Risk Analysis of Covid-19 Patient Mortality Using Extended Cox Model
Survival analysis is a collection of methods for evaluate data
related to time from start to finish a special event (can be
death/recovery) with given censorship status to be a comparison of
endurance ability human life (Cread,2020).
Based on this definition, this study chose survival analysis to
determine the cause of death of COVID-19 patients. This study used data
on Covid-19 patients obtained from the Mexican Government, with response
variables, namely time and status (censored or not) and predictor
variables, namely patient laboratory results. in the form of a history
of illness that has been suffered by a Covid-19 patient. The data to be
analyzed is too large and heterogeneous, so clustering is carried out
using the K-Means Clustering algorithm. certain clusters and clarify
conclusions. After clustering the data on COVID-19 patients, it was
continued by conducting a survival analysis on the two clusters that
were formed, namely applying the extended cox model which was estimated
using the Breslow partial likelihood method and finally the model
suitability test was carried out.
This research on the risk analysis of the death of Covid-19 patients is
expected to provide insight into the factors that influence the death of
Covid-19 patients so as to assist medical personnel in providing
appropriate treatment for patients who have these factors. The following
is a flowchart of this research
1. Data Preparation
At this stage, it is done preparing the library used and importing data for this research
library(lubridate)
library(survival)
library(survminer)
library(ggplot2)
library(dplyr)
library(factoextra)
library(FactoMineR)CovidData<-read.csv2("covid.csv")
head(CovidData) id sex patient_type entry_date date_symptoms date_died intubed
1 1636bf 0 2 12/01/2020 09/01/2020 13/01/2020 1
2 7.98E+02 0 2 12/01/2020 12/01/2020 14/01/2020 2
3 1673d6 1 2 13/01/2020 10/01/2020 15/01/2020 2
4 1045fa 1 2 12/01/2020 12/01/2020 29/01/2020 2
5 1abb1c 1 2 12/01/2020 04/01/2020 30/01/2020 2
6 09ab8c 0 2 06/02/2020 05/02/2020 08/02/2020 2
pneumonia age pregnancy diabetes copd asthma inmsupr hypertension
1 1 48 0 0 0 0 0 0
2 1 74 0 0 0 0 0 0
3 1 45 0 98 0 98 98 0
4 1 75 0 0 0 0 0 1
5 1 54 0 1 0 0 0 0
6 1 55 0 0 1 1 0 1
other_disease cardiovascular obesity renal_chronic tobacco
1 2 0 0 0 0
2 2 1 0 0 1
3 2 0 0 0 0
4 1 0 1 0 0
5 2 0 1 0 0
6 2 1 1 0 0
contact_other_covid covid_res icu
1 99 2 2
2 99 2 2
3 99 2 1
4 99 2 2
5 99 2 1
6 99 2 12. Data Identification
In this study, we did not use all the columns in the
covid data, so we discarded unneeded variables by
subsetting.
CovidData=CovidData[,-c(1,3,4,7,16,21,22,23)]
The following is a description of each column:
1. Sex: Identifies the sex of the patient (0: male & 1:
female).
2. date_symptoms: Identifies the date on which the
patient’s symptoms began.
3. data_died: Identifies the date the patient died.
4. pneumonia:Identifies if the patient was diagnosed with
pneumonia (0: No & 1: yes).
5. age: Identifies the age of the patient.
6. pregnancy: Identifies if the patient is pregnant (0:No
& 1:Yes).
7. diabetes: Identifies if the patient has a diagnosis of
diabetes (0: No & 1: Yes).
8. copd: Identifies if the patient has a diagnosis of
Chronic obstructive pulmonary disease (COPD) (0: No & 1:Yes).
9. asthma: Identifies if the patient has a diagnosis of
asthma (0: No & 1: Yes).
10. inmsupr:Identifies if the patient has immunosuppression
(0: No & 1: Yes) 11. hypertension:Identifies if the
patient has a diagnosis of hypertension (0:No & 1:Yes).
12. cardiovascular: Identifies if the patient has a
diagnosis of cardiovascular disease (0: No & 1: Yes).
13. obesity: Identifies if the patient is diagnosed with
obesity (0: No & 1: Yes).
14. renal_chronic: Identifies if the patient has a
diagnosis of chronic kidney failure (0: No & 1: Yes).
15. tobacco: Identifies if the patient is a tobacco user
(0: No & 1: Yes).
3. Data Acquistion
Data acquistion is done so that the data format is in accordance with the objectives of the analysis.
3.1. Check Type Data
str(CovidData)'data.frame': 125650 obs. of 15 variables:
$ sex : int 0 0 1 1 1 0 0 1 1 0 ...
$ date_symptoms : chr "09/01/2020" "12/01/2020" "10/01/2020" "12/01/2020" ...
$ date_died : chr "13/01/2020" "14/01/2020" "15/01/2020" "29/01/2020" ...
$ pneumonia : int 1 1 1 1 1 1 1 1 1 1 ...
$ age : int 48 74 45 75 54 55 63 68 32 15 ...
$ pregnancy : int 0 0 0 0 0 0 0 0 0 0 ...
$ diabetes : int 0 0 98 0 1 0 0 0 0 0 ...
$ copd : int 0 0 0 0 0 1 0 0 0 0 ...
$ asthma : int 0 0 98 0 0 1 0 0 0 0 ...
$ inmsupr : int 0 0 98 0 0 0 0 0 1 0 ...
$ hypertension : int 0 0 0 1 0 1 1 1 1 0 ...
$ cardiovascular: int 0 1 0 0 0 1 0 0 0 0 ...
$ obesity : int 0 0 0 1 1 1 0 1 0 0 ...
$ renal_chronic : int 0 0 0 0 0 0 0 0 1 0 ...
$ tobacco : int 0 1 0 0 0 0 0 0 0 0 ...
Note the results of the type check above, date_symptoms
and date_died are still in chr form, they should
be in the form of date. the variables pneumonia,
pregnancy, diabetes, copd,
asthma, inmsupr, hypertension,
cardiovascular, obesity,
renal_chronic, tobaco should also be in factor
form but because doing survival analysis can be directly identified so
that no need be changed into the form of factor data
type.
CovidData$date_died <- as.Date(CovidData$date_died, format = "%d/%m/%y")
CovidData$date_symptoms <- as.Date(CovidData$date_symptoms, format = "%d/%m/%y")
str(CovidData)'data.frame': 125650 obs. of 15 variables:
$ sex : int 0 0 1 1 1 0 0 1 1 0 ...
$ date_symptoms : Date, format: "2020-01-09" "2020-01-12" ...
$ date_died : Date, format: "2020-01-13" "2020-01-14" ...
$ pneumonia : int 1 1 1 1 1 1 1 1 1 1 ...
$ age : int 48 74 45 75 54 55 63 68 32 15 ...
$ pregnancy : int 0 0 0 0 0 0 0 0 0 0 ...
$ diabetes : int 0 0 98 0 1 0 0 0 0 0 ...
$ copd : int 0 0 0 0 0 1 0 0 0 0 ...
$ asthma : int 0 0 98 0 0 1 0 0 0 0 ...
$ inmsupr : int 0 0 98 0 0 0 0 0 1 0 ...
$ hypertension : int 0 0 0 1 0 1 1 1 1 0 ...
$ cardiovascular: int 0 1 0 0 0 1 0 0 0 0 ...
$ obesity : int 0 0 0 1 1 1 0 1 0 0 ...
$ renal_chronic : int 0 0 0 0 0 0 0 0 1 0 ...
$ tobacco : int 0 1 0 0 0 0 0 0 0 0 ...3.2. Feature Engineering
building the column time as the response variable in
this study, this variable is obtained from the date of death of the
patient minus the date when he was first positive for Covid-19.
mathematically written as follows:
\[ waktu = datedied - date symptoms \]
CovidData$waktu<-CovidData$date_died - CovidData$date_symptoms
#lalu diubah ketipe data integer
CovidData$waktu<-as.integer(CovidData$waktu)
head(CovidData) sex date_symptoms date_died pneumonia age pregnancy diabetes copd asthma
1 0 2020-01-09 2020-01-13 1 48 0 0 0 0
2 0 2020-01-12 2020-01-14 1 74 0 0 0 0
3 1 2020-01-10 2020-01-15 1 45 0 98 0 98
4 1 2020-01-12 2020-01-29 1 75 0 0 0 0
5 1 2020-01-04 2020-01-30 1 54 0 1 0 0
6 0 2020-02-05 2020-02-08 1 55 0 0 1 1
inmsupr hypertension cardiovascular obesity renal_chronic tobacco waktu
1 0 0 0 0 0 0 4
2 0 0 1 0 0 1 2
3 98 0 0 0 0 0 5
4 0 1 0 1 0 0 17
5 0 0 0 1 0 0 26
6 0 1 1 1 0 0 3
Then make the column status as the response variable in
this study
CovidData = CovidData %>%
mutate(status = ifelse(is.na(waktu), 0, 1))
head(CovidData) sex date_symptoms date_died pneumonia age pregnancy diabetes copd asthma
1 0 2020-01-09 2020-01-13 1 48 0 0 0 0
2 0 2020-01-12 2020-01-14 1 74 0 0 0 0
3 1 2020-01-10 2020-01-15 1 45 0 98 0 98
4 1 2020-01-12 2020-01-29 1 75 0 0 0 0
5 1 2020-01-04 2020-01-30 1 54 0 1 0 0
6 0 2020-02-05 2020-02-08 1 55 0 0 1 1
inmsupr hypertension cardiovascular obesity renal_chronic tobacco waktu
1 0 0 0 0 0 0 4
2 0 0 1 0 0 1 2
3 98 0 0 0 0 0 5
4 0 1 0 1 0 0 17
5 0 0 0 1 0 0 26
6 0 1 1 1 0 0 3
status
1 1
2 1
3 1
4 1
5 1
6 14. Data Filtering
At the data filtering stage, checking for missing values ​​and outliers is carried out.
3.1 Check missing value
anyNA(CovidData)[1] TRUE3.2 Check Outlier
boxplot(CovidData)
5. Data Validation
The presence of a missing value in the time column then
inputs the missing value by filling in the empty value of 95 because the
maximum value of the ‘time’ variable is 93 days so it is rounded up to
95 days. So the time that is worth 95 is the patient who can
survive.
CovidData$waktu[is.na(CovidData$waktu)] <- 95
head(CovidData) sex date_symptoms date_died pneumonia age pregnancy diabetes copd asthma
1 0 2020-01-09 2020-01-13 1 48 0 0 0 0
2 0 2020-01-12 2020-01-14 1 74 0 0 0 0
3 1 2020-01-10 2020-01-15 1 45 0 98 0 98
4 1 2020-01-12 2020-01-29 1 75 0 0 0 0
5 1 2020-01-04 2020-01-30 1 54 0 1 0 0
6 0 2020-02-05 2020-02-08 1 55 0 0 1 1
inmsupr hypertension cardiovascular obesity renal_chronic tobacco waktu
1 0 0 0 0 0 0 4
2 0 0 1 0 0 1 2
3 98 0 0 0 0 0 5
4 0 1 0 1 0 0 17
5 0 0 0 1 0 0 26
6 0 1 1 1 0 0 3
status
1 1
2 1
3 1
4 1
5 1
6 1
The data on age is very diverse, so it is necessary to create a new
column to group the age variable into old and young age.
According to WHO, a person is said to be young when the age is less than
or equal to 55 years and is said to be old when more than 55 years.
CovidData = CovidData %>%
mutate(Age = ifelse(age <= 55, 0, 1))
CovidData = CovidData[,-c(2,3,5)]
head(CovidData) sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
1 0 1 0 0 0 0 0 0
2 0 1 0 0 0 0 0 0
3 1 1 0 98 0 98 98 0
4 1 1 0 0 0 0 0 1
5 1 1 0 1 0 0 0 0
6 0 1 0 0 1 1 0 1
cardiovascular obesity renal_chronic tobacco waktu status Age
1 0 0 0 0 4 1 0
2 1 0 0 1 2 1 1
3 0 0 0 0 5 1 0
4 0 1 0 0 17 1 1
5 0 1 0 0 26 1 0
6 1 1 0 0 3 1 06. Data Cleaning
The next step is to delete outlier data in the columns
pregnancy, copd, asthma,
inmsupr, hypertension,
cardiovascular, obesity,
renal chronic, tobacco,pneumonia
, diabetes and waktu.
CovidData <- subset(CovidData, pregnancy!= 98)
CovidData <- subset(CovidData, copd!= 98)
CovidData <- subset(CovidData, asthma!= 98)
CovidData <- subset(CovidData, inmsupr!= 98)
CovidData <- subset(CovidData, hypertension!= 98)
CovidData <- subset(CovidData, cardiovascular!= 98)
CovidData <- subset(CovidData, obesity!= 98)
CovidData <- subset(CovidData, renal_chronic!= 98)
CovidData <- subset(CovidData, tobacco!= 98)
CovidData <- subset(CovidData, pneumonia!= 99)
CovidData <- subset(CovidData, diabetes!= 98)
CovidData <- subset(CovidData, waktu > 0)
head(CovidData) sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
1 0 1 0 0 0 0 0 0
2 0 1 0 0 0 0 0 0
4 1 1 0 0 0 0 0 1
5 1 1 0 1 0 0 0 0
6 0 1 0 0 1 1 0 1
7 0 1 0 0 0 0 0 1
cardiovascular obesity renal_chronic tobacco waktu status Age
1 0 0 0 0 4 1 0
2 1 0 0 1 2 1 1
4 0 1 0 0 17 1 1
5 0 1 0 0 26 1 0
6 1 1 0 0 3 1 0
7 0 0 0 0 14 1 17. Scaling
CovidDataScale = scale(CovidData)
head(CovidDataScale) sex pneumonia pregnancy diabetes copd asthma inmsupr
1 -0.8752406 1.438927 -0.07518716 -0.5025649 -0.1616108 -0.1652522 -0.1387816
2 -0.8752406 1.438927 -0.07518716 -0.5025649 -0.1616108 -0.1652522 -0.1387816
4 1.1425337 1.438927 -0.07518716 -0.5025649 -0.1616108 -0.1652522 -0.1387816
5 1.1425337 1.438927 -0.07518716 1.9897767 -0.1616108 -0.1652522 -0.1387816
6 -0.8752406 1.438927 -0.07518716 -0.5025649 6.1876555 6.0513084 -0.1387816
7 -0.8752406 1.438927 -0.07518716 -0.5025649 -0.1616108 -0.1652522 -0.1387816
hypertension cardiovascular obesity renal_chronic tobacco waktu
1 -0.5659387 -0.1788443 -0.5017843 -0.1858564 -0.2973432 -1.764437
2 -0.5659387 5.5914099 -0.5017843 -0.1858564 3.3630899 -1.817003
4 1.7669615 -0.1788443 1.9928722 -0.1858564 -0.2973432 -1.422758
5 -0.5659387 -0.1788443 1.9928722 -0.1858564 -0.2973432 -1.186211
6 1.7669615 5.5914099 1.9928722 -0.1858564 -0.2973432 -1.790720
7 1.7669615 -0.1788443 -0.5017843 -0.1858564 -0.2973432 -1.501607
status Age
1 1.58511 -0.7196612
2 1.58511 1.3895316
4 1.58511 1.3895316
5 1.58511 -0.7196612
6 1.58511 -0.7196612
7 1.58511 1.38953168. Clustering Data
8.1 K-optimum Selection
The selection of optimum k is done objectively by using visualization elbow method.
kmeansTunning <- function(data, maxK) {
withinall <- NULL
total_k <- NULL
for (i in 2:maxK) {
set.seed(40)
temp <- kmeans(data,i)$tot.withinss
withinall <- append(withinall, temp)
total_k <- append(total_k,i)
}
plot(x = total_k, y = withinall, type = "o", xlab = "Number of Cluster", ylab = "Total wss")
abline(h = 1080, col = "firebrick3", lty = 2)
}
kmeansTunning(CovidDataScale, maxK = 10)
Based on the existing output, the Elbow method with a K value that drops
drastically and forms an elbow is found at \(K=3\) and \(K43\). The following is an application of
the k-means algorithm with the optimum k equal to 3
8.2 K-means Algoritma
RNGkind(sample.kind = "Rounding")
set.seed(10000)
clusterDataCovid <- kmeans(x = CovidDataScale, centers = 3)
str(clusterDataCovid)List of 9
$ cluster : Named int [1:123991] 3 2 3 3 3 3 3 3 3 3 ...
..- attr(*, "names")= chr [1:123991] "1" "2" "4" "5" ...
$ centers : num [1:3, 1:15] 0.0961 -0.3659 -0.1185 -0.3816 0.0789 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:3] "1" "2" "3"
.. ..$ : chr [1:15] "sex" "pneumonia" "pregnancy" "diabetes" ...
$ totss : num 1859850
$ withinss : num [1:3] 696938 168998 564143
$ tot.withinss: num 1430079
$ betweenss : num 429771
$ size : int [1:3] 80039 10054 33898
$ iter : int 2
$ ifault : int 0
- attr(*, "class")= chr "kmeans"8.3 Cluster profiling
CovidData$cluster <- as.factor(clusterDataCovid$cluster)
head(CovidData) sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
1 0 1 0 0 0 0 0 0
2 0 1 0 0 0 0 0 0
4 1 1 0 0 0 0 0 1
5 1 1 0 1 0 0 0 0
6 0 1 0 0 1 1 0 1
7 0 1 0 0 0 0 0 1
cardiovascular obesity renal_chronic tobacco waktu status Age cluster
1 0 0 0 0 4 1 0 3
2 1 0 0 1 2 1 1 2
4 0 1 0 0 17 1 1 3
5 0 1 0 0 26 1 0 3
6 1 1 0 0 3 1 0 3
7 0 0 0 0 14 1 1 3CovidProfile <- CovidData %>%
group_by(cluster) %>%
summarise_all(.funs = "mean")
CovidProfile# A tibble: 3 x 16
cluster sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
<fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1 0.481 0.147 0.00800 0.117 0.00848 0.0292 0.00980 0.153
2 2 0.252 0.363 0.00149 0.226 0.0740 0.0278 0.0261 0.263
3 3 0.375 0.737 0.00124 0.395 0.0511 0.0201 0.0383 0.448
# ... with 7 more variables: cardiovascular <dbl>, obesity <dbl>,
# renal_chronic <dbl>, tobacco <dbl>, waktu <dbl>, status <dbl>, Age <dbl>CovidProfile %>%
tidyr::pivot_longer(-cluster) %>%
group_by(name) %>%
summarize(cluster_min_val = which.min(value),
cluster_max_val = which.max(value))# A tibble: 15 x 3
name cluster_min_val cluster_max_val
<chr> <int> <int>
1 Age 1 3
2 asthma 3 1
3 cardiovascular 1 3
4 copd 1 2
5 diabetes 1 3
6 hypertension 1 3
7 inmsupr 1 3
8 obesity 1 2
9 pneumonia 1 3
10 pregnancy 3 1
11 renal_chronic 1 3
12 sex 2 1
13 status 1 3
14 tobacco 1 2
15 waktu 3 18.3 Visualize clustering
library(factoextra)
fviz_cluster(object = clusterDataCovid,
data = CovidDataScale,
legend = "right",geom = "point")
9. Analisis Survival
Survival analysis will be applied to 3 clusters, namely cluster 2 and cluster 3. Cluster 1 is not included because in cluster 1 almost all patients survived while in this study the event was death.
