2],
truth=simulated_data$label,
cluster=factor(cutree(a_hclust,3)))
gridExtra::grid.arrange(
ggplot(result_data,aes(x=x,y=y,color=truth))+geom_point()+theme_bw(),
ggplot(result_data,aes(x=x,y=y,color=cluster))+geom_point()+theme_bw(),ncol=2)
Dendrogram