Supervised Learning : Survival Analysis and Descriptive Modelling for a Three-Group Right-Censored Data with Time-Independent Variables Using Cox Proportional Hazards Model
John Pauline Pineda
May 6, 2022
1. Table of Contents
This project implements the survival analysis and descriptive modelling steps for a two-group right-censored data with time-independent variables using the Cox Proportional Hazards Model with various helpful packages in R. The Kaplan-Meier Survival Curves and Log-Rank Test were applied during the differential analysis of the survival data between groups. All predictors’ prognostic significance were individually and simultaneously evaluated using Univariate and Multivariate Cox Proportional Hazards Models, respectively. The discrimination power of the resulting models were assessed using the Harrel’s Concordance Index. The final prognostic model was internally validated using Bootstrap Validation with Optimism Estimation and evaluated for compliance on all required model assumptions using the appropriate diagnostics. All results were consolidated in a Summary presented at the end of the document.
Survival analysis corresponds to a set of statistical approaches for time-to-event data, where the outcome variable of interest is the time until an event occurs. Descriptive modelling involves the formulation of statistical models to identify patterns and relationships that can be used for statistical inferences given the predictors and response variables. The methods applied in this study (mostly contained in the survival package) attempt to explore the relationship between factors and both the survival time and event outcomes, while evaluating their effects through statistical hypotheses testing.
1.1 Sample Data
The Cancer dataset from the book Supervised Machine Learning was used for this illustrated example.
Preliminary dataset assessment:
[A] 228 Rows (observations composed of advanced lung cancer patients)
[B] 9 Columns (variables)
[B.1] 1/9 Factor variable = ph.ecog (factor) referring to the ECOG performance score (0=best, 3=worst) which describes the level of functioning of patients in terms of their ability to care for themselves, daily activity, and physical ability.
[B.1.1] Asymptomatic = ECOG performance score 0 (asymptomatic)
[B.1.2] Ambulatory = ECOG performance score 1 (symptomatic but completely ambulatory)
[B.1.3] Bedridden = ECOG performance score 2 (symptomatic but <50% in bed) or ECOG performance score 3 (symptomatic but >50% in bed)
[B.2] 1/9 Censoring variable = status (factor)
[B.2.1] 1 = event, patient died before the end of the study
[B.2.2] 0 = censored or non-event, patient remains alive until the end of the study, lost to follow-up, experiences a different event that makes further follow-up impossible or withdraws before the end of the study
[B.3] 1/9 Response variables = time (numeric)
[B.3.1] time = time in days a patient stays alive up to the point of the patient’s death or being censored
[B.4] 1/9 Covariate variable = age (numeric)
[B.4.1] age = patient’s age in years during the conduct of the study
[B.5] 1/9 Covariate variable = sex (factor)
[B.5.1] sex = patient’s sex at birth
[B.6] 1/9 Covariate variable = ph.karno (numeric)
[B.6.1] ph.karno = Karnofsky performance score (bad=0,good=100) rated by physician
[B.7] 1/9 Covariate variable = pat.karno: (numeric)
[B.7.1] pat.karno = Karnofsky performance score (bad=0,good=100) rated by physician
[B.8] 1/9 Covariate variable = meal.cal (numeric)
[B.8.1] meal.cal = calories consumed at meals
[B.9] 1/9 Covariate variable = wt.loss (numeric)
[B.9.1] wt.loss = weight loss in last six months
Code Chunk | Output
##################################
# Loading R libraries
##################################
library(moments)
library(car)
library(multcomp)
library(effects)
library(psych)
library(ggplot2)
library(dplyr)
library(ggpubr)
library(rstatix)
library(ggfortify)
library(trend)
library(survival)
library(rms)
library(survminer)
library(Hmisc)
library(finalfit)
library(knitr)
library(gtsummary)
##################################
# Loading the complete dataset
##################################
data(cancer)
##################################
# Reading and creating the complete dataset
##################################
DBP.Complete <- cancer
##################################
# Performing a general exploration of the dataset
##################################
dim(DBP.Complete)## [1] 228 10str(DBP.Complete)## 'data.frame': 228 obs. of 10 variables:
## $ inst : num 3 3 3 5 1 12 7 11 1 7 ...
## $ time : num 306 455 1010 210 883 ...
## $ status : num 2 2 1 2 2 1 2 2 2 2 ...
## $ age : num 74 68 56 57 60 74 68 71 53 61 ...
## $ sex : num 1 1 1 1 1 1 2 2 1 1 ...
## $ ph.ecog : num 1 0 0 1 0 1 2 2 1 2 ...
## $ ph.karno : num 90 90 90 90 100 50 70 60 70 70 ...
## $ pat.karno: num 100 90 90 60 90 80 60 80 80 70 ...
## $ meal.cal : num 1175 1225 NA 1150 NA ...
## $ wt.loss : num NA 15 15 11 0 0 10 1 16 34 ...summary(DBP.Complete)## inst time status age
## Min. : 1.00 Min. : 5.0 Min. :1.000 Min. :39.00
## 1st Qu.: 3.00 1st Qu.: 166.8 1st Qu.:1.000 1st Qu.:56.00
## Median :11.00 Median : 255.5 Median :2.000 Median :63.00
## Mean :11.09 Mean : 305.2 Mean :1.724 Mean :62.45
## 3rd Qu.:16.00 3rd Qu.: 396.5 3rd Qu.:2.000 3rd Qu.:69.00
## Max. :33.00 Max. :1022.0 Max. :2.000 Max. :82.00
## NA's :1
## sex ph.ecog ph.karno pat.karno
## Min. :1.000 Min. :0.0000 Min. : 50.00 Min. : 30.00
## 1st Qu.:1.000 1st Qu.:0.0000 1st Qu.: 75.00 1st Qu.: 70.00
## Median :1.000 Median :1.0000 Median : 80.00 Median : 80.00
## Mean :1.395 Mean :0.9515 Mean : 81.94 Mean : 79.96
## 3rd Qu.:2.000 3rd Qu.:1.0000 3rd Qu.: 90.00 3rd Qu.: 90.00
## Max. :2.000 Max. :3.0000 Max. :100.00 Max. :100.00
## NA's :1 NA's :1 NA's :3
## meal.cal wt.loss
## Min. : 96.0 Min. :-24.000
## 1st Qu.: 635.0 1st Qu.: 0.000
## Median : 975.0 Median : 7.000
## Mean : 928.8 Mean : 9.832
## 3rd Qu.:1150.0 3rd Qu.: 15.750
## Max. :2600.0 Max. : 68.000
## NA's :47 NA's :14##################################
# Creating standard labels for certain variables
##################################
DBP.Complete$ph.ecog <- factor(DBP.Complete$ph.ecog,
levels = c(3, 2, 1, 0),
labels = c("Bedridden", "Bedridden", "Ambulatory","Asymptomatic"))
DBP.Complete$sex <- factor(DBP.Complete$sex,
levels = c(1, 2),
labels = c("Male", "Female"))
DBP.Complete$statuslevel <- factor(DBP.Complete$status,
levels = c(1, 2),
labels = c(0, 1))
DBP.Complete$status <- ifelse(DBP.Complete$status==2,1,0)
##################################
# Creating an analysis dataset without the subject information column
##################################
DBP.Analysis <- DBP.Complete[,-1]
##################################
# Creating a response-covariate dataset without the treatment column
##################################
DBP.Response.Covariate <- DBP.Analysis[,-5]
##################################
# Formulating a data type assessment summary
##################################
PDA <- DBP.Analysis
(PDA.Summary <- data.frame(
Column.Index=c(1:length(names(PDA))),
Column.Name= names(PDA),
Column.Type=sapply(PDA, function(x) class(x)),
row.names=NULL)
)## Column.Index Column.Name Column.Type
## 1 1 time numeric
## 2 2 status numeric
## 3 3 age numeric
## 4 4 sex factor
## 5 5 ph.ecog factor
## 6 6 ph.karno numeric
## 7 7 pat.karno numeric
## 8 8 meal.cal numeric
## 9 9 wt.loss numeric
## 10 10 statuslevel factor1.2 Data Quality Assessment
[A] Missing observations noted for 5 variables with NA.Count>0 and Fill.Rate<1.0.
[A.1] ph.ecog variable (factor)
[A.2] ph.karno variable (numeric)
[A.3] pat.karno variable (numeric)
[A.4] meal.cal variable (numeric)
[A.5] wt.loss variable (numeric)
[B] No low variance (Unique.Count.Ratio<0.01 or First.Second.Mode.Ratio>5) noted for any response variable.
[C] No high skewness (Skewness>3 or Skewness<(-3)) noted for any response variable.
[D] Row filtering and column filtering were both applied to address quality issues in the data.
[D.1] 1 patient with missing information for ph.ecog variable removed.
[D.2] 4 variable columns ph.karno, pat.karno, meal.cal and wt.loss with low fill rates removed.