9.1 Cluster 1
DataCluster1 <- CovidData%>%
filter(cluster == 1)
DataCluster1[,c("sex","pneumonia","pregnancy","diabetes","copd","asthma","inmsupr","hypertension","cardiovascular","obesity","renal_chronic","tobacco","status","Age")] <- lapply(DataCluster1[,c("sex","pneumonia","pregnancy","diabetes","copd","asthma","inmsupr","hypertension","cardiovascular","obesity","renal_chronic","tobacco","status","Age")],as.factor)
summary(DataCluster1) sex pneumonia pregnancy diabetes copd asthma inmsupr
0:41507 0:68285 0:79399 0:70689 0:79360 0:77704 0:79255
1:38532 1:11754 1: 640 1: 9350 1: 679 1: 2335 1: 784
hypertension cardiovascular obesity renal_chronic tobacco waktu
0:67796 0:78898 0:65841 0:79223 0:80039 Min. :36.00
1:12243 1: 1141 1:14198 1: 816 1st Qu.:95.00
Median :95.00
Mean :94.99
3rd Qu.:95.00
Max. :95.00
status Age cluster
0:80020 0:64128 1:80039
1: 19 1:15911 2: 0
3: 0
9.2 Cluster 2
DataCluster2 <- CovidData%>%
filter(cluster == 2)
DataCluster2[,c("sex","pneumonia","pregnancy","diabetes","copd","asthma","inmsupr","hypertension","cardiovascular","obesity","renal_chronic","status","tobacco","Age")] <- lapply(DataCluster2[,c("sex","pneumonia","pregnancy","diabetes","copd","asthma","inmsupr","hypertension","cardiovascular","obesity","renal_chronic","status","tobacco","Age")],as.factor)
summary(DataCluster2) sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
0:7516 0:6408 0:10039 0:7783 0:9310 0:9774 0:9792 0:7413
1:2538 1:3646 1: 15 1:2271 1: 744 1: 280 1: 262 1:2641
cardiovascular obesity renal_chronic tobacco waktu status
0:9527 0:7119 0:9617 1:10054 Min. : 1.00 0:6796
1: 527 1:2935 1: 437 1st Qu.:15.00 1:3258
Median :95.00
Mean :67.89
3rd Qu.:95.00
Max. :95.00
Age cluster
0:6412 1: 0
1:3642 2:10054
3: 0
DataCluster2<- CovidData %>%
filter(cluster == 2)
head(DataCluster2) sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
1 0 1 0 0 0 0 0 0
2 1 1 0 0 0 0 0 1
3 0 1 0 0 0 1 1 1
4 0 0 0 0 0 0 0 1
5 0 1 0 1 0 0 0 1
6 0 1 0 0 0 0 0 1
cardiovascular obesity renal_chronic tobacco waktu status Age cluster
1 1 0 0 1 2 1 1 2
2 0 1 0 1 9 1 1 2
3 0 0 0 1 22 1 0 2
4 0 0 0 1 11 1 1 2
5 0 0 0 1 4 1 1 2
6 0 1 0 1 10 1 1 2Before applying the extended cox model, it is necessary to test whether all variables are independent of time. There are two approaches to the proportional hazard assumption test, namely the graphical approach and the GOF approach.
a. Pendekatan Grafik
Variabel sex
fit<-survfit(Surv(waktu,status)~ sex, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "Jenis Kelamin",
legend.labs = c("Laki-Laki", "Perempuan")
)
Variabel pneumonia
fit<-survfit(Surv(waktu,status)~ pneumonia, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "Pneumonia",
legend.labs = c("no Pneumonia", "yes pneumonia")
)
Variabel diabetes
fit<-survfit(Surv(waktu,status)~ diabetes, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "Diabetes",
legend.labs = c("no Diabetes", "yes Diabetes")
)
Variabel Hypertension
fit<-survfit(Surv(waktu,status)~ hypertension, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "Hyperetension",
legend.labs = c("no hypertension", "yes hypertension")
)
Variabel obesity
fit<-survfit(Surv(waktu,status)~ obesity, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "Obesity",
legend.labs = c("no obesity", "yes obesity")
)
Variabel renal chronic
fit<-survfit(Surv(waktu,status)~ renal_chronic, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "Renal Chronic",
legend.labs = c("no renal chronic", "yes renal chronic")
)
Variabel Age
fit<-survfit(Surv(waktu,status)~ Age, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "Age",
legend.labs = c("young", "old")
)
Variabel COPD
fit<-survfit(Surv(waktu,status)~ copd, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "copd"
)
Variabel inmsupr
fit<-survfit(Surv(waktu,status)~ inmsupr, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "inmsupr",
legend.labs = c("no inmsupr", "yes inmsupr")
)
Variabel asthma
fit<-survfit(Surv(waktu,status)~ asthma, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "asthma",
legend.labs = c("no asthma", "yes asthma")
)
Variabel cardiovascular
fit<-survfit(Surv(waktu,status)~ cardiovascular, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "Cardiovascular",
legend.labs = c("No Cardivascular", "Yes Cardivascular")
)
Variabel pregnancy
fit<-survfit(Surv(waktu,status)~ pregnancy, data=DataCluster2)
ggsurvplot(fit, data = DataCluster2, fun = "cumhaz",
legend = "top",
legend.title = "Prgenancy",
legend.labs = c("No Pregnancy", "Yes Pregnancy")
)
b. Pendekatan GOF
fit_cluster2<-coxph(Surv(waktu,status)~ sex+pneumonia+Age+hypertension+obesity+diabetes+renal_chronic+inmsupr+asthma+cardiovascular+copd+pregnancy, data = DataCluster2)
cek_fitt_all2<-cox.zph(fit_cluster2, transform="km", global=TRUE)
print(cek_fitt_all2) chisq df p
sex 5.76e+00 1 0.016
pneumonia 7.42e+01 1 < 2e-16
Age 3.70e+01 1 1.2e-09
hypertension 1.44e+00 1 0.230
obesity 1.74e+00 1 0.188
diabetes 9.29e-01 1 0.335
renal_chronic 2.36e+00 1 0.124
inmsupr 8.66e-01 1 0.352
asthma 2.27e-02 1 0.880
cardiovascular 4.73e-01 1 0.491
copd 3.92e+00 1 0.048
pregnancy 4.31e-03 1 0.948
GLOBAL 1.21e+02 12 < 2e-16
There are 2 variables that do not meet the proportional hazard
assumption, namely: pneumoniadan Age . then
these two variables will be interacted with the time function, namely
the heavside function for each variable. To be able to determine the
heavside function is to look at the survival probability graph.
c. Identification of Covariate Non Proportional Hazard
Variabel Age
# VARIABEL Age
fit<-survfit(Surv(waktu,status)~ Age , data=DataCluster2)
summary(fit)Call: survfit(formula = Surv(waktu, status) ~ Age, data = DataCluster2)
Age=0
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 6412 19 0.997 0.000679 0.996 0.998
2 6393 26 0.993 0.001043 0.991 0.995
3 6367 47 0.986 0.001485 0.983 0.989
4 6320 51 0.978 0.001844 0.974 0.981
5 6269 61 0.968 0.002192 0.964 0.972
6 6208 67 0.958 0.002513 0.953 0.963
7 6141 73 0.946 0.002814 0.941 0.952
8 6068 70 0.935 0.003069 0.929 0.941
9 5998 57 0.927 0.003258 0.920 0.933
10 5941 72 0.915 0.003477 0.909 0.922
11 5869 55 0.907 0.003632 0.900 0.914
12 5814 74 0.895 0.003825 0.888 0.903
13 5740 33 0.890 0.003907 0.882 0.898
14 5707 48 0.883 0.004020 0.875 0.890
15 5659 33 0.877 0.004096 0.869 0.885
16 5626 37 0.872 0.004177 0.863 0.880
17 5589 32 0.867 0.004245 0.858 0.875
18 5557 13 0.865 0.004272 0.856 0.873
19 5544 24 0.861 0.004322 0.852 0.869
20 5520 19 0.858 0.004360 0.849 0.867
21 5501 12 0.856 0.004384 0.848 0.865
22 5489 15 0.854 0.004413 0.845 0.862
23 5474 8 0.852 0.004429 0.844 0.861
24 5466 5 0.852 0.004438 0.843 0.860
25 5461 7 0.851 0.004452 0.842 0.859
26 5454 11 0.849 0.004473 0.840 0.858
27 5443 3 0.848 0.004479 0.840 0.857
28 5440 2 0.848 0.004482 0.839 0.857
29 5438 5 0.847 0.004492 0.839 0.856
30 5433 2 0.847 0.004496 0.838 0.856
31 5431 6 0.846 0.004507 0.837 0.855
32 5425 1 0.846 0.004509 0.837 0.855
33 5424 3 0.845 0.004514 0.837 0.854
34 5421 2 0.845 0.004518 0.836 0.854
36 5419 2 0.845 0.004522 0.836 0.854
37 5417 1 0.845 0.004524 0.836 0.854
41 5416 1 0.845 0.004525 0.836 0.853
42 5415 1 0.844 0.004527 0.836 0.853
43 5414 1 0.844 0.004529 0.835 0.853
44 5413 1 0.844 0.004531 0.835 0.853
45 5412 1 0.844 0.004533 0.835 0.853
46 5411 1 0.844 0.004535 0.835 0.853
50 5410 1 0.844 0.004536 0.835 0.853
59 5409 1 0.843 0.004538 0.835 0.852
Age=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 3642 50 0.986 0.00193 0.982 0.990
2 3592 71 0.967 0.00297 0.961 0.973
3 3521 99 0.940 0.00395 0.932 0.947
4 3422 126 0.905 0.00486 0.896 0.915
5 3296 154 0.863 0.00570 0.852 0.874
6 3142 148 0.822 0.00634 0.810 0.835
7 2994 153 0.780 0.00686 0.767 0.794
8 2841 152 0.738 0.00728 0.724 0.753
9 2689 135 0.701 0.00758 0.687 0.716
10 2554 133 0.665 0.00782 0.650 0.680
11 2421 128 0.630 0.00800 0.614 0.645
12 2293 123 0.596 0.00813 0.580 0.612
13 2170 90 0.571 0.00820 0.555 0.587
14 2080 91 0.546 0.00825 0.530 0.563
15 1989 92 0.521 0.00828 0.505 0.537
16 1897 75 0.500 0.00829 0.484 0.517
17 1822 53 0.486 0.00828 0.470 0.502
18 1769 50 0.472 0.00827 0.456 0.488
19 1719 56 0.457 0.00825 0.441 0.473
20 1663 36 0.447 0.00824 0.431 0.463
21 1627 39 0.436 0.00822 0.420 0.452
22 1588 27 0.429 0.00820 0.413 0.445
23 1561 17 0.424 0.00819 0.408 0.440
24 1544 25 0.417 0.00817 0.401 0.433
25 1519 17 0.412 0.00816 0.397 0.429
26 1502 10 0.410 0.00815 0.394 0.426
27 1492 11 0.407 0.00814 0.391 0.423
28 1481 11 0.404 0.00813 0.388 0.420
29 1470 13 0.400 0.00812 0.384 0.416
30 1457 10 0.397 0.00811 0.382 0.414
31 1447 11 0.394 0.00810 0.379 0.410
32 1436 4 0.393 0.00809 0.378 0.409
33 1432 3 0.392 0.00809 0.377 0.409
34 1429 4 0.391 0.00809 0.376 0.407
35 1425 5 0.390 0.00808 0.374 0.406
36 1420 3 0.389 0.00808 0.374 0.405
38 1417 4 0.388 0.00807 0.372 0.404
39 1413 1 0.388 0.00807 0.372 0.404
40 1412 3 0.387 0.00807 0.371 0.403
41 1409 1 0.387 0.00807 0.371 0.403
42 1408 1 0.386 0.00807 0.371 0.402
43 1407 3 0.386 0.00806 0.370 0.402
44 1404 1 0.385 0.00806 0.370 0.401
46 1403 2 0.385 0.00806 0.369 0.401
47 1401 1 0.384 0.00806 0.369 0.401
48 1400 2 0.384 0.00806 0.368 0.400
49 1398 1 0.384 0.00806 0.368 0.400
50 1397 2 0.383 0.00806 0.368 0.399
51 1395 1 0.383 0.00805 0.367 0.399
53 1394 1 0.382 0.00805 0.367 0.399
56 1393 1 0.382 0.00805 0.367 0.398
58 1392 1 0.382 0.00805 0.366 0.398
59 1391 1 0.382 0.00805 0.366 0.398
60 1390 1 0.381 0.00805 0.366 0.397
63 1389 1 0.381 0.00805 0.366 0.397ggsurvplot(fit, data = DataCluster2,
pval = TRUE, conf.int = TRUE,
risk.table = TRUE, # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))
Note the graph of the elderly patient’s speed drops drastically on day 30 but after day 30 it was constant until the end of the study. so the function of the upper side is
\[ g(t)= \begin{cases} 1, & \mbox{if}\ t\mbox{ < 30} \\ 0, & \mbox{if}\ t\mbox{ >= 30} \end{cases}\]
Variabel Pneumonia
# VARIABEL Pneumonia
fit<-survfit(Surv(waktu,status)~ pneumonia , data=DataCluster2)
summary(fit)Call: survfit(formula = Surv(waktu, status) ~ pneumonia, data = DataCluster2)
pneumonia=0
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 6408 16 0.998 0.000623 0.996 0.999
2 6392 30 0.993 0.001055 0.991 0.995
3 6362 37 0.987 0.001412 0.984 0.990
4 6325 44 0.980 0.001741 0.977 0.984
5 6281 51 0.972 0.002053 0.968 0.976
6 6230 65 0.962 0.002386 0.957 0.967
7 6165 69 0.951 0.002689 0.946 0.957
8 6096 56 0.943 0.002906 0.937 0.948
9 6040 51 0.935 0.003088 0.929 0.941
10 5989 58 0.926 0.003279 0.919 0.932
11 5931 45 0.919 0.003417 0.912 0.925
12 5886 48 0.911 0.003556 0.904 0.918
13 5838 29 0.907 0.003636 0.899 0.914
14 5809 28 0.902 0.003712 0.895 0.909
15 5781 32 0.897 0.003795 0.890 0.905
16 5749 22 0.894 0.003850 0.886 0.901
17 5727 23 0.890 0.003907 0.883 0.898
18 5704 13 0.888 0.003938 0.880 0.896
19 5691 22 0.885 0.003990 0.877 0.893
20 5669 17 0.882 0.004030 0.874 0.890
21 5652 9 0.881 0.004050 0.873 0.889
22 5643 10 0.879 0.004073 0.871 0.887
23 5633 6 0.878 0.004087 0.870 0.886
24 5627 2 0.878 0.004091 0.870 0.886
25 5625 5 0.877 0.004102 0.869 0.885
26 5620 9 0.876 0.004123 0.868 0.884
27 5611 4 0.875 0.004131 0.867 0.883
28 5607 3 0.875 0.004138 0.866 0.883
29 5604 5 0.874 0.004149 0.866 0.882
30 5599 5 0.873 0.004160 0.865 0.881
31 5594 4 0.872 0.004169 0.864 0.881
32 5590 2 0.872 0.004173 0.864 0.880
33 5588 2 0.872 0.004177 0.864 0.880
34 5586 1 0.872 0.004180 0.863 0.880
35 5585 1 0.871 0.004182 0.863 0.880
36 5584 1 0.871 0.004184 0.863 0.879
40 5583 1 0.871 0.004186 0.863 0.879
41 5582 1 0.871 0.004188 0.863 0.879
42 5581 1 0.871 0.004190 0.863 0.879
43 5580 2 0.870 0.004195 0.862 0.879
47 5578 1 0.870 0.004197 0.862 0.879
49 5577 1 0.870 0.004199 0.862 0.878
51 5576 1 0.870 0.004201 0.862 0.878
58 5575 1 0.870 0.004203 0.862 0.878
pneumonia=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 3646 53 0.985 0.00198 0.982 0.989
2 3593 67 0.967 0.00295 0.961 0.973
3 3526 109 0.937 0.00402 0.929 0.945
4 3417 133 0.901 0.00495 0.891 0.910
5 3284 164 0.856 0.00582 0.844 0.867
6 3120 150 0.815 0.00644 0.802 0.827
7 2970 157 0.772 0.00695 0.758 0.785
8 2813 166 0.726 0.00739 0.712 0.741
9 2647 141 0.687 0.00768 0.672 0.703
10 2506 147 0.647 0.00791 0.632 0.663
11 2359 138 0.609 0.00808 0.594 0.625
12 2221 149 0.568 0.00820 0.552 0.585
13 2072 94 0.543 0.00825 0.527 0.559
14 1978 111 0.512 0.00828 0.496 0.529
15 1867 93 0.487 0.00828 0.471 0.503
16 1774 90 0.462 0.00826 0.446 0.478
17 1684 62 0.445 0.00823 0.429 0.461
18 1622 50 0.431 0.00820 0.415 0.448
19 1572 58 0.415 0.00816 0.400 0.432
20 1514 38 0.405 0.00813 0.389 0.421
21 1476 42 0.393 0.00809 0.378 0.409
22 1434 32 0.385 0.00806 0.369 0.401
23 1402 19 0.379 0.00804 0.364 0.395
24 1383 28 0.372 0.00800 0.356 0.388
25 1355 19 0.366 0.00798 0.351 0.382
26 1336 12 0.363 0.00796 0.348 0.379
27 1324 10 0.360 0.00795 0.345 0.376
28 1314 10 0.358 0.00794 0.342 0.374
29 1304 13 0.354 0.00792 0.339 0.370
30 1291 7 0.352 0.00791 0.337 0.368
31 1284 13 0.349 0.00789 0.333 0.364
32 1271 3 0.348 0.00789 0.333 0.364
33 1268 4 0.347 0.00788 0.332 0.362
34 1264 5 0.345 0.00787 0.330 0.361
35 1259 4 0.344 0.00787 0.329 0.360
36 1255 4 0.343 0.00786 0.328 0.359
37 1251 1 0.343 0.00786 0.328 0.359
38 1250 4 0.342 0.00785 0.327 0.357
39 1246 1 0.341 0.00785 0.326 0.357
40 1245 2 0.341 0.00785 0.326 0.357
41 1243 1 0.341 0.00785 0.326 0.356
42 1242 1 0.340 0.00785 0.325 0.356
43 1241 2 0.340 0.00784 0.325 0.356
44 1239 2 0.339 0.00784 0.324 0.355
45 1237 1 0.339 0.00784 0.324 0.355
46 1236 3 0.338 0.00783 0.323 0.354
48 1233 2 0.338 0.00783 0.323 0.353
50 1231 3 0.337 0.00783 0.322 0.353
53 1228 1 0.337 0.00783 0.322 0.352
56 1227 1 0.336 0.00782 0.321 0.352
59 1226 2 0.336 0.00782 0.321 0.351
60 1224 1 0.335 0.00782 0.320 0.351
63 1223 1 0.335 0.00782 0.320 0.351ggsurvplot(fit, data = DataCluster2,
pval = TRUE, conf.int = TRUE,
risk.table = TRUE, # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))
Notice the graph speed of pneumonia patients dropped rapidly on day 31 but after day 31 it was constant until the end of the study. so the heavside function is
\[ g(t)= \begin{cases} 1, & \mbox{if}\ t\mbox{ < 31} \\ 0, & \mbox{if}\ t\mbox{ >= 31} \end{cases}\]
d. Build Time Function
DataCluster2= DataCluster2 %>%
mutate(interval1 = ifelse(waktu<= 30, 0, 30),
interval2 = ifelse(waktu<= 31, 0, 31))
head(DataCluster2) sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
1 0 1 0 0 0 0 0 0
2 1 1 0 0 0 0 0 1
3 0 1 0 0 0 1 1 1
4 0 0 0 0 0 0 0 1
5 0 1 0 1 0 0 0 1
6 0 1 0 0 0 0 0 1
cardiovascular obesity renal_chronic tobacco waktu status Age cluster
1 1 0 0 1 2 1 1 2
2 0 1 0 1 9 1 1 2
3 0 0 0 1 22 1 0 2
4 0 0 0 1 11 1 1 2
5 0 0 0 1 4 1 1 2
6 0 1 0 1 10 1 1 2
interval1 interval2
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
6 0 0t.Age_1 = t(DataCluster2$Age)*(1-(DataCluster2$interval1)/30)
t.Age_2 = t(DataCluster2$Age)*(DataCluster2$interval1/30)
Age_t1 = t(t.Age_1 )
Age_t2 = t(t.Age_2)t.pneumonia_1 = t(DataCluster2$pneumonia)*(1-(DataCluster2$interval2)/31)
t.pneumonia_2 = t(DataCluster2$pneumonia)*(DataCluster2$interval2/31)
pneumonia_t1 = t(t.pneumonia_1 )
pneumonia_t2 = t(t.pneumonia_2)DataCluster2=cbind(DataCluster2,pneumonia_t1,pneumonia_t2,Age_t1,Age_t2)
head(DataCluster2) sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
1 0 1 0 0 0 0 0 0
2 1 1 0 0 0 0 0 1
3 0 1 0 0 0 1 1 1
4 0 0 0 0 0 0 0 1
5 0 1 0 1 0 0 0 1
6 0 1 0 0 0 0 0 1
cardiovascular obesity renal_chronic tobacco waktu status Age cluster
1 1 0 0 1 2 1 1 2
2 0 1 0 1 9 1 1 2
3 0 0 0 1 22 1 0 2
4 0 0 0 1 11 1 1 2
5 0 0 0 1 4 1 1 2
6 0 1 0 1 10 1 1 2
interval1 interval2 pneumonia_t1 pneumonia_t2 Age_t1 Age_t2
1 0 0 1 0 1 0
2 0 0 1 0 1 0
3 0 0 1 0 0 0
4 0 0 0 0 1 0
5 0 0 1 0 1 0
6 0 0 1 0 1 0e. Model Extended Cox
Fit_Model_Cluster2<-coxph(Surv(waktu,status)~ sex+hypertension+obesity+pregnancy+diabetes+renal_chronic+cardiovascular+copd+Age_t1+Age_t2+pneumonia_t1+pneumonia_t2+asthma+inmsupr, data = DataCluster2, method = "breslow")
summary(Fit_Model_Cluster2)Call:
coxph(formula = Surv(waktu, status) ~ sex + hypertension + obesity +
pregnancy + diabetes + renal_chronic + cardiovascular + copd +
Age_t1 + Age_t2 + pneumonia_t1 + pneumonia_t2 + asthma +
inmsupr, data = DataCluster2, method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
sex -0.19410 0.82358 0.04741 -4.094 4.23e-05 ***
hypertension 0.17217 1.18788 0.04038 4.264 2.01e-05 ***
obesity 0.07216 1.07483 0.03839 1.880 0.060173 .