The pre-processed dataset was composed of the following:
[A] 227 Rows (observations composed of advanced lung cancer patients)
[B] 5 Columns (variables)
[B.1] 1/5 Factor variable = ph.ecog (factor) referring to the ECOG performance score (0=best, 3=worst) which describes the level of functioning of patients in terms of their ability to care for themselves, daily activity, and physical ability.
[B.1.1] Asymptomatic = ECOG performance score 0 (asymptomatic)
[B.1.2] Ambulatory = ECOG performance score 1 (symptomatic but completely ambulatory)
[B.1.3] Bedridden = ECOG performance score 2 (symptomatic but <50% in bed) or ECOG performance score 3 (symptomatic but >50% in bed)
[B.2] 1/5 Censoring variable = status (factor)
[B.2.1] 1 = event, patient died before the end of the study
[B.2.2] 0 = censored or non-event, patient remains alive until the end of the study, lost to follow-up, experiences a different event that makes further follow-up impossible or withdraws before the end of the study
[B.3] 1/5 Response variables = time (numeric)
[B.3.1] time = time in days a patient stays alive up to the point of the patient’s death or being censored
[B.4] 1/5 Covariate variable = age (numeric)
[B.4.1] age = patient’s age in years during the conduct of the study
[B.5] 1/5 Covariate variable = sex (factor)
[B.5.1] sex = patient’s sex at birth
Code Chunk | Output
##################################
# Loading dataset
##################################
DQA <- DBP.Analysis
##################################
# Listing all predictors
##################################
DQA.Predictors <- DQA[,!names(DQA) %in% c("time","status")]
##################################
# Formulating an overall data quality assessment summary
##################################
(DQA.Summary <- data.frame(
Column.Index=c(1:length(names(DQA))),
Column.Name= names(DQA),
Column.Type=sapply(DQA, function(x) class(x)),
Row.Count=sapply(DQA, function(x) nrow(DQA)),
NA.Count=sapply(DQA,function(x)sum(is.na(x))),
Fill.Rate=sapply(DQA,function(x)format(round((sum(!is.na(x))/nrow(DQA)),3),nsmall=3)),
row.names=NULL)
)## Column.Index Column.Name Column.Type Row.Count NA.Count Fill.Rate
## 1 1 time numeric 228 0 1.000
## 2 2 status numeric 228 0 1.000
## 3 3 age numeric 228 0 1.000
## 4 4 sex factor 228 0 1.000
## 5 5 ph.ecog factor 228 1 0.996
## 6 6 ph.karno numeric 228 1 0.996
## 7 7 pat.karno numeric 228 3 0.987
## 8 8 meal.cal numeric 228 47 0.794
## 9 9 wt.loss numeric 228 14 0.939
## 10 10 statuslevel factor 228 0 1.000##################################
# Listing all numeric predictors
##################################
DQA.Predictors.Numeric <- as.data.frame(DQA.Predictors[,sapply(DQA.Predictors, is.numeric)])
if (length(names(DQA.Predictors.Numeric))>0) {
print(paste0("There are ",
(length(names(DQA.Predictors.Numeric))),
" numeric predictor variable(s)."))
} else {
print("There are no numeric predictor variables.")
}## [1] "There are 5 numeric predictor variable(s)."##################################
# Listing all factor predictors
##################################
DQA.Predictors.Factor <- as.data.frame(DQA.Predictors[,sapply(DQA.Predictors, is.factor)])
if (length(names(DQA.Predictors.Factor))>0) {
print(paste0("There are ",
(length(names(DQA.Predictors.Factor))),
" factor predictor variable(s)."))
} else {
print("There are no factor predictor variables.")
}## [1] "There are 3 factor predictor variable(s)."##################################
# Checking for missing observations
##################################
if ((nrow(DQA.Summary[DQA.Summary$NA.Count>0,]))>0){
print(paste0("Missing observations noted for ",
(nrow(DQA.Summary[DQA.Summary$NA.Count>0,])),
" variable(s) with NA.Count>0 and Fill.Rate<1.0."))
DQA.Summary[DQA.Summary$NA.Count>0,]
} else {
print("No missing observations noted.")