pregnancy -0.23207 0.79289 0.70956 -0.327 0.743616
diabetes 0.20050 1.22202 0.03929 5.103 3.34e-07 ***
renal_chronic 0.33003 1.39101 0.06551 5.038 4.71e-07 ***
cardiovascular 0.13308 1.14235 0.06372 2.088 0.036754 *
copd 0.19493 1.21522 0.05206 3.745 0.000181 ***
Age_t1 1.16687 3.21192 0.05712 20.429 < 2e-16 ***
Age_t2 -1.22458 0.29388 0.13660 -8.964 < 2e-16 ***
pneumonia_t1 1.96898 7.16339 0.06120 32.171 < 2e-16 ***
pneumonia_t2 -1.08519 0.33784 0.14840 -7.313 2.62e-13 ***
asthma -0.25033 0.77854 0.12031 -2.081 0.037463 *
inmsupr 0.18399 1.20201 0.08393 2.192 0.028358 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
sex 0.8236 1.2142 0.7505 0.9038
hypertension 1.1879 0.8418 1.0975 1.2857
obesity 1.0748 0.9304 0.9969 1.1588
pregnancy 0.7929 1.2612 0.1974 3.1856
diabetes 1.2220 0.8183 1.1314 1.3198
renal_chronic 1.3910 0.7189 1.2234 1.5816
cardiovascular 1.1423 0.8754 1.0082 1.2943
copd 1.2152 0.8229 1.0973 1.3458
Age_t1 3.2119 0.3113 2.8718 3.5924
Age_t2 0.2939 3.4027 0.2249 0.3841
pneumonia_t1 7.1634 0.1396 6.3536 8.0763
pneumonia_t2 0.3378 2.9600 0.2526 0.4519
asthma 0.7785 1.2844 0.6150 0.9856
inmsupr 1.2020 0.8319 1.0197 1.4169
Concordance= 0.887 (se = 0.002 )
Likelihood ratio test= 7541 on 14 df, p=<2e-16
Wald test = 5979 on 14 df, p=<2e-16
Score (logrank) test = 11944 on 14 df, p=<2e-16d. Hazard Ratio
ggforest(Fit_Model_Cluster2, main = "Hazard Ratio")
f. Pengujian Signifikansi
Uji Partial Likelihood
Fit_Model_Cluster2$loglik[1] -29457.50 -25687.17Uji Wald Test
Variabel Sex
## Variabel sex
Fit_Model_Sex<-coxph(Surv(waktu,status)~ sex, data = DataCluster2, method = "breslow")
summary(Fit_Model_Sex)Call:
coxph(formula = Surv(waktu, status) ~ sex, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
sex -0.57546 0.56245 0.04658 -12.35 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
sex 0.5624 1.778 0.5134 0.6162
Concordance= 0.548 (se = 0.004 )
Likelihood ratio test= 172.3 on 1 df, p=<2e-16
Wald test = 152.6 on 1 df, p=<2e-16
Score (logrank) test = 156.9 on 1 df, p=<2e-16Variabel peneumonia
## Variabel Pneumonia
Fit_Model_Pneumonia1<-coxph(Surv(waktu,status)~ pneumonia_t1, data = DataCluster2, method = "breslow")
summary(Fit_Model_Pneumonia1)Call:
coxph(formula = Surv(waktu, status) ~ pneumonia_t1, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
pneumonia_t1 3.22421 25.13362 0.04442 72.58 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
pneumonia_t1 25.13 0.03979 23.04 27.42
Concordance= 0.798 (se = 0.003 )
Likelihood ratio test= 6494 on 1 df, p=<2e-16
Wald test = 5268 on 1 df, p=<2e-16
Score (logrank) test = 10081 on 1 df, p=<2e-16Fit_Model_Pneumonia2<-coxph(Surv(waktu,status)~ pneumonia_t2, data = DataCluster2, method = "breslow")
summary(Fit_Model_Pneumonia2)Call:
coxph(formula = Surv(waktu, status) ~ pneumonia_t2, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
pneumonia_t2 -2.46067 0.08538 0.14396 -17.09 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
pneumonia_t2 0.08538 11.71 0.06439 0.1132
Concordance= 0.57 (se = 0.002 )
Likelihood ratio test= 731.1 on 1 df, p=<2e-16
Wald test = 292.1 on 1 df, p=<2e-16
Score (logrank) test = 472.6 on 1 df, p=<2e-16Variabel Diabetes
## Variabel Diabetes
Fit_Model_Diabetes<-coxph(Surv(waktu,status)~ diabetes, data = DataCluster2, method = "breslow")
summary(Fit_Model_Diabetes)Call:
coxph(formula = Surv(waktu, status) ~ diabetes, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
diabetes 0.98345 2.67365 0.03605 27.28 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
diabetes 2.674 0.374 2.491 2.869
Concordance= 0.599 (se = 0.004 )
Likelihood ratio test= 670.4 on 1 df, p=<2e-16
Wald test = 744.2 on 1 df, p=<2e-16
Score (logrank) test = 805.5 on 1 df, p=<2e-16Variabel Hypertension
## Variabel hypertension
Fit_Model_Hypertension<-coxph(Surv(waktu,status)~ hypertension, data = DataCluster2, method = "breslow")
summary(Fit_Model_Hypertension)Call:
coxph(formula = Surv(waktu, status) ~ hypertension, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
hypertension 1.02681 2.79216 0.03536 29.04 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
hypertension 2.792 0.3581 2.605 2.993
Concordance= 0.613 (se = 0.004 )
Likelihood ratio test= 780.9 on 1 df, p=<2e-16
Wald test = 843.3 on 1 df, p=<2e-16
Score (logrank) test = 919.1 on 1 df, p=<2e-16Variabel Obesity
## Variabel Obesity
Fit_Model_obesity<-coxph(Surv(waktu,status)~ obesity, data = DataCluster2, method = "breslow")
summary(Fit_Model_obesity)Call:
coxph(formula = Surv(waktu, status) ~ obesity, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
obesity 0.11730 1.12446 0.03777 3.106 0.0019 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
obesity 1.124 0.8893 1.044 1.211
Concordance= 0.512 (se = 0.004 )
Likelihood ratio test= 9.5 on 1 df, p=0.002
Wald test = 9.65 on 1 df, p=0.002
Score (logrank) test = 9.66 on 1 df, p=0.002Variabel Renal Chronic
### variabel renal_chronic
Fit_Model_RenalChronic<-coxph(Surv(waktu,status)~ renal_chronic, data = DataCluster2, method = "breslow")
summary(Fit_Model_RenalChronic)Call:
coxph(formula = Surv(waktu, status) ~ renal_chronic, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
renal_chronic 1.06039 2.88750 0.06171 17.18 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
renal_chronic 2.887 0.3463 2.559 3.259
Concordance= 0.529 (se = 0.002 )
Likelihood ratio test= 223.3 on 1 df, p=<2e-16
Wald test = 295.2 on 1 df, p=<2e-16
Score (logrank) test = 323.9 on 1 df, p=<2e-16Variabel Age
## Variabel Age
Fit_Model_Age1<-coxph(Surv(waktu,status)~ Age_t1, data = DataCluster2, method = "breslow")
summary(Fit_Model_Age1)Call:
coxph(formula = Surv(waktu, status) ~ Age_t1, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
Age_t1 3.01112 20.31005 0.04172 72.17 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
Age_t1 20.31 0.04924 18.72 22.04
Concordance= 0.778 (se = 0.004 )
Likelihood ratio test= 5805 on 1 df, p=<2e-16
Wald test = 5209 on 1 df, p=<2e-16
Score (logrank) test = 9377 on 1 df, p=<2e-16## Variabel Age
Fit_Model_Age2<-coxph(Surv(waktu,status)~ Age_t2, data = DataCluster2, method = "breslow")
summary(Fit_Model_Age2)Call:
coxph(formula = Surv(waktu, status) ~ Age_t2, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
Age_t2 -2.42686 0.08831 0.13141 -18.47 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
Age_t2 0.08831 11.32 0.06826 0.1143
Concordance= 0.579 (se = 0.002 )
Likelihood ratio test= 828.9 on 1 df, p=<2e-16
Wald test = 341.1 on 1 df, p=<2e-16
Score (logrank) test = 544.8 on 1 df, p=<2e-16Variabel COPD
## Variabel COPD
Fit_Model_copd<-coxph(Surv(waktu,status)~ copd, data = DataCluster2, method = "breslow")
summary(Fit_Model_copd)Call:
coxph(formula = Surv(waktu, status) ~ copd, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
copd 1.08107 2.94784 0.04933 21.91 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
copd 2.948 0.3392 2.676 3.247
Concordance= 0.548 (se = 0.003 )
Likelihood ratio test= 372.9 on 1 df, p=<2e-16
Wald test = 480.2 on 1 df, p=<2e-16
Score (logrank) test = 528.6 on 1 df, p=<2e-16Variabel Inmsupr
## Variabel inmsupr
Fit_Model_inmsupr<-coxph(Surv(waktu,status)~ inmsupr, data = DataCluster2, method = "breslow")
summary(Fit_Model_inmsupr)Call:
coxph(formula = Surv(waktu, status) ~ inmsupr, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
inmsupr 0.95039 2.58673 0.07994 11.89 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
inmsupr 2.587 0.3866 2.212 3.025
Concordance= 0.516 (se = 0.002 )
Likelihood ratio test= 107.9 on 1 df, p=<2e-16
Wald test = 141.3 on 1 df, p=<2e-16
Score (logrank) test = 152.3 on 1 df, p=<2e-16Variabel Asthma
## Variabel Asthma
Fit_Model_Asthma<-coxph(Surv(waktu,status)~ asthma, data = DataCluster2, method = "breslow")
summary(Fit_Model_Asthma)Call:
coxph(formula = Surv(waktu, status) ~ asthma, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
asthma -0.2655 0.7668 0.1184 -2.243 0.0249 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
asthma 0.7668 1.304 0.608 0.9671
Concordance= 0.503 (se = 0.001 )
Likelihood ratio test= 5.48 on 1 df, p=0.02
Wald test = 5.03 on 1 df, p=0.02
Score (logrank) test = 5.06 on 1 df, p=0.02Variabel Cardivascular
## Variabel Cardiovascular
Fit_Model_Cardivascular<-coxph(Surv(waktu,status)~ cardiovascular, data = DataCluster2, method = "breslow")
summary(Fit_Model_Cardivascular)Call:
coxph(formula = Surv(waktu, status) ~ cardiovascular, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
cardiovascular 0.89826 2.45532 0.05917 15.18 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
cardiovascular 2.455 0.4073 2.186 2.757
Concordance= 0.529 (se = 0.002 )
Likelihood ratio test= 182.2 on 1 df, p=<2e-16
Wald test = 230.4 on 1 df, p=<2e-16
Score (logrank) test = 246.3 on 1 df, p=<2e-16Variabel Pregnancy
## Variabel Pregnancy
Fit_Model_Pregnancy<-coxph(Surv(waktu,status)~ pregnancy, data = DataCluster2, method = "breslow")
summary(Fit_Model_Pregnancy)Call:
coxph(formula = Surv(waktu, status) ~ pregnancy, data = DataCluster2,
method = "breslow")
n= 10054, number of events= 3258
coef exp(coef) se(coef) z Pr(>|z|)
pregnancy -1.0061 0.3656 0.7073 -1.422 0.155
exp(coef) exp(-coef) lower .95 upper .95
pregnancy 0.3656 2.735 0.09141 1.463
Concordance= 0.501 (se = 0 )
Likelihood ratio test= 2.91 on 1 df, p=0.09
Wald test = 2.02 on 1 df, p=0.2
Score (logrank) test = 2.2 on 1 df, p=0.19.3 Cluster 3
DataCluster3<- CovidData %>%
filter(cluster == 3)
DataCluster3[,c("sex","pneumonia","pregnancy","diabetes","copd","asthma","inmsupr","hypertension","cardiovascular","obesity","renal_chronic","tobacco","status","Age")] <- lapply(DataCluster3[,c("sex","pneumonia","pregnancy","diabetes","copd","asthma","inmsupr","hypertension","cardiovascular","obesity","renal_chronic","tobacco","status","Age")],as.factor)
summary(DataCluster3) sex pneumonia pregnancy diabetes copd asthma inmsupr
0:21185 0: 8917 0:33856 0:20517 0:32165 0:33217 0:32601
1:12713 1:24981 1: 42 1:13381 1: 1733 1: 681 1: 1297
hypertension cardiovascular obesity renal_chronic tobacco waktu
0:18703 0:31723 0:26091 0:31011 0:33880 Min. : 1.00
1:15195 1: 2175 1: 7807 1: 2887 1: 18 1st Qu.: 6.00
Median :10.00
Mean :15.76
3rd Qu.:16.00
Max. :95.00
status Age cluster
0: 1876 0:11145 1: 0
1:32022 1:22753 2: 0
3:33898
DataCluster3<- CovidData %>%
filter(cluster == 3)
head(DataCluster3) sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
1 0 1 0 0 0 0 0 0
2 1 1 0 0 0 0 0 1
3 1 1 0 1 0 0 0 0
4 0 1 0 0 1 1 0 1
5 0 1 0 0 0 0 0 1
6 1 1 0 0 0 0 0 1
cardiovascular obesity renal_chronic tobacco waktu status Age cluster
1 0 0 0 0 4 1 0 3
2 0 1 0 0 17 1 1 3
3 0 1 0 0 26 1 0 3
4 1 1 0 0 3 1 0 3
5 0 0 0 0 14 1 1 3
6 0 1 0 0 2 1 1 3
Before applying the extended cox model, it is necessary to test whether all variables are independent of time. There are two approaches to the proportional hazard assumption test, namely the graphical approach and the GOF approach.
a. Pendekatan Grafik
Variabel sex
fit<-survfit(Surv(waktu,status)~ sex, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "Jenis Kelamin",
legend.labs = c("Laki-Laki", "Perempuan")
)
Variabel pneumonia
fit<-survfit(Surv(waktu,status)~ pneumonia, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "Pneumonia",
legend.labs = c("no Pneumonia", "yes pneumonia")
)
Variabel Pregnancy
fit<-survfit(Surv(waktu,status)~ pregnancy, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "Pregnancy",
legend.labs = c("no pregnancy", "yes pregnancy")
)
Variabel diabetes
fit<-survfit(Surv(waktu,status)~ diabetes, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "Diabetes",
legend.labs = c("no Diabetes", "yes Diabetes")
)
Variabel Hypertension
fit<-survfit(Surv(waktu,status)~ hypertension, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "Hyperetension",
legend.labs = c("no hypertension", "yes hypertension")
)
Variabel obesity
fit<-survfit(Surv(waktu,status)~ obesity, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "Obesity",
legend.labs = c("no obesity", "yes obesity")
)
Variabel renal chronic
fit<-survfit(Surv(waktu,status)~ renal_chronic, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "Renal Chronic",
legend.labs = c("no renal chronic", "yes renal chronic")
)
Variabel tobacco
fit<-survfit(Surv(waktu,status)~ tobacco, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "Tobacco",
legend.labs = c("no tobacco", "yes tobacco")
)
Variabel Age
fit<-survfit(Surv(waktu,status)~ Age, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "Age",
legend.labs = c("Young", "Old")
)
Variabel COPD
fit<-survfit(Surv(waktu,status)~ copd, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "COPD",
legend.labs = c("no COPD", "yes COPD")
)
Variabel inmsupr
fit<-survfit(Surv(waktu,status)~ inmsupr, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "inmsupr",
legend.labs = c("no inmsupr", "yes inmsupr")
)
Variabel asthma
fit<-survfit(Surv(waktu,status)~ asthma, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "asthma",
legend.labs = c("no asthma", "yes asthma")
)
Variabel cardiovascular
fit<-survfit(Surv(waktu,status)~ cardiovascular, data=DataCluster3)
ggsurvplot(fit, data = DataCluster3, fun = "cumhaz",
legend = "top",
legend.title = "Cardiovascular",
legend.labs = c("No Cardiovascular", "Yes Cardiovascular")
)
b. Pendekatan GOF
fit_cluster3<-coxph(Surv(waktu,status)~ sex+pneumonia+Age+pregnancy+hypertension+obesity+tobacco+diabetes+renal_chronic+inmsupr+asthma+cardiovascular+copd, data = DataCluster3)
cek_fitt_all3<-cox.zph(fit_cluster3, transform="km", global=TRUE)
print(cek_fitt_all3) chisq df p
sex 1.42e+02 1 <2e-16
pneumonia 4.36e-01 1 0.51
Age 2.27e+02 1 <2e-16
pregnancy 1.11e-02 1 0.92
hypertension 7.44e+02 1 <2e-16
obesity 6.49e-01 1 0.42
tobacco 1.33e-02 1 0.91
diabetes 9.48e+02 1 <2e-16
renal_chronic 5.78e+02 1 <2e-16
inmsupr 1.23e+02 1 <2e-16
asthma 1.39e+00 1 0.24
cardiovascular 2.84e+02 1 <2e-16
copd 1.67e+02 1 <2e-16
GLOBAL 1.93e+03 13 <2e-16
There are 8 variables that do not meet the proportional hazard
assumption, namely: Sex, Age,
hypertension,
diabetes,renal_chronic, inmsupr,
cardiovascular, copd with a significance level
of 10%. then these eight variables will be interacted with the time
function, namely the heavside function on each variable. To be able to
determine the heavside function is to look at the survival probability
graph.
c. Identification of Covariate Non Proportional Hazard
Variabel Sex
# VARIABEL Sex
fit<-survfit(Surv(waktu,status)~ sex , data=DataCluster3)
summary(fit)Call: survfit(formula = Surv(waktu, status) ~ sex, data = DataCluster3)
sex=0
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 21185 495 0.9766 0.00104 0.9746 0.9787
2 20690 658 0.9456 0.00156 0.9425 0.9486
3 20032 839 0.9060 0.00201 0.9020 0.9099
4 19193 1072 0.8554 0.00242 0.8506 0.8601
5 18121 1243 0.7967 0.00277 0.7913 0.8021
6 16878 1291 0.7358 0.00303 0.7298 0.7417
7 15587 1376 0.6708 0.00323 0.6645 0.6772
8 14211 1398 0.6048 0.00336 0.5983 0.6114
9 12813 1332 0.5419 0.00342 0.5353 0.5487
10 11481 1247 0.4831 0.00343 0.4764 0.4899
11 10234 1062 0.4329 0.00340 0.4263 0.4397
12 9172 1060 0.3829 0.00334 0.3764 0.3895
13 8112 914 0.3398 0.00325 0.3335 0.3462
14 7198 811 0.3015 0.00315 0.2954 0.3077
15 6387 775 0.2649 0.00303 0.2590 0.2709
16 5612 672 0.2332 0.00291 0.2276 0.2389
17 4940 604 0.2047 0.00277 0.1993 0.2102
18 4336 514 0.1804 0.00264 0.1753 0.1857
19 3822 445 0.1594 0.00251 0.1546 0.1644
20 3377 358 0.1425 0.00240 0.1379 0.1473
21 3019 275 0.1295 0.00231 0.1251 0.1341
22 2744 259 0.1173 0.00221 0.1130 0.1217
23 2485 218 0.1070 0.00212 0.1029 0.1113
24 2267 193 0.0979 0.00204 0.0940 0.1020
25 2074 176 0.0896 0.00196 0.0858 0.0935
26 1898 125 0.0837 0.00190 0.0800 0.0875
27 1773 103 0.0788 0.00185 0.0753 0.0825
28 1670 113 0.0735 0.00179 0.0701 0.0771
29 1557 69 0.0702 0.00176 0.0669 0.0738
30 1488 86 0.0662 0.00171 0.0629 0.0696
31 1402 49 0.0639 0.00168 0.0607 0.0672
32 1353 44 0.0618 0.00165 0.0586 0.0651
33 1309 42 0.0598 0.00163 0.0567 0.0631
34 1267 33 0.0582 0.00161 0.0552 0.0615
35 1234 35 0.0566 0.00159 0.0536 0.0598
36 1199 30 0.0552 0.00157 0.0522 0.0583
37 1169 21 0.0542 0.00156 0.0512 0.0573
38 1148 18 0.0533 0.00154 0.0504 0.0565
39 1130 17 0.0525 0.00153 0.0496 0.0556
40 1113 15 0.0518 0.00152 0.0489 0.0549
41 1098 13 0.0512 0.00151 0.0483 0.0543
42 1085 13 0.0506 0.00151 0.0477 0.0536
43 1072 9 0.0502 0.00150 0.0473 0.0532
44 1063 8 0.0498 0.00149 0.0470 0.0528
45 1055 11 0.0493 0.00149 0.0464 0.0523
46 1044 7 0.0489 0.00148 0.0461 0.0519
47 1037 6 0.0487 0.00148 0.0459 0.0517
48 1031 7 0.0483 0.00147 0.0455 0.0513
49 1024 6 0.0481 0.00147 0.0453 0.0510
50 1018 3 0.0479 0.00147 0.0451 0.0509
51 1015 7 0.0476 0.00146 0.0448 0.0505
52 1008 4 0.0474 0.00146 0.0446 0.0503
53 1004 3 0.0473 0.00146 0.0445 0.0502
54 1001 3 0.0471 0.00146 0.0443 0.0500
55 998 2 0.0470 0.00145 0.0442 0.0500
56 996 4 0.0468 0.00145 0.0441 0.0498
57 992 1 0.0468 0.00145 0.0440 0.0497
58 991 2 0.0467 0.00145 0.0439 0.0496
59 989 4 0.0465 0.00145 0.0437 0.0494
60 985 1 0.0464 0.00145 0.0437 0.0494
61 984 1 0.0464 0.00145 0.0437 0.0493
62 983 1 0.0464 0.00144 0.0436 0.0493
63 982 1 0.0463 0.00144 0.0436 0.0492
65 981 1 0.0463 0.00144 0.0435 0.0492
73 980 1 0.0462 0.00144 0.0435 0.0491
74 979 2 0.0461 0.00144 0.0434 0.0490
76 977 1 0.0461 0.00144 0.0433 0.0490
78 976 1 0.0460 0.00144 0.0433 0.0489
sex=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 12713 325 0.9744 0.00140 0.9717 0.9772
2 12388 468 0.9376 0.00214 0.9334 0.9418
3 11920 598 0.8906 0.00277 0.8852 0.8960
4 11322 733 0.8329 0.00331 0.8265 0.8394
5 10589 804 0.7697 0.00373 0.7624 0.7770
6 9785 815 0.7056 0.00404 0.6977 0.7135
7 8970 881 0.6363 0.00427 0.6280 0.6447
8 8089 780 0.5749 0.00438 0.5664 0.5836
9 7309 779 0.5136 0.00443 0.5050 0.5224
10 6530 721 0.4569 0.00442 0.4484 0.4657
11 5809 577 0.4115 0.00436 0.4031 0.4202
12 5232 573 0.3665 0.00427 0.3582 0.3749
13 4659 486 0.3282 0.00416 0.3202 0.3365
14 4173 441 0.2936 0.00404 0.2857 0.3016
15 3732 423 0.2603 0.00389 0.2528 0.2680
16 3309 362 0.2318 0.00374 0.2246 0.2393
17 2947 283 0.2095 0.00361 0.2026 0.2167
18 2664 254 0.1896 0.00348 0.1829 0.1965
19 2410 202 0.1737 0.00336 0.1672 0.1804
20 2208 170 0.1603 0.00325 0.1541 0.1668
21 2038 170 0.1469 0.00314 0.1409 0.1532
22 1868 126 0.1370 0.00305 0.1312 0.1431
23 1742 109 0.1285 0.00297 0.1228 0.1344
24 1633 97 0.1208 0.00289 0.1153 0.1266
25 1536 90 0.1137 0.00282 0.1084 0.1194
26 1446 70 0.1082 0.00276 0.1030 0.1138
27 1376 67 0.1030 0.00270 0.0978 0.1084
28 1309 45 0.0994 0.00265 0.0944 0.1048
29 1264 55 0.0951 0.00260 0.0901 0.1003
30 1209 38 0.0921 0.00256 0.0872 0.0973
31 1171 43 0.0887 0.00252 0.0839 0.0938
32 1128 28 0.0865 0.00249 0.0818 0.0916
33 1100 23 0.0847 0.00247 0.0800 0.0897
34 1077 26 0.0827 0.00244 0.0780 0.0876
35 1051 16 0.0814 0.00243 0.0768 0.0863
36 1035 19 0.0799 0.00240 0.0753 0.0848
37 1016 17 0.0786 0.00239 0.0740 0.0834
38 999 14 0.0775 0.00237 0.0730 0.0823
39 985 8 0.0769 0.00236 0.0724 0.0816
40 977 11 0.0760 0.00235 0.0715 0.0807
41 966 11 0.0751 0.00234 0.0707 0.0798
42 955 6 0.0746 0.00233 0.0702 0.0794
43 949 5 0.0743 0.00233 0.0698 0.0790
44 944 3 0.0740 0.00232 0.0696 0.0787
45 941 4 0.0737 0.00232 0.0693 0.0784
46 937 2 0.0735 0.00232 0.0691 0.0782
47 935 2 0.0734 0.00231 0.0690 0.0781
48 933 4 0.0731 0.00231 0.0687 0.0777
49 929 4 0.0728 0.00230 0.0684 0.0774
50 925 1 0.0727 0.00230 0.0683 0.0773
51 924 4 0.0724 0.00230 0.0680 0.0770
52 920 4 0.0721 0.00229 0.0677 0.0767
53 916 3 0.0718 0.00229 0.0675 0.0764
54 913 3 0.0716 0.00229 0.0672 0.0762
56 910 2 0.0714 0.00228 0.0671 0.0760
57 908 2 0.0713 0.00228 0.0669 0.0759
66 906 1 0.0712 0.00228 0.0669 0.0758
70 905 1 0.0711 0.00228 0.0668 0.0757
72 904 1 0.0710 0.00228 0.0667 0.0756
77 903 1 0.0710 0.00228 0.0666 0.0756
93 902 1 0.0709 0.00228 0.0665 0.0755ggsurvplot(fit, data = DataCluster3,
pval = TRUE, conf.int = TRUE,
risk.table = TRUE, # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))
Fungsi waktu dalam variabel ini menggunakan fungsi waktu \(t\) karena variabel sex memiliki nevent pada variabel ini tidak konstan pada selang waktu tertentu
Variabel Age
# VARIABEL Age
fit<-survfit(Surv(waktu,status)~ Age , data=DataCluster3)
summary(fit)Call: survfit(formula = Surv(waktu, status) ~ Age, data = DataCluster3)
Age=0
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 11145 312 0.9720 0.001563 0.96895 0.9751
2 10833 393 0.9367 0.002306 0.93223 0.9413
3 10440 484 0.8933 0.002924 0.88760 0.8991
4 9956 609 0.8387 0.003484 0.83187 0.8455
5 9347 673 0.7783 0.003935 0.77061 0.7860
6 8674 689 0.7165 0.004269 0.70815 0.7249
7 7985 733 0.6507 0.004516 0.64190 0.6596
8 7252 728 0.5854 0.004667 0.57630 0.5946
9 6524 706 0.5220 0.004732 0.51284 0.5314
10 5818 660 0.4628 0.004723 0.45364 0.4722
11 5158 573 0.4114 0.004661 0.40236 0.4206
12 4585 587 0.3587 0.004543 0.34993 0.3677
13 3998 494 0.3144 0.004398 0.30590 0.3231
14 3504 445 0.2745 0.004227 0.26631 0.2829
15 3059 435 0.2354 0.004019 0.22770 0.2435
16 2624 348 0.2042 0.003819 0.19687 0.2118
17 2276 314 0.1760 0.003608 0.16911 0.1833
18 1962 281 0.1508 0.003390 0.14433 0.1576
19 1681 240 0.1293 0.003178 0.12321 0.1357
20 1441 184 0.1128 0.002996 0.10706 0.1188
21 1257 165 0.0980 0.002816 0.09261 0.1037
22 1092 136 0.0858 0.002653 0.08073 0.0911
23 956 122 0.0748 0.002492 0.07010 0.0799
24 834 99 0.0659 0.002351 0.06150 0.0707
25 735 94 0.0575 0.002205 0.05335 0.0620
26 641 60 0.0521 0.002106 0.04816 0.0564
27 581 63 0.0465 0.001994 0.04273 0.0506
28 518 57 0.0414 0.001886 0.03783 0.0452
29 461 47 0.0371 0.001791 0.03380 0.0408
30 414 45 0.0331 0.001695 0.02995 0.0366
31 369 28 0.0306 0.001631 0.02756 0.0340
32 341 29 0.0280 0.001563 0.02509 0.0312
33 312 26 0.0257 0.001498 0.02289 0.0288
34 286 24 0.0235 0.001435 0.02086 0.0265
35 262 8 0.0228 0.001414 0.02018 0.0257
36 254 20 0.0210 0.001358 0.01850 0.0238
37 234 20 0.0192 0.001300 0.01682 0.0219
38 214 12 0.0181 0.001264 0.01581 0.0208
39 202 10 0.0172 0.001233 0.01497 0.0198
40 192 8 0.0165 0.001207 0.01431 0.0191
41 184 9 0.0157 0.001178 0.01356 0.0182
42 175 5 0.0153 0.001161 0.01314 0.0177
43 170 4 0.0149 0.001147 0.01281 0.0173
44 166 4 0.0145 0.001134 0.01248 0.0169
45 162 8 0.0138 0.001106 0.01181 0.0162
46 154 3 0.0135 0.001095 0.01156 0.0159
47 151 2 0.0134 0.001088 0.01140 0.0157
48 149 4 0.0130 0.001073 0.01107 0.0153
49 145 2 0.0128 0.001066 0.01090 0.0151
50 143 3 0.0126 0.001055 0.01066 0.0148
51 140 4 0.0122 0.001040 0.01033 0.0144
52 136 1 0.0121 0.001036 0.01024 0.0143
53 135 3 0.0118 0.001025 0.01000 0.0140
54 132 2 0.0117 0.001017 0.00983 0.0138
56 130 2 0.0115 0.001009 0.00967 0.0136
57 128 2 0.0113 0.001001 0.00950 0.0134
59 126 1 0.0112 0.000998 0.00942 0.0134
60 125 1 0.0111 0.000994 0.00934 0.0133
62 124 1 0.0110 0.000990 0.00926 0.0132
66 123 1 0.0109 0.000986 0.00918 0.0131
76 122 1 0.0109 0.000982 0.00909 0.0130
Age=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 22753 508 0.9777 0.000979 0.9758 0.9796
2 22245 733 0.9455 0.001505 0.9425 0.9484
3 21512 953 0.9036 0.001957 0.8997 0.9074
4 20559 1196 0.8510 0.002361 0.8464 0.8556
5 19363 1374 0.7906 0.002697 0.7854 0.7959
6 17989 1417 0.7283 0.002949 0.7226 0.7341
7 16572 1524 0.6614 0.003137 0.6552 0.6675
8 15048 1450 0.5976 0.003251 0.5913 0.6040
9 13598 1405 0.5359 0.003306 0.5294 0.5424
10 12193 1308 0.4784 0.003312 0.4720 0.4849
11 10885 1066 0.4315 0.003284 0.4252 0.4380
12 9819 1046 0.3856 0.003227 0.3793 0.3920
13 8773 906 0.3458 0.003153 0.3396 0.3520
14 7867 807 0.3103 0.003067 0.3043 0.3164
15 7060 763 0.2768 0.002966 0.2710 0.2826
16 6297 686 0.2466 0.002858 0.2411 0.2523
17 5611 573 0.2214 0.002753 0.2161 0.2269
18 5038 487 0.2000 0.002652 0.1949 0.2053
19 4551 407 0.1821 0.002559 0.1772 0.1872
20 4144 344 0.1670 0.002473 0.1622 0.1719
21 3800 280 0.1547 0.002397 0.1501 0.1595
22 3520 249 0.1438 0.002326 0.1393 0.1484
23 3271 205 0.1348 0.002264 0.1304 0.1393
24 3066 191 0.1264 0.002203 0.1221 0.1307
25 2875 172 0.1188 0.002145 0.1147 0.1231
26 2703 135 0.1129 0.002098 0.1088 0.1171
27 2568 107 0.1082 0.002059 0.1042 0.1123
28 2461 101 0.1037 0.002021 0.0998 0.1078
29 2360 77 0.1003 0.001992 0.0965 0.1043
30 2283 79 0.0969 0.001961 0.0931 0.1008
31 2204 64 0.0941 0.001935 0.0903 0.0979
32 2140 43 0.0922 0.001918 0.0885 0.0960
33 2097 39 0.0904 0.001902 0.0868 0.0943
34 2058 35 0.0889 0.001887 0.0853 0.0927
35 2023 43 0.0870 0.001869 0.0834 0.0908
36 1980 29 0.0857 0.001856 0.0822 0.0895
37 1951 18 0.0850 0.001848 0.0814 0.0887
38 1933 20 0.0841 0.001840 0.0805 0.0878
39 1913 15 0.0834 0.001833 0.0799 0.0871
40 1898 18 0.0826 0.001825 0.0791 0.0863
41 1880 15 0.0820 0.001819 0.0785 0.0856
42 1865 14 0.0814 0.001812 0.0779 0.0850
43 1851 10 0.0809 0.001808 0.0774 0.0845
44 1841 7 0.0806 0.001805 0.0771 0.0842
45 1834 7 0.0803 0.001802 0.0768 0.0839
46 1827 6 0.0800 0.001799 0.0766 0.0836
47 1821 6 0.0798 0.001796 0.0763 0.0834
48 1815 7 0.0795 0.001793 0.0760 0.0831
49 1808 8 0.0791 0.001789 0.0757 0.0827
50 1800 1 0.0791 0.001789 0.0756 0.0827
51 1799 7 0.0788 0.001786 0.0753 0.0823
52 1792 7 0.0785 0.001783 0.0750 0.0820
53 1785 3 0.0783 0.001781 0.0749 0.0819
54 1782 4 0.0781 0.001779 0.0747 0.0817
55 1778 2 0.0781 0.001778 0.0746 0.0816
56 1776 4 0.0779 0.001777 0.0745 0.0814
57 1772 1 0.0778 0.001776 0.0744 0.0814
58 1771 2 0.0777 0.001775 0.0743 0.0813
59 1769 3 0.0776 0.001774 0.0742 0.0812
61 1766 1 0.0776 0.001773 0.0742 0.0811
63 1765 1 0.0775 0.001773 0.0741 0.0811
65 1764 1 0.0775 0.001772 0.0741 0.0810
70 1763 1 0.0774 0.001772 0.0740 0.0810
72 1762 1 0.0774 0.001772 0.0740 0.0809
73 1761 1 0.0774 0.001771 0.0740 0.0809
74 1760 2 0.0773 0.001770 0.0739 0.0808
77 1758 1 0.0772 0.001770 0.0738 0.0808
78 1757 1 0.0772 0.001769 0.0738 0.0807
93 1756 1 0.0771 0.001769 0.0737 0.0807ggsurvplot(fit, data = DataCluster3,
pval = TRUE, conf.int = TRUE,
risk.table = TRUE, # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))
Note the graph of the elderly patient’s speed drops drastically on day 27 but after day 27 it was constant until the end of the study. so the function is
\[ g(t)= \begin{cases} 1, & \mbox{jika}\ t\mbox{ < 27} \\ 0, & \mbox{jika}\ t\mbox{ >= 27} \end{cases}\]
Variabel Hypertension
# VARIABEL hypertension
fit<-survfit(Surv(waktu,status)~ hypertension , data=DataCluster3)
summary(fit)Call: survfit(formula = Surv(waktu, status) ~ hypertension, data = DataCluster3)
hypertension=0
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 18703 478 0.97444 0.001154 0.97218 0.97671
2 18225 624 0.94108 0.001722 0.93771 0.94446
3 17601 819 0.89729 0.002220 0.89295 0.90165
4 16782 1022 0.84265 0.002663 0.83744 0.84788
5 15760 1138 0.78180 0.003020 0.77590 0.78774
6 14622 1160 0.71978 0.003284 0.71337 0.72624
7 13462 1254 0.65273 0.003481 0.64594 0.65959
8 12208 1233 0.58680 0.003601 0.57979 0.59390
9 10975 1242 0.52040 0.003653 0.51329 0.52761
10 9733 1139 0.45950 0.003644 0.45241 0.46670
11 8594 943 0.40908 0.003595 0.40209 0.41619
12 7651 943 0.35866 0.003507 0.35185 0.36560
13 6708 846 0.31343 0.003392 0.30685 0.32014
14 5862 752 0.27322 0.003258 0.26691 0.27968
15 5110 687 0.23649 0.003107 0.23047 0.24266
16 4423 600 0.20441 0.002949 0.19871 0.21027
17 3823 526 0.17628 0.002786 0.17090 0.18183
18 3297 465 0.15142 0.002621 0.14637 0.15664
19 2832 403 0.12987 0.002458 0.12514 0.13478
20 2429 307 0.11346 0.002319 0.10900 0.11810
21 2122 293 0.09779 0.002172 0.09363 0.10214
22 1829 242 0.08485 0.002038 0.08095 0.08894
23 1587 221 0.07304 0.001903 0.06940 0.07686
24 1366 174 0.06373 0.001786 0.06033 0.06733
25 1192 163 0.05502 0.001667 0.05185 0.05838
26 1029 122 0.04849 0.001571 0.04551 0.05167
27 907 105 0.04288 0.001481 0.04007 0.04588
28 802 109 0.03705 0.001381 0.03444 0.03986
29 693 75 0.03304 0.001307 0.03058 0.03571
30 618 70 0.02930 0.001233 0.02698 0.03182
31 548 58 0.02620 0.001168 0.02401 0.02859
32 490 38 0.02417 0.001123 0.02206 0.02647
33 452 36 0.02224 0.001078 0.02023 0.02446
34 416 30 0.02064 0.001040 0.01870 0.02278
35 386 32 0.01893 0.000996 0.01707 0.02098
36 354 32 0.01722 0.000951 0.01545 0.01919
37 322 26 0.01583 0.000913 0.01414 0.01772
38 296 20 0.01476 0.000882 0.01313 0.01659
39 276 17 0.01385 0.000854 0.01227 0.01563
40 259 15 0.01305 0.000830 0.01152 0.01478
41 244 15 0.01224 0.000804 0.01077 0.01393
42 229 13 0.01155 0.000781 0.01011 0.01319
43 216 6 0.01123 0.000770 0.00982 0.01284
44 210 7 0.01085 0.000758 0.00947 0.01245
45 203 11 0.01027 0.000737 0.00892 0.01182
46 192 6 0.00994 0.000726 0.00862 0.01147
47 186 6 0.00962 0.000714 0.00832 0.01113
48 180 7 0.00925 0.000700 0.00797 0.01073
49 173 6 0.00893 0.000688 0.00768 0.01038
50 167 2 0.00882 0.000684 0.00758 0.01027
51 165 8 0.00839 0.000667 0.00718 0.00981
52 157 5 0.00813 0.000657 0.00694 0.00952
53 152 3 0.00797 0.000650 0.00679 0.00935
54 149 3 0.00781 0.000644 0.00664 0.00918
55 146 2 0.00770 0.000639 0.00654 0.00906
56 144 3 0.00754 0.000632 0.00640 0.00889
58 141 1 0.00749 0.000630 0.00635 0.00883
59 140 3 0.00733 0.000624 0.00620 0.00865
60 137 1 0.00727 0.000621 0.00615 0.00860
61 136 1 0.00722 0.000619 0.00610 0.00854
63 135 1 0.00716 0.000617 0.00605 0.00848
65 134 1 0.00711 0.000614 0.00600 0.00842
66 133 1 0.00706 0.000612 0.00595 0.00837
72 132 1 0.00700 0.000610 0.00591 0.00831
73 131 1 0.00695 0.000607 0.00586 0.00825
74 130 1 0.00690 0.000605 0.00581 0.00819
78 129 1 0.00684 0.000603 0.00576 0.00813
hypertension=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 15195 342 0.977 0.00120 0.975 0.980
2 14853 502 0.944 0.00186 0.941 0.948
3 14351 618 0.904 0.00239 0.899 0.908
4 13733 783 0.852 0.00288 0.847 0.858
5 12950 909 0.792 0.00329 0.786 0.799
6 12041 946 0.730 0.00360 0.723 0.737
7 11095 1003 0.664 0.00383 0.657 0.672
8 10092 945 0.602 0.00397 0.594 0.610
9 9147 869 0.545 0.00404 0.537 0.553
10 8278 829 0.490 0.00406 0.482 0.498
11 7449 696 0.444 0.00403 0.437 0.452
12 6753 690 0.399 0.00397 0.391 0.407
13 6063 554 0.363 0.00390 0.355 0.370
14 5509 500 0.330 0.00381 0.322 0.337
15 5009 511 0.296 0.00370 0.289 0.303
16 4498 434 0.267 0.00359 0.261 0.275
17 4064 361 0.244 0.00348 0.237 0.251
18 3703 303 0.224 0.00338 0.217 0.230
19 3400 244 0.208 0.00329 0.201 0.214
20 3156 221 0.193 0.00320 0.187 0.200
21 2935 152 0.183 0.00314 0.177 0.189
22 2783 143 0.174 0.00307 0.168 0.180
23 2640 106 0.167 0.00302 0.161 0.173
24 2534 116 0.159 0.00297 0.153 0.165
25 2418 103 0.152 0.00292 0.147 0.158
26 2315 73 0.148 0.00288 0.142 0.153
27 2242 65 0.143 0.00284 0.138 0.149
28 2177 49 0.140 0.00282 0.135 0.146
29 2128 49 0.137 0.00279 0.131 0.142
30 2079 54 0.133 0.00276 0.128 0.139
31 2025 34 0.131 0.00274 0.126 0.137
32 1991 34 0.129 0.00272 0.124 0.134
33 1957 29 0.127 0.00270 0.122 0.132
34 1928 29 0.125 0.00268 0.120 0.130
35 1899 19 0.124 0.00267 0.119 0.129
36 1880 17 0.123 0.00266 0.118 0.128
37 1863 12 0.122 0.00265 0.117 0.127
38 1851 12 0.121 0.00265 0.116 0.126
39 1839 8 0.121 0.00264 0.115 0.126
40 1831 11 0.120 0.00263 0.115 0.125
41 1820 9 0.119 0.00263 0.114 0.124
42 1811 6 0.119 0.00262 0.114 0.124
43 1805 8 0.118 0.00262 0.113 0.124
44 1797 4 0.118 0.00262 0.113 0.123
45 1793 4 0.118 0.00261 0.113 0.123
46 1789 3 0.118 0.00261 0.113 0.123
47 1786 2 0.117 0.00261 0.112 0.123
48 1784 4 0.117 0.00261 0.112 0.122
49 1780 4 0.117 0.00261 0.112 0.122
50 1776 2 0.117 0.00261 0.112 0.122
51 1774 3 0.117 0.00260 0.112 0.122
52 1771 3 0.116 0.00260 0.111 0.122
53 1768 3 0.116 0.00260 0.111 0.121
54 1765 3 0.116 0.00260 0.111 0.121
56 1762 3 0.116 0.00260 0.111 0.121
57 1759 3 0.116 0.00259 0.111 0.121
58 1756 1 0.115 0.00259 0.111 0.121
59 1755 1 0.115 0.00259 0.110 0.121
62 1754 1 0.115 0.00259 0.110 0.121
70 1753 1 0.115 0.00259 0.110 0.120
74 1752 1 0.115 0.00259 0.110 0.120
76 1751 1 0.115 0.00259 0.110 0.120
77 1750 1 0.115 0.00259 0.110 0.120
93 1749 1 0.115 0.00259 0.110 0.120ggsurvplot(fit, data = DataCluster3,
pval = TRUE, conf.int = TRUE,
risk.table = "abs_pct", # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))
Pay attention to the graph of the speed of the hypertension patient dropping rapidly on the 31st day but after the 31st day it was constant until the end of the study. so the function of the upper side is
\[ g(t)= \begin{cases} 1, & \mbox{jika}\ t\mbox{ < 31} \\ 0, & \mbox{jika}\ t\mbox{ >= 31} \end{cases}\] ##### Variabel Diabetes
# VARIABEL diabetes
fit<-survfit(Surv(waktu,status)~ diabetes, data=DataCluster3)
summary(fit)Call: survfit(formula = Surv(waktu, status) ~ diabetes, data = DataCluster3)
diabetes=0
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 20517 500 0.9756 0.001076 0.9735 0.9777
2 20017 659 0.9435 0.001612 0.9404 0.9467
3 19358 851 0.9020 0.002075 0.8980 0.9061
4 18507 1063 0.8502 0.002491 0.8454 0.8551
5 17444 1256 0.7890 0.002849 0.7834 0.7946
6 16188 1271 0.7271 0.003110 0.7210 0.7332
7 14917 1368 0.6604 0.003306 0.6539 0.6669
8 13549 1347 0.5947 0.003427 0.5880 0.6015
9 12202 1318 0.5305 0.003484 0.5237 0.5374
10 10884 1273 0.4684 0.003484 0.4617 0.4753
11 9611 1042 0.4177 0.003443 0.4110 0.4245
12 8569 1030 0.3675 0.003366 0.3609 0.3741
13 7539 922 0.3225 0.003263 0.3162 0.3290
14 6617 822 0.2824 0.003143 0.2764 0.2887
15 5795 774 0.2447 0.003001 0.2389 0.2507
16 5021 684 0.2114 0.002850 0.2059 0.2170
17 4337 597 0.1823 0.002695 0.1771 0.1876
18 3740 526 0.1567 0.002538 0.1518 0.1617
19 3214 444 0.1350 0.002386 0.1304 0.1398
20 2770 355 0.1177 0.002250 0.1134 0.1222
21 2415 289 0.1036 0.002128 0.0995 0.1079
22 2126 281 0.0899 0.001997 0.0861 0.0939
23 1845 236 0.0784 0.001877 0.0748 0.0822
24 1609 197 0.0688 0.001767 0.0654 0.0724
25 1412 177 0.0602 0.001660 0.0570 0.0635
26 1235 125 0.0541 0.001579 0.0511 0.0573
27 1110 113 0.0486 0.001501 0.0457 0.0516
28 997 107 0.0434 0.001422 0.0407 0.0463
29 890 87 0.0391 0.001354 0.0366 0.0419
30 803 87 0.0349 0.001281 0.0325 0.0375
31 716 67 0.0316 0.001222 0.0293 0.0341
32 649 46 0.0294 0.001179 0.0272 0.0318
33 603 43 0.0273 0.001138 0.0252 0.0296
34 560 37 0.0255 0.001100 0.0234 0.0277
35 523 39 0.0236 0.001060 0.0216 0.0258
36 484 38 0.0217 0.001018 0.0198 0.0238
37 446 31 0.0202 0.000983 0.0184 0.0222
38 415 20 0.0193 0.000959 0.0175 0.0212
39 395 13 0.0186 0.000944 0.0169 0.0206
40 382 19 0.0177 0.000920 0.0160 0.0196
41 363 19 0.0168 0.000896 0.0151 0.0186
42 344 13 0.0161 0.000880 0.0145 0.0180
43 331 8 0.0157 0.000869 0.0141 0.0175
44 323 6 0.0155 0.000861 0.0139 0.0172
45 317 10 0.0150 0.000848 0.0134 0.0167
46 307 5 0.0147 0.000841 0.0132 0.0165
47 302 7 0.0144 0.000831 0.0128 0.0161
48 295 8 0.0140 0.000820 0.0125 0.0157
49 287 7 0.0136 0.000810 0.0121 0.0153
50 280 3 0.0135 0.000806 0.0120 0.0152
51 277 7 0.0132 0.000796 0.0117 0.0148
52 270 6 0.0129 0.000787 0.0114 0.0145
53 264 2 0.0128 0.000784 0.0113 0.0144
54 262 2 0.0127 0.000781 0.0112 0.0143
55 260 1 0.0126 0.000779 0.0112 0.0142
56 259 5 0.0124 0.000772 0.0110 0.0140
57 254 2 0.0123 0.000769 0.0109 0.0139
58 252 1 0.0122 0.000767 0.0108 0.0138
59 251 3 0.0121 0.000763 0.0107 0.0137
60 248 1 0.0120 0.000761 0.0106 0.0136
61 247 1 0.0120 0.000760 0.0106 0.0136
62 246 1 0.0119 0.000758 0.0105 0.0135
65 245 1 0.0119 0.000757 0.0105 0.0135
66 244 1 0.0118 0.000755 0.0105 0.0134
70 243 1 0.0118 0.000754 0.0104 0.0134
72 242 1 0.0117 0.000752 0.0104 0.0133
73 241 1 0.0117 0.000751 0.0103 0.0133
74 240 1 0.0116 0.000749 0.0103 0.0132
78 239 1 0.0116 0.000748 0.0102 0.0132
93 238 1 0.0116 0.000746 0.0102 0.0131
diabetes=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 13381 320 0.976 0.00132 0.974 0.979
2 13061 467 0.941 0.00203 0.937 0.945
3 12594 586 0.897 0.00262 0.892 0.903
4 12008 742 0.842 0.00315 0.836 0.848
5 11266 791 0.783 0.00356 0.776 0.790
6 10475 835 0.720 0.00388 0.713 0.728
7 9640 889 0.654 0.00411 0.646 0.662
8 8751 831 0.592 0.00425 0.584 0.600
9 7920 793 0.533 0.00431 0.524 0.541
10 7127 695 0.481 0.00432 0.472 0.489
11 6432 597 0.436 0.00429 0.428 0.445
12 5835 603 0.391 0.00422 0.383 0.399
13 5232 478 0.355 0.00414 0.347 0.363
14 4754 430 0.323 0.00404 0.315 0.331
15 4324 424 0.291 0.00393 0.284 0.299
16 3900 350 0.265 0.00382 0.258 0.273
17 3550 290 0.244 0.00371 0.236 0.251
18 3260 242 0.226 0.00361 0.219 0.233
19 3018 203 0.210 0.00352 0.204 0.217
20 2815 173 0.197 0.00344 0.191 0.204
21 2642 156 0.186 0.00336 0.179 0.192
22 2486 104 0.178 0.00331 0.172 0.185
23 2382 91 0.171 0.00326 0.165 0.178
24 2291 93 0.164 0.00320 0.158 0.171
25 2198 89 0.158 0.00315 0.152 0.164
26 2109 70 0.152 0.00311 0.146 0.159
27 2039 57 0.148 0.00307 0.142 0.154
28 1982 51 0.144 0.00304 0.138 0.150
29 1931 37 0.142 0.00301 0.136 0.148
30 1894 37 0.139 0.00299 0.133 0.145
31 1857 25 0.137 0.00297 0.131 0.143
32 1832 26 0.135 0.00295 0.129 0.141
33 1806 22 0.133 0.00294 0.128 0.139
34 1784 22 0.132 0.00292 0.126 0.138
35 1762 12 0.131 0.00291 0.125 0.137
36 1750 11 0.130 0.00291 0.124 0.136
37 1739 7 0.129 0.00290 0.124 0.135
38 1732 12 0.129 0.00289 0.123 0.134
39 1720 12 0.128 0.00288 0.122 0.133
40 1708 7 0.127 0.00288 0.122 0.133
41 1701 5 0.127 0.00288 0.121 0.133
42 1696 6 0.126 0.00287 0.121 0.132
43 1690 6 0.126 0.00287 0.120 0.132
44 1684 5 0.125 0.00286 0.120 0.131
45 1679 5 0.125 0.00286 0.120 0.131
46 1674 4 0.125 0.00286 0.119 0.131
47 1670 1 0.125 0.00286 0.119 0.130
48 1669 3 0.125 0.00285 0.119 0.130
49 1666 3 0.124 0.00285 0.119 0.130
50 1663 1 0.124 0.00285 0.119 0.130
51 1662 4 0.124 0.00285 0.118 0.130
52 1658 2 0.124 0.00285 0.118 0.129
53 1656 4 0.123 0.00284 0.118 0.129
54 1652 4 0.123 0.00284 0.118 0.129
55 1648 1 0.123 0.00284 0.118 0.129
56 1647 1 0.123 0.00284 0.118 0.129
57 1646 1 0.123 0.00284 0.117 0.129
58 1645 1 0.123 0.00284 0.117 0.129
59 1644 1 0.123 0.00284 0.117 0.128
63 1643 1 0.123 0.00284 0.117 0.128
74 1642 1 0.123 0.00284 0.117 0.128
76 1641 1 0.123 0.00283 0.117 0.128
77 1640 1 0.122 0.00283 0.117 0.128ggsurvplot(fit, data = DataCluster3,
pval = TRUE, conf.int = TRUE,
risk.table = "nrisk_cumcensor", # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))
Notice the graph speed of the diabetes patient drops rapidly on day 31st but after the 31st day constant until the end of the study. so the heavside function is
\[ g(t)= \begin{cases} 1, & \mbox{jika}\ t\mbox{ < 30} \\ 0, & \mbox{jika}\ t\mbox{ >= 30} \end{cases}\]
Variabel Renal Chronic
# VARIABEL Renal Chronic
fit<-survfit(Surv(waktu,status)~ renal_chronic, data=DataCluster3)
summary(fit)Call: survfit(formula = Surv(waktu, status) ~ renal_chronic, data = DataCluster3)
renal_chronic=0
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 31011 721 0.9768 0.000856 0.9751 0.9784
2 30290 1015 0.9440 0.001305 0.9415 0.9466
3 29275 1254 0.9036 0.001676 0.9003 0.9069
4 28021 1604 0.8519 0.002017 0.8479 0.8558
5 26417 1847 0.7923 0.002304 0.7878 0.7968
6 24570 1898 0.7311 0.002518 0.7262 0.7360
7 22672 2066 0.6645 0.002681 0.6592 0.6697
8 20606 1997 0.6001 0.002782 0.5946 0.6056
9 18609 1938 0.5376 0.002831 0.5321 0.5432
10 16671 1856 0.4777 0.002836 0.4722 0.4833
11 14815 1542 0.4280 0.002810 0.4225 0.4336
12 13273 1532 0.3786 0.002754 0.3732 0.3840
13 11741 1316 0.3362 0.002683 0.3310 0.3415
14 10425 1187 0.2979 0.002597 0.2928 0.3030
15 9238 1129 0.2615 0.002495 0.2566 0.2664
16 8109 986 0.2297 0.002389 0.2251 0.2344
17 7123 851 0.2023 0.002281 0.1978 0.2068
18 6272 719 0.1791 0.002177 0.1748 0.1834
19 5553 622 0.1590 0.002077 0.1550 0.1631
20 4931 493 0.1431 0.001989 0.1393 0.1471
21 4438 414 0.1298 0.001908 0.1261 0.1336
22 4024 368 0.1179 0.001831 0.1144 0.1215
23 3656 312 0.1078 0.001761 0.1044 0.1113
24 3344 281 0.0988 0.001694 0.0955 0.1021
25 3063 245 0.0909 0.001632 0.0877 0.0941
26 2818 182 0.0850 0.001584 0.0820 0.0882
27 2636 164 0.0797 0.001538 0.0768 0.0828
28 2472 152 0.0748 0.001494 0.0719 0.0778
29 2320 116 0.0711 0.001459 0.0683 0.0740
30 2204 116 0.0673 0.001423 0.0646 0.0702
31 2088 86 0.0646 0.001395 0.0619 0.0674
32 2002 68 0.0624 0.001373 0.0597 0.0651
33 1934 61 0.0604 0.001353 0.0578 0.0631
34 1873 56 0.0586 0.001334 0.0560 0.0613
35 1817 50 0.0570 0.001316 0.0545 0.0596
36 1767 47 0.0555 0.001300 0.0530 0.0581
37 1720 34 0.0544 0.001288 0.0519 0.0570
38 1686 29 0.0534 0.001277 0.0510 0.0560
39 1657 22 0.0527 0.001269 0.0503 0.0553
40 1635 23 0.0520 0.001261 0.0496 0.0545
41 1612 22 0.0513 0.001252 0.0489 0.0538
42 1590 18 0.0507 0.001246 0.0483 0.0532
43 1572 14 0.0502 0.001240 0.0479 0.0527
44 1558 11 0.0499 0.001236 0.0475 0.0524
45 1547 14 0.0494 0.001231 0.0471 0.0519
46 1533 9 0.0491 0.001228 0.0468 0.0516
47 1524 8 0.0489 0.001224 0.0465 0.0513
48 1516 11 0.0485 0.001220 0.0462 0.0510
49 1505 9 0.0482 0.001217 0.0459 0.0507
50 1496 3 0.0481 0.001216 0.0458 0.0506
51 1493 10 0.0478 0.001212 0.0455 0.0503
52 1483 8 0.0476 0.001209 0.0453 0.0500
53 1475 4 0.0474 0.001207 0.0451 0.0499
54 1471 5 0.0473 0.001205 0.0450 0.0497
55 1466 2 0.0472 0.001204 0.0449 0.0496
56 1464 5 0.0470 0.001202 0.0447 0.0495
57 1459 1 0.0470 0.001202 0.0447 0.0494
58 1458 2 0.0470 0.001201 0.0447 0.0494
59 1456 4 0.0468 0.001200 0.0445 0.0492
60 1452 1 0.0468 0.001199 0.0445 0.0492
61 1451 1 0.0468 0.001199 0.0445 0.0492
62 1450 1 0.0467 0.001198 0.0444 0.0491
63 1449 1 0.0467 0.001198 0.0444 0.0491
65 1448 1 0.0467 0.001198 0.0444 0.0491
66 1447 1 0.0466 0.001197 0.0443 0.0490
70 1446 1 0.0466 0.001197 0.0443 0.0490
72 1445 1 0.0466 0.001197 0.0443 0.0490
73 1444 1 0.0465 0.001196 0.0442 0.0489
74 1443 2 0.0465 0.001195 0.0442 0.0489
76 1441 1 0.0464 0.001195 0.0442 0.0488
77 1440 1 0.0464 0.001195 0.0441 0.0488
78 1439 1 0.0464 0.001194 0.0441 0.0488
renal_chronic=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 2887 99 0.966 0.00339 0.959 0.972
2 2788 111 0.927 0.00483 0.918 0.937
3 2677 183 0.864 0.00638 0.851 0.876
4 2494 201 0.794 0.00752 0.780 0.809
5 2293 200 0.725 0.00831 0.709 0.741
6 2093 208 0.653 0.00886 0.636 0.671
7 1885 191 0.587 0.00916 0.569 0.605
8 1694 181 0.524 0.00929 0.506 0.543
9 1513 173 0.464 0.00928 0.446 0.483
10 1340 112 0.425 0.00920 0.408 0.444
11 1228 97 0.392 0.00908 0.374 0.410
12 1131 101 0.357 0.00892 0.340 0.375
13 1030 84 0.328 0.00874 0.311 0.345
14 946 65 0.305 0.00857 0.289 0.322
15 881 69 0.281 0.00837 0.265 0.298
16 812 48 0.265 0.00821 0.249 0.281
17 764 36 0.252 0.00808 0.237 0.269
18 728 49 0.235 0.00789 0.220 0.251
19 679 25 0.227 0.00779 0.212 0.242
20 654 35 0.214 0.00764 0.200 0.230
21 619 31 0.204 0.00750 0.189 0.219
22 588 17 0.198 0.00741 0.184 0.213
23 571 15 0.193 0.00734 0.179 0.208
24 556 9 0.189 0.00729 0.176 0.204
25 547 21 0.182 0.00718 0.169 0.197
26 526 13 0.178 0.00711 0.164 0.192
27 513 6 0.176 0.00708 0.162 0.190
28 507 6 0.174 0.00705 0.160 0.188
29 501 8 0.171 0.00700 0.158 0.185
30 493 8 0.168 0.00696 0.155 0.182
31 485 6 0.166 0.00692 0.153 0.180
32 479 4 0.165 0.00690 0.152 0.179
33 475 4 0.163 0.00688 0.150 0.177
34 471 3 0.162 0.00686 0.149 0.176
35 468 1 0.162 0.00685 0.149 0.176
36 467 2 0.161 0.00684 0.148 0.175
37 465 4 0.160 0.00682 0.147 0.174
38 461 3 0.159 0.00680 0.146 0.173
39 458 3 0.158 0.00678 0.145 0.171
40 455 3 0.157 0.00676 0.144 0.170
41 452 2 0.156 0.00675 0.143 0.170
42 450 1 0.156 0.00674 0.143 0.169
45 449 1 0.155 0.00674 0.143 0.169
49 448 1 0.155 0.00673 0.142 0.169
50 447 1 0.154 0.00673 0.142 0.168
51 446 1 0.154 0.00672 0.142 0.168
53 445 2 0.153 0.00671 0.141 0.167
54 443 1 0.153 0.00670 0.141 0.167
56 442 1 0.153 0.00670 0.140 0.166
57 441 2 0.152 0.00668 0.140 0.166
93 439 1 0.152 0.00668 0.139 0.165ggsurvplot(fit, data = DataCluster3,
pval = TRUE, conf.int = TRUE,
risk.table = TRUE, # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))
Notice the graph speed of the renal chronic patient drops rapidly on day 31st but after the 31st day constant until the end of the study. so the heavside function is
\[ g(t)= \begin{cases} 1, & \mbox{if}\ t\mbox{ < 31} \\ 0, & \mbox{if}\ t\mbox{ >= 31} \end{cases}\] ##### Varaibel inmsupr
# VARIABEL inmsupr
fit<-survfit(Surv(waktu,status)~ inmsupr, data=DataCluster3)
summary(fit)Call: survfit(formula = Surv(waktu, status) ~ inmsupr, data = DataCluster3)
inmsupr=0
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 32601 766 0.9765 0.000839 0.9749 0.9781
2 31835 1058 0.9441 0.001273 0.9416 0.9465
3 30777 1355 0.9025 0.001643 0.8993 0.9057
4 29422 1720 0.8497 0.001979 0.8459 0.8536
5 27702 1964 0.7895 0.002258 0.7851 0.7939
6 25738 2031 0.7272 0.002467 0.7224 0.7320
7 23707 2173 0.6605 0.002623 0.6554 0.6657
8 21534 2087 0.5965 0.002717 0.5912 0.6019
9 19447 2057 0.5334 0.002763 0.5280 0.5389
10 17390 1910 0.4748 0.002766 0.4694 0.4803
11 15480 1581 0.4263 0.002739 0.4210 0.4317
12 13899 1576 0.3780 0.002685 0.3728 0.3833
13 12323 1367 0.3361 0.002616 0.3310 0.3412
14 10956 1220 0.2986 0.002535 0.2937 0.3037
15 9736 1155 0.2632 0.002439 0.2585 0.2680
16 8581 1007 0.2323 0.002339 0.2278 0.2370
17 7574 861 0.2059 0.002240 0.2016 0.2104
18 6713 742 0.1832 0.002142 0.1790 0.1874
19 5971 633 0.1637 0.002049 0.1598 0.1678
20 5338 516 0.1479 0.001966 0.1441 0.1518
21 4822 433 0.1346 0.001890 0.1310 0.1384
22 4389 368 0.1233 0.001821 0.1198 0.1270
23 4021 320 0.1135 0.001757 0.1101 0.1170
24 3701 282 0.1049 0.001697 0.1016 0.1083
25 3419 256 0.0970 0.001639 0.0939 0.1003
26 3163 190 0.0912 0.001594 0.0881 0.0944
27 2973 166 0.0861 0.001554 0.0831 0.0892
28 2807 157 0.0813 0.001513 0.0784 0.0843
29 2650 119 0.0776 0.001482 0.0748 0.0806
30 2531 120 0.0740 0.001449 0.0712 0.0769
31 2411 90 0.0712 0.001424 0.0685 0.0740
32 2321 69 0.0691 0.001404 0.0664 0.0719
33 2252 63 0.0671 0.001386 0.0645 0.0699
34 2189 58 0.0654 0.001369 0.0627 0.0681
35 2131 49 0.0639 0.001354 0.0613 0.0666
36 2082 46 0.0625 0.001340 0.0599 0.0651
37 2036 37 0.0613 0.001329 0.0588 0.0640
38 1999 32 0.0603 0.001319 0.0578 0.0630
39 1967 25 0.0596 0.001311 0.0571 0.0622
40 1942 25 0.0588 0.001303 0.0563 0.0614
41 1917 24 0.0581 0.001295 0.0556 0.0607
42 1893 19 0.0575 0.001289 0.0550 0.0601
43 1874 12 0.0571 0.001285 0.0547 0.0597
44 1862 11 0.0568 0.001282 0.0543 0.0593
45 1851 15 0.0563 0.001277 0.0539 0.0589
46 1836 9 0.0560 0.001274 0.0536 0.0586
47 1827 8 0.0558 0.001271 0.0534 0.0583
48 1819 11 0.0555 0.001268 0.0530 0.0580
49 1808 9 0.0552 0.001265 0.0528 0.0577
50 1799 3 0.0551 0.001264 0.0527 0.0576
51 1796 10 0.0548 0.001260 0.0524 0.0573
52 1786 8 0.0545 0.001258 0.0521 0.0571
53 1778 6 0.0544 0.001256 0.0519 0.0569
54 1772 6 0.0542 0.001254 0.0518 0.0567
55 1766 2 0.0541 0.001253 0.0517 0.0566
56 1764 5 0.0540 0.001251 0.0516 0.0565
57 1759 2 0.0539 0.001251 0.0515 0.0564
58 1757 2 0.0538 0.001250 0.0514 0.0563
59 1755 3 0.0537 0.001249 0.0513 0.0562
60 1752 1 0.0537 0.001249 0.0513 0.0562
61 1751 1 0.0537 0.001248 0.0513 0.0562
62 1750 1 0.0536 0.001248 0.0513 0.0562
63 1749 1 0.0536 0.001248 0.0512 0.0561
65 1748 1 0.0536 0.001247 0.0512 0.0561
66 1747 1 0.0536 0.001247 0.0512 0.0561
70 1746 1 0.0535 0.001247 0.0511 0.0560
72 1745 1 0.0535 0.001246 0.0511 0.0560
73 1744 1 0.0535 0.001246 0.0511 0.0560
74 1743 2 0.0534 0.001245 0.0510 0.0559
76 1741 1 0.0534 0.001245 0.0510 0.0559
77 1740 1 0.0533 0.001245 0.0510 0.0558
78 1739 1 0.0533 0.001244 0.0509 0.0558
93 1738 1 0.0533 0.001244 0.0509 0.0558
inmsupr=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 1297 54 0.958 0.00555 0.9476 0.969
2 1243 68 0.906 0.00811 0.8902 0.922
3 1175 82 0.843 0.01011 0.8231 0.863
4 1093 85 0.777 0.01155 0.7549 0.800
5 1008 83 0.713 0.01256 0.6890 0.738
6 925 75 0.655 0.01320 0.6300 0.682
7 850 84 0.591 0.01365 0.5644 0.618
8 766 91 0.520 0.01387 0.4939 0.548
9 675 54 0.479 0.01387 0.4524 0.507
10 621 58 0.434 0.01376 0.4079 0.462
11 563 58 0.389 0.01354 0.3637 0.417
12 505 57 0.345 0.01320 0.3205 0.372
13 448 33 0.320 0.01295 0.2956 0.346
14 415 32 0.295 0.01267 0.2715 0.321
15 383 43 0.262 0.01221 0.2393 0.287
16 340 27 0.241 0.01188 0.2191 0.266
17 313 26 0.221 0.01153 0.1998 0.245
18 287 26 0.201 0.01113 0.1806 0.224
19 261 14 0.190 0.01090 0.1702 0.213
20 247 12 0.181 0.01070 0.1614 0.203
21 235 12 0.172 0.01048 0.1526 0.194
22 223 17 0.159 0.01015 0.1401 0.180
23 206 7 0.153 0.01001 0.1350 0.174
24 199 8 0.147 0.00984 0.1292 0.168
25 191 10 0.140 0.00962 0.1219 0.160
26 181 5 0.136 0.00951 0.1183 0.156
27 176 4 0.133 0.00942 0.1154 0.152
28 172 1 0.132 0.00939 0.1147 0.152
29 171 5 0.128 0.00928 0.1110 0.148
30 166 4 0.125 0.00918 0.1081 0.144
31 162 2 0.123 0.00913 0.1067 0.143
32 160 3 0.121 0.00906 0.1045 0.140
33 157 2 0.120 0.00901 0.1031 0.139
34 155 1 0.119 0.00898 0.1024 0.138
35 154 2 0.117 0.00893 0.1009 0.136
36 152 3 0.115 0.00885 0.0988 0.134
37 149 1 0.114 0.00883 0.0981 0.133
40 148 1 0.113 0.00880 0.0973 0.132
43 147 2 0.112 0.00875 0.0959 0.130
49 145 1 0.111 0.00872 0.0952 0.130
50 144 1 0.110 0.00870 0.0945 0.129
51 143 1 0.109 0.00867 0.0937 0.128
56 142 1 0.109 0.00864 0.0930 0.127
57 141 1 0.108 0.00862 0.0923 0.126
59 140 1 0.107 0.00859 0.0916 0.125ggsurvplot(fit, data = DataCluster3,
pval = TRUE, conf.int = TRUE,
risk.table = TRUE, # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))
Notice the graph speed of the inmsupr patient drops rapidly on day 17 but after the 17th day constant until the end of the study. so the heavside function is
\[ g(t)= \begin{cases} 1, & \mbox{jika}\ t\mbox{ < 17} \\ 0, & \mbox{jika}\ t\mbox{ >= 17} \end{cases}\]
Variabel Cardivascular
# VARIABEL Cardiovascular
fit<-survfit(Surv(waktu,status)~ cardiovascular, data=DataCluster3)
summary(fit)Call: survfit(formula = Surv(waktu, status) ~ cardiovascular, data = DataCluster3)
cardiovascular=0
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 31723 728 0.9771 0.000841 0.9754 0.9787
2 30995 1040 0.9443 0.001288 0.9417 0.9468
3 29955 1310 0.9030 0.001662 0.8997 0.9062
4 28645 1681 0.8500 0.002005 0.8461 0.8539
5 26964 1913 0.7897 0.002288 0.7852 0.7942
6 25051 1988 0.7270 0.002501 0.7221 0.7319
7 23063 2109 0.6605 0.002659 0.6553 0.6658
8 20954 2060 0.5956 0.002755 0.5902 0.6010
9 18894 2018 0.5320 0.002802 0.5265 0.5375
10 16876 1859 0.4734 0.002803 0.4679 0.4789
11 15017 1543 0.4247 0.002775 0.4193 0.4302
12 13474 1551 0.3758 0.002719 0.3706 0.3812
13 11923 1332 0.3339 0.002648 0.3287 0.3391
14 10591 1191 0.2963 0.002564 0.2913 0.3014
15 9400 1141 0.2603 0.002464 0.2556 0.2652
16 8259 979 0.2295 0.002361 0.2249 0.2342
17 7280 850 0.2027 0.002257 0.1983 0.2072
18 6430 735 0.1795 0.002155 0.1753 0.1838
19 5695 612 0.1602 0.002060 0.1562 0.1643
20 5083 503 0.1444 0.001973 0.1406 0.1483
21 4580 429 0.1309 0.001893 0.1272 0.1346
22 4151 370 0.1192 0.001819 0.1157 0.1228
23 3781 312 0.1094 0.001752 0.1060 0.1128
24 3469 277 0.1006 0.001689 0.0974 0.1040
25 3192 254 0.0926 0.001628 0.0895 0.0959
26 2938 181 0.0869 0.001582 0.0839 0.0901
27 2757 159 0.0819 0.001540 0.0789 0.0850
28 2598 155 0.0770 0.001497 0.0741 0.0800
29 2443 114 0.0734 0.001464 0.0706 0.0763
30 2329 119 0.0697 0.001429 0.0669 0.0725
31 2210 87 0.0669 0.001403 0.0642 0.0697
32 2123 69 0.0647 0.001382 0.0621 0.0675
33 2054 59 0.0629 0.001363 0.0603 0.0656
34 1995 56 0.0611 0.001345 0.0585 0.0638
35 1939 49 0.0596 0.001329 0.0570 0.0622
36 1890 47 0.0581 0.001313 0.0556 0.0607
37 1843 37 0.0569 0.001301 0.0544 0.0595
38 1806 31 0.0560 0.001290 0.0535 0.0585
39 1775 24 0.0552 0.001282 0.0527 0.0578
40 1751 25 0.0544 0.001273 0.0520 0.0570
41 1726 23 0.0537 0.001265 0.0513 0.0562
42 1703 18 0.0531 0.001259 0.0507 0.0556
43 1685 13 0.0527 0.001255 0.0503 0.0552
44 1672 11 0.0524 0.001251 0.0500 0.0549
45 1661 14 0.0519 0.001246 0.0495 0.0544
46 1647 8 0.0517 0.001243 0.0493 0.0542
47 1639 8 0.0514 0.001240 0.0490 0.0539
48 1631 10 0.0511 0.001236 0.0487 0.0536
49 1621 9 0.0508 0.001233 0.0485 0.0533
50 1612 4 0.0507 0.001232 0.0483 0.0532
51 1608 11 0.0503 0.001228 0.0480 0.0528
52 1597 7 0.0501 0.001225 0.0478 0.0526
53 1590 6 0.0499 0.001223 0.0476 0.0524
54 1584 6 0.0497 0.001221 0.0474 0.0522
55 1578 1 0.0497 0.001220 0.0474 0.0522
56 1577 4 0.0496 0.001219 0.0473 0.0520
57 1573 3 0.0495 0.001218 0.0472 0.0519
58 1570 2 0.0494 0.001217 0.0471 0.0519
59 1568 4 0.0493 0.001216 0.0470 0.0517
60 1564 1 0.0493 0.001215 0.0469 0.0517
61 1563 1 0.0492 0.001215 0.0469 0.0517
62 1562 1 0.0492 0.001214 0.0469 0.0516
63 1561 1 0.0492 0.001214 0.0469 0.0516
65 1560 1 0.0491 0.001214 0.0468 0.0516
66 1559 1 0.0491 0.001213 0.0468 0.0515
70 1558 1 0.0491 0.001213 0.0468 0.0515
72 1557 1 0.0490 0.001213 0.0467 0.0515
73 1556 1 0.0490 0.001212 0.0467 0.0515
74 1555 2 0.0490 0.001211 0.0466 0.0514
76 1553 1 0.0489 0.001211 0.0466 0.0514
77 1552 1 0.0489 0.001211 0.0466 0.0513
78 1551 1 0.0489 0.001210 0.0465 0.0513
93 1550 1 0.0488 0.001210 0.0465 0.0513
cardiovascular=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 2175 92 0.958 0.00432 0.949 0.966
2 2083 86 0.918 0.00588 0.907 0.930
3 1997 127 0.860 0.00745 0.845 0.874
4 1870 124 0.803 0.00853 0.786 0.820
5 1746 134 0.741 0.00939 0.723 0.760
6 1612 118 0.687 0.00994 0.668 0.707
7 1494 148 0.619 0.01041 0.599 0.640
8 1346 118 0.565 0.01063 0.544 0.586
9 1228 93 0.522 0.01071 0.501 0.543
10 1135 109 0.472 0.01070 0.451 0.493
11 1026 96 0.428 0.01061 0.407 0.449
12 930 82 0.390 0.01046 0.370 0.411
13 848 68 0.359 0.01028 0.339 0.379
14 780 61 0.331 0.01009 0.311 0.351
15 719 57 0.304 0.00987 0.286 0.324
16 662 55 0.279 0.00962 0.261 0.299
17 607 37 0.262 0.00943 0.244 0.281
18 570 33 0.247 0.00925 0.229 0.266
19 537 35 0.231 0.00903 0.214 0.249
20 502 25 0.219 0.00887 0.203 0.237
21 477 16 0.212 0.00876 0.195 0.230
22 461 15 0.205 0.00866 0.189 0.223
23 446 15 0.198 0.00855 0.182 0.216
24 431 13 0.192 0.00845 0.176 0.209
25 418 12 0.187 0.00835 0.171 0.204
26 406 14 0.180 0.00824 0.165 0.197
27 392 11 0.175 0.00815 0.160 0.192
28 381 3 0.174 0.00813 0.159 0.190
29 378 10 0.169 0.00804 0.154 0.186
30 368 5 0.167 0.00800 0.152 0.183
31 363 5 0.165 0.00795 0.150 0.181
32 358 3 0.163 0.00792 0.148 0.180
33 355 6 0.160 0.00787 0.146 0.177
34 349 3 0.159 0.00784 0.144 0.175
35 346 2 0.158 0.00782 0.144 0.174
36 344 2 0.157 0.00781 0.143 0.173
37 342 1 0.157 0.00780 0.142 0.173
38 341 1 0.156 0.00779 0.142 0.172
39 340 1 0.156 0.00778 0.141 0.172
40 339 1 0.155 0.00777 0.141 0.171
41 338 1 0.155 0.00776 0.140 0.171
42 337 1 0.154 0.00775 0.140 0.170
43 336 1 0.154 0.00774 0.140 0.170
45 335 1 0.154 0.00773 0.139 0.169
46 334 1 0.153 0.00772 0.139 0.169
48 333 1 0.153 0.00771 0.138 0.169
49 332 1 0.152 0.00770 0.138 0.168
52 331 1 0.152 0.00769 0.137 0.168
55 330 1 0.151 0.00768 0.137 0.167
56 329 2 0.150 0.00766 0.136 0.166ggsurvplot(fit, data = DataCluster3,
pval = TRUE, conf.int = TRUE,
risk.table = TRUE, # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))
Notice the graph speed of the cardivascular patient drops rapidly on day 21st but after the 21st day constant until the end of the study. so the heavside function is
\[ g(t)= \begin{cases} 1, & \mbox{jika}\ t\mbox{ < 21} \\ 0, & \mbox{jika}\ t\mbox{ >= 21} \end{cases}\]
Variabel copd
fit<-survfit(Surv(waktu,status)~ copd , data=DataCluster3)
summary(fit)Call: survfit(formula = Surv(waktu, status) ~ copd, data = DataCluster3)
copd=0
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 32165 766 0.9762 0.00085 0.9745 0.9779
2 31399 1060 0.9432 0.00129 0.9407 0.9458
3 30339 1356 0.9011 0.00166 0.8978 0.9043
4 28983 1714 0.8478 0.00200 0.8439 0.8517
5 27269 1927 0.7879 0.00228 0.7834 0.7924
6 25342 1972 0.7266 0.00249 0.7217 0.7315
7 23370 2132 0.6603 0.00264 0.6551 0.6655
8 21238 2066 0.5961 0.00274 0.5907 0.6014
9 19172 2011 0.5335 0.00278 0.5281 0.5390
10 17161 1889 0.4748 0.00278 0.4694 0.4803
11 15272 1564 0.4262 0.00276 0.4208 0.4316
12 13708 1572 0.3773 0.00270 0.3720 0.3826
13 12136 1346 0.3355 0.00263 0.3303 0.3407
14 10790 1201 0.2981 0.00255 0.2932 0.3032
15 9589 1149 0.2624 0.00245 0.2576 0.2672
16 8440 993 0.2315 0.00235 0.2270 0.2362
17 7447 854 0.2050 0.00225 0.2006 0.2094
18 6593 745 0.1818 0.00215 0.1776 0.1861
19 5848 630 0.1622 0.00206 0.1582 0.1663
20 5218 510 0.1464 0.00197 0.1426 0.1503
21 4708 430 0.1330 0.00189 0.1293 0.1368
22 4278 377 0.1213 0.00182 0.1178 0.1249
23 3901 311 0.1116 0.00176 0.1082 0.1151
24 3590 282 0.1028 0.00169 0.0996 0.1062
25 3308 258 0.0948 0.00163 0.0917 0.0981
26 3050 182 0.0892 0.00159 0.0861 0.0923
27 2868 166 0.0840 0.00155 0.0810 0.0871
28 2702 154 0.0792 0.00151 0.0763 0.0822
29 2548 119 0.0755 0.00147 0.0727 0.0785
30 2429 122 0.0717 0.00144 0.0690 0.0746
31 2307 88 0.0690 0.00141 0.0663 0.0718
32 2219 66 0.0669 0.00139 0.0643 0.0697
33 2153 60 0.0651 0.00138 0.0624 0.0678
34 2093 58 0.0633 0.00136 0.0607 0.0660
35 2035 51 0.0617 0.00134 0.0591 0.0644
36 1984 48 0.0602 0.00133 0.0576 0.0628
37 1936 37 0.0590 0.00131 0.0565 0.0617
38 1899 30 0.0581 0.00130 0.0556 0.0607
39 1869 25 0.0573 0.00130 0.0548 0.0599
40 1844 25 0.0566 0.00129 0.0541 0.0591
41 1819 24 0.0558 0.00128 0.0534 0.0584
42 1795 17 0.0553 0.00127 0.0528 0.0578
43 1778 13 0.0549 0.00127 0.0524 0.0574
44 1765 9 0.0546 0.00127 0.0522 0.0571
45 1756 14 0.0542 0.00126 0.0517 0.0567
46 1742 9 0.0539 0.00126 0.0515 0.0564
47 1733 7 0.0537 0.00126 0.0513 0.0562
48 1726 11 0.0533 0.00125 0.0509 0.0558
49 1715 9 0.0530 0.00125 0.0506 0.0555
50 1706 4 0.0529 0.00125 0.0505 0.0554
51 1702 10 0.0526 0.00124 0.0502 0.0551
52 1692 8 0.0524 0.00124 0.0500 0.0548
53 1684 6 0.0522 0.00124 0.0498 0.0547
54 1678 6 0.0520 0.00124 0.0496 0.0545
55 1672 1 0.0520 0.00124 0.0496 0.0544
56 1671 5 0.0518 0.00124 0.0494 0.0543
57 1666 3 0.0517 0.00123 0.0493 0.0542
58 1663 2 0.0516 0.00123 0.0493 0.0541
59 1661 4 0.0515 0.00123 0.0492 0.0540
60 1657 1 0.0515 0.00123 0.0491 0.0540
61 1656 1 0.0515 0.00123 0.0491 0.0539
62 1655 1 0.0514 0.00123 0.0491 0.0539
63 1654 1 0.0514 0.00123 0.0490 0.0539
65 1653 1 0.0514 0.00123 0.0490 0.0538
70 1652 1 0.0513 0.00123 0.0490 0.0538
72 1651 1 0.0513 0.00123 0.0489 0.0538
73 1650 1 0.0513 0.00123 0.0489 0.0537
74 1649 2 0.0512 0.00123 0.0489 0.0537
76 1647 1 0.0512 0.00123 0.0488 0.0536
78 1646 1 0.0511 0.00123 0.0488 0.0536
copd=1
time n.risk n.event survival std.err lower 95% CI upper 95% CI
1 1733 54 0.969 0.00417 0.961 0.977
2 1679 66 0.931 0.00610 0.919 0.943
3 1613 81 0.884 0.00769 0.869 0.899
4 1532 91 0.832 0.00899 0.814 0.849
5 1441 120 0.762 0.01023 0.742 0.783
6 1321 134 0.685 0.01116 0.663 0.707
7 1187 125 0.613 0.01170 0.590 0.636
8 1062 112 0.548 0.01195 0.525 0.572
9 950 100 0.490 0.01201 0.467 0.515
10 850 79 0.445 0.01194 0.422 0.469
11 771 75 0.402 0.01178 0.379 0.425
12 696 61 0.366 0.01157 0.344 0.390
13 635 54 0.335 0.01134 0.314 0.358
14 581 51 0.306 0.01107 0.285 0.328
15 530 49 0.278 0.01076 0.257 0.299
16 481 41 0.254 0.01046 0.234 0.275
17 440 33 0.235 0.01018 0.216 0.256
18 407 23 0.222 0.00998 0.203 0.242
19 384 17 0.212 0.00981 0.193 0.232
20 367 18 0.201 0.00963 0.183 0.221
21 349 15 0.193 0.00948 0.175 0.212
22 334 8 0.188 0.00939 0.171 0.207
23 326 16 0.179 0.00921 0.162 0.198
24 310 8 0.174 0.00911 0.157 0.193
25 302 8 0.170 0.00902 0.153 0.188
26 294 13 0.162 0.00885 0.146 0.180
27 281 4 0.160 0.00880 0.143 0.178
28 277 4 0.158 0.00875 0.141 0.176
29 273 5 0.155 0.00869 0.139 0.173
30 268 2 0.153 0.00866 0.137 0.171
31 266 4 0.151 0.00861 0.135 0.169
32 262 6 0.148 0.00852 0.132 0.165
33 256 5 0.145 0.00845 0.129 0.162
34 251 1 0.144 0.00844 0.129 0.162
36 250 1 0.144 0.00843 0.128 0.161
37 249 1 0.143 0.00841 0.128 0.161
38 248 2 0.142 0.00838 0.126 0.159
40 246 1 0.141 0.00837 0.126 0.159
42 245 2 0.140 0.00834 0.125 0.158
43 243 1 0.140 0.00833 0.124 0.157
44 242 2 0.138 0.00830 0.123 0.156
45 240 1 0.138 0.00828 0.123 0.155
47 239 1 0.137 0.00827 0.122 0.155
49 238 1 0.137 0.00825 0.122 0.154
51 237 1 0.136 0.00824 0.121 0.153
55 236 1 0.136 0.00822 0.120 0.153
56 235 1 0.135 0.00821 0.120 0.152
66 234 1 0.134 0.00819 0.119 0.152
77 233 1 0.134 0.00818 0.119 0.151
93 232 1 0.133 0.00816 0.118 0.150ggsurvplot(fit, data = DataCluster3,
pval = TRUE, conf.int = TRUE,
risk.table = TRUE, # Add risk table
risk.table.col = "strata", # Change risk table color by groups
linetype = "strata", # Change line type by groups
surv.median.line = "hv", # Specify median survival
ggtheme = theme_bw(), # Change ggplot2 theme
palette = c("#E7B800", "#2E9FDF"))
Notice the graph speed of the copd patient drops rapidly on day 21st but after the 21st day constant until the end of the study. so the heavside function is
sehingga ke-empat tersebut diinterkasikan dengan fungsi waktu masing-masing. namun sebelumnya membuat kolom interval yaitu jika t lebih besar atau sama dengan 25 maka nilanya 25 tapi kalau tidak nilainya 0
DataCluster3= DataCluster3 %>%
mutate(interval0 = ifelse(waktu<= 17, 0, 17),
interval1 = ifelse(waktu<= 21, 0, 21),
interval2 = ifelse(waktu<= 26, 0, 26),
interval3 = ifelse(waktu<= 27, 0, 27),
interval4 = ifelse(waktu<= 30, 0, 30),
interval5 = ifelse(waktu<= 31, 0, 31))
head(DataCluster3) sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
1 0 1 0 0 0 0 0 0
2 1 1 0 0 0 0 0 1
3 1 1 0 1 0 0 0 0
4 0 1 0 0 1 1 0 1
5 0 1 0 0 0 0 0 1
6 1 1 0 0 0 0 0 1
cardiovascular obesity renal_chronic tobacco waktu status Age cluster
1 0 0 0 0 4 1 0 3
2 0 1 0 0 17 1 1 3
3 0 1 0 0 26 1 0 3
4 1 1 0 0 3 1 0 3
5 0 0 0 0 14 1 1 3
6 0 1 0 0 2 1 1 3
interval0 interval1 interval2 interval3 interval4 interval5
1 0 0 0 0 0 0
2 0 0 0 0 0 0
3 17 21 0 0 0 0
4 0 0 0 0 0 0
5 0 0 0 0 0 0
6 0 0 0 0 0 0t.Age_1 = t(DataCluster3$Age)*(1-(DataCluster3$interval3)/27)
t.Age_2 = t(DataCluster3$Age)*(DataCluster3$interval3/27)
Age_t1 = t(t.Age_1 )
Age_t2 = t(t.Age_2)t.hypertension_1 = t(DataCluster3$hypertension)*(1-(DataCluster3$interval5)/31)
t.hypertension_2 = t(DataCluster3$hypertension)*(DataCluster3$interval5/31)
hypertension_t1 = t(t.hypertension_1 )
hypertension_t2 = t(t.hypertension_2)t.diabetes_1 = t(DataCluster3$diabetes)*(1-(DataCluster3$interval4)/30)
t.diabetes_2 = t(DataCluster3$diabetes)*(DataCluster3$interval4/30)
diabetes_t1 = t(t.diabetes_1 )
diabetes_t2 = t(t.diabetes_2)t.renal_chronic_1 = t(DataCluster3$renal_chronic)*(1-(DataCluster3$interval5)/31)
t.renal_chronic_2 = t(DataCluster3$renal_chronic)*(DataCluster3$interval5/31)
renal_chronic_t1 = t(t.renal_chronic_1 )
renal_chronic_t2 = t(t.renal_chronic_2)t.inmsupr_1 = t(DataCluster3$inmsupr)*(1-(DataCluster3$interval0)/17)
t.inmsupr_2 = t(DataCluster3$inmsupr)*(DataCluster3$interval0/17)
inmsupr_t1 = t(t.inmsupr_1 )
inmsupr_t2 = t(t.inmsupr_2)t.cardiovascular_1 = t(DataCluster3$cardiovascular)*(1-(DataCluster3$interval1)/21)
t.cardiovascular_2 = t(DataCluster3$cardiovascular)*(DataCluster3$interval1/21)
cardiovascular_t1 = t(t.cardiovascular_1)
cardiovascular_t2 = t(t.cardiovascular_2)t.copd_1 = t(DataCluster3$copd)*(1-(DataCluster3$interval2)/26)
t.copd_2 = t(DataCluster3$copd)*(DataCluster3$interval2/26)
copd_t1 = t(t.copd_1)
copd_t2 = t(t.copd_2)DataCluster3=cbind(DataCluster3,diabetes_t1,diabetes_t2,hypertension_t1,hypertension_t2,inmsupr_t2,inmsupr_t1,Age_t1,Age_t2,renal_chronic_t1,renal_chronic_t2, cardiovascular_t1, cardiovascular_t2,copd_t1,copd_t2 )
head(DataCluster3) sex pneumonia pregnancy diabetes copd asthma inmsupr hypertension
1 0 1 0 0 0 0 0 0
2 1 1 0 0 0 0 0 1
3 1 1 0 1 0 0 0 0
4 0 1 0 0 1 1 0 1
5 0 1 0 0 0 0 0 1
6 1 1 0 0 0 0 0 1
cardiovascular obesity renal_chronic tobacco waktu status Age cluster
1 0 0 0 0 4 1 0 3
2 0 1 0 0 17 1 1 3
3 0 1 0 0 26 1 0 3
4 1 1 0 0 3 1 0 3
5 0 0 0 0 14 1 1 3
6 0 1 0 0 2 1 1 3
interval0 interval1 interval2 interval3 interval4 interval5 diabetes_t1
1 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0
3 17 21 0 0 0 0 1
4 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0
diabetes_t2 hypertension_t1 hypertension_t2 inmsupr_t2 inmsupr_t1 Age_t1
1 0 0 0 0 0 0
2 0 1 0 0 0 1
3 0 0 0 0 0 0
4 0 1 0 0 0 0
5 0 1 0 0 0 1
6 0 1 0 0 0 1
Age_t2 renal_chronic_t1 renal_chronic_t2 cardiovascular_t1 cardiovascular_t2
1 0 0 0 0 0
2 0 0 0 0 0
3 0 0 0 0 0
4 0 0 0 1 0
5 0 0 0 0 0
6 0 0 0 0 0
copd_t1 copd_t2
1 0 0
2 0 0
3 0 0
4 1 0
5 0 0
6 0 0e. Model Extended Cox with Breslow Method
Fit_Model_Cluster3<-coxph(Surv(waktu,status)~ sex:waktu+ pregnancy + hypertension_t1 + hypertension_t2 + obesity +tobacco + diabetes_t1 + diabetes_t1+ diabetes_t2+ renal_chronic_t1+ renal_chronic_t2+cardiovascular_t1 + cardiovascular_t2 + copd_t1+copd_t2 +inmsupr_t1+inmsupr_t2+asthma+ pneumonia+Age_t1+Age_t2, data = DataCluster3, method = "breslow")
summary(Fit_Model_Cluster3)Call:
coxph(formula = Surv(waktu, status) ~ sex:waktu + pregnancy +
hypertension_t1 + hypertension_t2 + obesity + tobacco + diabetes_t1 +
diabetes_t1 + diabetes_t2 + renal_chronic_t1 + renal_chronic_t2 +
cardiovascular_t1 + cardiovascular_t2 + copd_t1 + copd_t2 +
inmsupr_t1 + inmsupr_t2 + asthma + pneumonia + Age_t1 + Age_t2,
data = DataCluster3, method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
pregnancy 0.478162 1.613107 0.155086 3.083 0.00205 **
hypertension_t1 0.070258 1.072785 0.012601 5.576 2.47e-08 ***
hypertension_t2 -1.458452 0.232596 0.084676 -17.224 < 2e-16 ***
obesity 0.031958 1.032474 0.013579 2.354 0.01859 *
tobacco 0.070656 1.073212 0.237981 0.297 0.76654
diabetes_t1 0.131178 1.140170 0.012500 10.494 < 2e-16 ***
diabetes_t2 -1.590603 0.203803 0.085284 -18.651 < 2e-16 ***
renal_chronic_t1 0.186827 1.205419 0.022211 8.411 < 2e-16 ***
renal_chronic_t2 -1.361185 0.256357 0.163891 -8.305 < 2e-16 ***
cardiovascular_t1 0.227788 1.255819 0.025519 8.926 < 2e-16 ***
cardiovascular_t2 -1.089287 0.336456 0.088060 -12.370 < 2e-16 ***
copd_t1 0.180774 1.198144 0.027211 6.643 3.07e-11 ***
copd_t2 -0.792847 0.452555 0.145433 -5.452 4.99e-08 ***
inmsupr_t1 0.475481 1.608788 0.032635 14.570 < 2e-16 ***
inmsupr_t2 -1.062567 0.345568 0.083057 -12.793 < 2e-16 ***
asthma -0.007220 0.992806 0.040200 -0.180 0.85747
pneumonia -0.108917 0.896805 0.012572 -8.664 < 2e-16 ***
Age_t1 0.153747 1.166196 0.012645 12.159 < 2e-16 ***
Age_t2 -1.574002 0.207214 0.044965 -35.005 < 2e-16 ***
sex:waktu -0.026835 0.973522 0.000738 -36.360 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
pregnancy 1.6131 0.6199 1.1903 2.1861
hypertension_t1 1.0728 0.9322 1.0466 1.0996
hypertension_t2 0.2326 4.2993 0.1970 0.2746
obesity 1.0325 0.9685 1.0054 1.0603
tobacco 1.0732 0.9318 0.6732 1.7110
diabetes_t1 1.1402 0.8771 1.1126 1.1684
diabetes_t2 0.2038 4.9067 0.1724 0.2409
renal_chronic_t1 1.2054 0.8296 1.1541 1.2591
renal_chronic_t2 0.2564 3.9008 0.1859 0.3535
cardiovascular_t1 1.2558 0.7963 1.1946 1.3202
cardiovascular_t2 0.3365 2.9722 0.2831 0.3998
copd_t1 1.1981 0.8346 1.1359 1.2638
copd_t2 0.4526 2.2097 0.3403 0.6018
inmsupr_t1 1.6088 0.6216 1.5091 1.7151
inmsupr_t2 0.3456 2.8938 0.2937 0.4067
asthma 0.9928 1.0072 0.9176 1.0742
pneumonia 0.8968 1.1151 0.8750 0.9192
Age_t1 1.1662 0.8575 1.1376 1.1955
Age_t2 0.2072 4.8259 0.1897 0.2263
sex:waktu 0.9735 1.0272 0.9721 0.9749
Concordance= 0.665 (se = 0.002 )
Likelihood ratio test= 19749 on 20 df, p=<2e-16
Wald test = 6897 on 20 df, p=<2e-16
Score (logrank) test = 10949 on 20 df, p=<2e-16Biasanya Anda dapat mengabaikan pesan tersebut, sebagian besar untuk informasi Anda. Itu hal utama yang perlu diperhatikan adalah Sebuah. Ketika salah satu koefisien menuju tak terhingga dalam model Cox, Wald uji signifikansi beta/se(beta) rusak, dan tidak lagi dapat diandalkan. Namun tes LR masih valid. Karenanya rutinitas seperti step AIC baik-baik saja. Begitu juga nilai prediksi, residu, dll. Sebenarnya itu hanya Uji Wald yang perlu diabaikan: didasarkan pada deret Taylor yang hanya tidak bekerja sejauh itu dari nol maka dari itu perlu membuang variabel yang menghasilkan infinity
d. Hazard Ratio
ggforest(Fit_Model_Cluster3, main = "Hazard Ratio")
e.Significance Test
Partial likelihood test
Fit_Model_Cluster3$loglik[1] -308877.9 -299003.5Wald test
Variabel Sex
## Variabel sex
Fit_Model_Sex<-coxph(Surv(waktu,status)~ waktu:sex, data = DataCluster3, method = "breslow")
summary(Fit_Model_Sex)Call:
coxph(formula = Surv(waktu, status) ~ waktu:sex, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
waktu:sex -0.0295498 0.9708825 0.0005443 -54.29 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
waktu:sex 0.9709 1.03 0.9698 0.9719
Concordance= 0.564 (se = 0.002 )
Likelihood ratio test= 5707 on 1 df, p=<2e-16
Wald test = 2947 on 1 df, p=<2e-16
Score (logrank) test = 3749 on 1 df, p=<2e-16Variabel peneumonia
## Variabel Pneumonia
Fit_Model_Pneumonia1<-coxph(Surv(waktu,status)~ pneumonia, data = DataCluster3, method = "breslow")
summary(Fit_Model_Pneumonia1)Call:
coxph(formula = Surv(waktu, status) ~ pneumonia, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
pneumonia -0.25575 0.77433 0.01258 -20.34 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
pneumonia 0.7743 1.291 0.7555 0.7937
Concordance= 0.526 (se = 0.001 )
Likelihood ratio test= 397.4 on 1 df, p=<2e-16
Wald test = 413.5 on 1 df, p=<2e-16
Score (logrank) test = 415.8 on 1 df, p=<2e-16Variabel Diabetes
## Variabel Diabetes
Fit_Model_Diabetes1<-coxph(Surv(waktu,status)~ diabetes_t1, data = DataCluster3, method = "breslow")
summary(Fit_Model_Diabetes1)Call:
coxph(formula = Surv(waktu, status) ~ diabetes_t1, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
diabetes_t1 0.43468 1.54447 0.01189 36.55 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
diabetes_t1 1.544 0.6475 1.509 1.581
Concordance= 0.542 (se = 0.001 )
Likelihood ratio test= 1282 on 1 df, p=<2e-16
Wald test = 1336 on 1 df, p=<2e-16
Score (logrank) test = 1356 on 1 df, p=<2e-16Fit_Model_Diabetes2<-coxph(Surv(waktu,status)~ diabetes_t2, data = DataCluster3, method = "breslow")
summary(Fit_Model_Diabetes2)Call:
coxph(formula = Surv(waktu, status) ~ diabetes_t2, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
diabetes_t2 -3.71769 0.02429 0.06898 -53.89 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
diabetes_t2 0.02429 41.17 0.02122 0.02781
Concordance= 0.554 (se = 0.001 )
Likelihood ratio test= 10857 on 1 df, p=<2e-16
Wald test = 2905 on 1 df, p=<2e-16
Score (logrank) test = 6756 on 1 df, p=<2e-16Variabel Hypertension
## Variabel hypertension
Fit_Model_Hypertension1<-coxph(Surv(waktu,status)~ hypertension_t1, data = DataCluster3, method = "breslow")
summary(Fit_Model_Hypertension1)Call:
coxph(formula = Surv(waktu, status) ~ hypertension_t1, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
hypertension_t1 0.41874 1.52004 0.01162 36.03 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
hypertension_t1 1.52 0.6579 1.486 1.555
Concordance= 0.539 (se = 0.002 )
Likelihood ratio test= 1265 on 1 df, p=<2e-16
Wald test = 1298 on 1 df, p=<2e-16
Score (logrank) test = 1316 on 1 df, p=<2e-16## Variabel hypertension
Fit_Model_Hypertension2<-coxph(Surv(waktu,status)~ hypertension_t2, data = DataCluster3, method = "breslow")
summary(Fit_Model_Hypertension2)Call:
coxph(formula = Surv(waktu, status) ~ hypertension_t2, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
hypertension_t2 -3.81281 0.02209 0.06600 -57.77 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
hypertension_t2 0.02209 45.28 0.01941 0.02514
Concordance= 0.558 (se = 0.001 )
Likelihood ratio test= 12022 on 1 df, p=<2e-16
Wald test = 3337 on 1 df, p=<2e-16
Score (logrank) test = 7461 on 1 df, p=<2e-16Variabel Obesity
## Variabel Obesity
Fit_Model_obesity<-coxph(Surv(waktu,status)~ obesity, data = DataCluster3, method = "breslow")
summary(Fit_Model_obesity)Call:
coxph(formula = Surv(waktu, status) ~ obesity, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
obesity -0.05728 0.94433 0.01335 -4.291 1.78e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
obesity 0.9443 1.059 0.9199 0.9694
Concordance= 0.505 (se = 0.001 )
Likelihood ratio test= 18.6 on 1 df, p=2e-05
Wald test = 18.41 on 1 df, p=2e-05
Score (logrank) test = 18.42 on 1 df, p=2e-05Variabel Renal Chronic
### variabel renal_chronic
Fit_Model_RenalChronic1<-coxph(Surv(waktu,status)~ renal_chronic_t1, data = DataCluster3, method = "breslow")
summary(Fit_Model_RenalChronic1)Call:
coxph(formula = Surv(waktu, status) ~ renal_chronic_t1, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
renal_chronic_t1 0.46925 1.59880 0.02128 22.05 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
renal_chronic_t1 1.599 0.6255 1.533 1.667
Concordance= 0.517 (se = 0.001 )
Likelihood ratio test= 427.6 on 1 df, p=<2e-16
Wald test = 486.3 on 1 df, p=<2e-16
Score (logrank) test = 495.3 on 1 df, p=<2e-16### variabel renal_chronic
Fit_Model_RenalChronic2<-coxph(Surv(waktu,status)~ renal_chronic_t2, data = DataCluster3, method = "breslow")
summary(Fit_Model_RenalChronic2)Call:
coxph(formula = Surv(waktu, status) ~ renal_chronic_t2, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
renal_chronic_t2 -3.55943 0.02845 0.15639 -22.76 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
renal_chronic_t2 0.02845 35.14 0.02094 0.03866
Concordance= 0.514 (se = 0.001 )
Likelihood ratio test= 2388 on 1 df, p=<2e-16
Wald test = 518 on 1 df, p=<2e-16
Score (logrank) test = 1350 on 1 df, p=<2e-16Variabel Age
## Variabel Age
Fit_Model_Age1<-coxph(Surv(waktu,status)~ Age_t1, data = DataCluster3, method = "breslow")
summary(Fit_Model_Age1)Call:
coxph(formula = Surv(waktu, status) ~ Age_t1, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
Age_t1 0.66469 1.94389 0.01239 53.63 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
Age_t1 1.944 0.5144 1.897 1.992
Concordance= 0.559 (se = 0.002 )
Likelihood ratio test= 3039 on 1 df, p=<2e-16
Wald test = 2876 on 1 df, p=<2e-16
Score (logrank) test = 2970 on 1 df, p=<2e-16## Variabel Age
Fit_Model_Age2<-coxph(Surv(waktu,status)~ Age_t2, data = DataCluster3, method = "breslow")
summary(Fit_Model_Age2)Call:
coxph(formula = Surv(waktu, status) ~ Age_t2, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
Age_t2 -3.03541 0.04805 0.04040 -75.14 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
Age_t2 0.04805 20.81 0.0444 0.05201
Concordance= 0.57 (se = 0.001 )
Likelihood ratio test= 12761 on 1 df, p=<2e-16
Wald test = 5646 on 1 df, p=<2e-16
Score (logrank) test = 8567 on 1 df, p=<2e-16Variabel COPD
## Variabel COPD
Fit_Model_copd<-coxph(Surv(waktu,status)~ copd_t1, data = DataCluster3, method = "breslow")
summary(Fit_Model_copd)Call:
coxph(formula = Surv(waktu, status) ~ copd_t1, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
copd_t1 0.42774 1.53379 0.02694 15.88 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
copd_t1 1.534 0.652 1.455 1.617
Concordance= 0.509 (se = 0.001 )
Likelihood ratio test= 222.4 on 1 df, p=<2e-16
Wald test = 252.1 on 1 df, p=<2e-16
Score (logrank) test = 255.9 on 1 df, p=<2e-16## Variabel COPD
Fit_Model_copd<-coxph(Surv(waktu,status)~ copd_t2, data = DataCluster3, method = "breslow")
summary(Fit_Model_copd)Call:
coxph(formula = Surv(waktu, status) ~ copd_t2, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
copd_t2 -2.77589 0.06229 0.14164 -19.6 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
copd_t2 0.06229 16.05 0.04719 0.08223
Concordance= 0.508 (se = 0 )
Likelihood ratio test= 1194 on 1 df, p=<2e-16
Wald test = 384.1 on 1 df, p=<2e-16
Score (logrank) test = 702.8 on 1 df, p=<2e-16Variabel Inmsupr
## Variabel inmsupr
Fit_Model_inmsupr1<-coxph(Surv(waktu,status)~ inmsupr_t1, data = DataCluster3, method = "breslow")
summary(Fit_Model_inmsupr1)Call:
coxph(formula = Surv(waktu, status) ~ inmsupr_t1, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
inmsupr_t1 0.67088 1.95595 0.03215 20.87 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
inmsupr_t1 1.956 0.5113 1.837 2.083
Concordance= 0.51 (se = 0.001 )
Likelihood ratio test= 357.6 on 1 df, p=<2e-16
Wald test = 435.5 on 1 df, p=<2e-16
Score (logrank) test = 452.1 on 1 df, p=<2e-16## Variabel inmsupr
Fit_Model_inmsupr2<-coxph(Surv(waktu,status)~ inmsupr_t2, data = DataCluster3, method = "breslow")
summary(Fit_Model_inmsupr2)Call:
coxph(formula = Surv(waktu, status) ~ inmsupr_t2, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
inmsupr_t2 -1.56192 0.20973 0.08249 -18.94 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
inmsupr_t2 0.2097 4.768 0.1784 0.2465
Concordance= 0.507 (se = 0 )
Likelihood ratio test= 638.8 on 1 df, p=<2e-16
Wald test = 358.6 on 1 df, p=<2e-16
Score (logrank) test = 437.6 on 1 df, p=<2e-16Variabel Asthma
## Variabel Asthma
Fit_Model_Asthma<-coxph(Surv(waktu,status)~ asthma, data = DataCluster3, method = "breslow")
summary(Fit_Model_Asthma)Call:
coxph(formula = Surv(waktu, status) ~ asthma, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
asthma -0.07176 0.93075 0.04002 -1.793 0.073 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
asthma 0.9308 1.074 0.8605 1.007
Concordance= 0.501 (se = 0 )
Likelihood ratio test= 3.29 on 1 df, p=0.07
Wald test = 3.22 on 1 df, p=0.07
Score (logrank) test = 3.22 on 1 df, p=0.07Variabel Cardivascular
## Variabel Cardiovascular
Fit_Model_Cardivascular1<-coxph(Surv(waktu,status)~ cardiovascular_t1, data = DataCluster3, method = "breslow")
summary(Fit_Model_Cardivascular1)Call:
coxph(formula = Surv(waktu, status) ~ cardiovascular_t1, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
cardiovascular_t1 0.51518 1.67393 0.02496 20.64 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
cardiovascular_t1 1.674 0.5974 1.594 1.758
Concordance= 0.512 (se = 0.001 )
Likelihood ratio test= 367.9 on 1 df, p=<2e-16
Wald test = 425.9 on 1 df, p=<2e-16
Score (logrank) test = 435.4 on 1 df, p=<2e-16## Variabel Cardiovascular
Fit_Model_Cardivascular2<-coxph(Surv(waktu,status)~ cardiovascular_t2, data = DataCluster3, method = "breslow")
summary(Fit_Model_Cardivascular2)Call:
coxph(formula = Surv(waktu, status) ~ cardiovascular_t2, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
cardiovascular_t2 -2.26781 0.10354 0.08672 -26.15 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
cardiovascular_t2 0.1035 9.658 0.08735 0.1227
Concordance= 0.513 (se = 0.001 )
Likelihood ratio test= 1640 on 1 df, p=<2e-16
Wald test = 683.9 on 1 df, p=<2e-16
Score (logrank) test = 1030 on 1 df, p=<2e-16Variabel Pregnancy
## Variabel Pregnancy
Fit_Model_Pregnancy<-coxph(Surv(waktu,status)~ pregnancy, data = DataCluster3, method = "breslow")
summary(Fit_Model_Pregnancy)Call:
coxph(formula = Surv(waktu, status) ~ pregnancy, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
pregnancy 0.2278 1.2558 0.1544 1.475 0.14
exp(coef) exp(-coef) lower .95 upper .95
pregnancy 1.256 0.7963 0.9279 1.7
Concordance= 0.5 (se = 0 )
Likelihood ratio test= 2.02 on 1 df, p=0.2
Wald test = 2.18 on 1 df, p=0.1
Score (logrank) test = 2.19 on 1 df, p=0.1Fit_Model_Pregnancy<-coxph(Surv(waktu,status)~ tobacco, data = DataCluster3, method = "breslow")
summary(Fit_Model_Pregnancy)Call:
coxph(formula = Surv(waktu, status) ~ tobacco, data = DataCluster3,
method = "breslow")
n= 33898, number of events= 32022
coef exp(coef) se(coef) z Pr(>|z|)
tobacco 0.8789 2.4082 0.2358 3.727 0.000194 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
tobacco 2.408 0.4153 1.517 3.823
Concordance= 0.5 (se = 0 )
Likelihood ratio test= 10.58 on 1 df, p=0.001
Wald test = 13.89 on 1 df, p=2e-04
Score (logrank) test = 14.81 on 1 df, p=1e-04