}## [1] "Missing observations noted for 5 variable(s) with NA.Count>0 and Fill.Rate<1.0."## Column.Index Column.Name Column.Type Row.Count NA.Count Fill.Rate
## 5 5 ph.ecog factor 228 1 0.996
## 6 6 ph.karno numeric 228 1 0.996
## 7 7 pat.karno numeric 228 3 0.987
## 8 8 meal.cal numeric 228 47 0.794
## 9 9 wt.loss numeric 228 14 0.939##################################
# Formulating a data quality assessment summary for numeric predictors
##################################
if (length(names(DQA.Predictors.Numeric))>0) {
##################################
# Formulating a function to determine the first mode
##################################
FirstModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
ux[tab == max(tab)]
}
##################################
# Formulating a function to determine the second mode
##################################
SecondModes <- function(x) {
ux <- unique(na.omit(x))
tab <- tabulate(match(x, ux))
fm = ux[tab == max(tab)]
sm = na.omit(x)[!(na.omit(x) %in% fm)]
usm <- unique(sm)
tabsm <- tabulate(match(sm, usm))
usm[tabsm == max(tabsm)]
}
(DQA.Predictors.Numeric.Summary <- data.frame(
Column.Name= names(DQA.Predictors.Numeric),
Column.Type=sapply(DQA.Predictors.Numeric, function(x) class(x)),
Unique.Count=sapply(DQA.Predictors.Numeric, function(x) length(unique(x))),
Unique.Count.Ratio=sapply(DQA.Predictors.Numeric, function(x) format(round((length(unique(x))/nrow(DQA.Predictors.Numeric)),3), nsmall=3)),
First.Mode.Value=sapply(DQA.Predictors.Numeric, function(x) format(round((FirstModes(x)[1]),3),nsmall=3)),
Second.Mode.Value=sapply(DQA.Predictors.Numeric, function(x) format(round((SecondModes(x)[1]),3),nsmall=3)),
First.Mode.Count=sapply(DQA.Predictors.Numeric, function(x) sum(na.omit(x) == FirstModes(x)[1])),
Second.Mode.Count=sapply(DQA.Predictors.Numeric, function(x) sum(na.omit(x) == SecondModes(x)[1])),
First.Second.Mode.Ratio=sapply(DQA.Predictors.Numeric, function(x) format(round((sum(na.omit(x) == FirstModes(x)[1])/sum(na.omit(x) == SecondModes(x)[1])),3), nsmall=3)),
Minimum=sapply(DQA.Predictors.Numeric, function(x) format(round(min(x,na.rm = TRUE),3), nsmall=3)),
Mean=sapply(DQA.Predictors.Numeric, function(x) format(round(mean(x,na.rm = TRUE),3), nsmall=3)),
Median=sapply(DQA.Predictors.Numeric, function(x) format(round(median(x,na.rm = TRUE),3), nsmall=3)),
Maximum=sapply(DQA.Predictors.Numeric, function(x) format(round(max(x,na.rm = TRUE),3), nsmall=3)),
Skewness=sapply(DQA.Predictors.Numeric, function(x) format(round(skewness(x,na.rm = TRUE),3), nsmall=3)),
Kurtosis=sapply(DQA.Predictors.Numeric, function(x) format(round(kurtosis(x,na.rm = TRUE),3), nsmall=3)),
Percentile25th=sapply(DQA.Predictors.Numeric, function(x) format(round(quantile(x,probs=0.25,na.rm = TRUE),3), nsmall=3)),
Percentile75th=sapply(DQA.Predictors.Numeric, function(x) format(round(quantile(x,probs=0.75,na.rm = TRUE),3), nsmall=3)),
row.names=NULL)
)
}## Column.Name Column.Type Unique.Count Unique.Count.Ratio First.Mode.Value
## 1 age numeric 42 0.184 60.000
## 2 ph.karno numeric 7 0.031 90.000
## 3 pat.karno numeric 9 0.039 90.000
## 4 meal.cal numeric 61 0.268 1025.000
## 5 wt.loss numeric 54 0.237 0.000
## Second.Mode.Value First.Mode.Count Second.Mode.Count First.Second.Mode.Ratio
## 1 74.000 11 10 1.100
## 2 80.000 74 67 1.104
## 3 80.000 60 51 1.176
## 4 1225.000 24 14 1.714
## 5 10.000 34 13 2.615
## Minimum Mean Median Maximum Skewness Kurtosis Percentile25th
## 1 39.000 62.447 63.000 82.000 -0.370 2.626 56.000
## 2 50.000 81.938 80.000 100.000 -0.571 2.827 75.000
## 3 30.000 79.956 80.000 100.000 -0.602 3.157 70.000
## 4 96.000 928.779 975.000 2600.000 1.013 6.423 635.000
## 5 -24.000 9.832 7.000 68.000 1.180 5.379 0.000
## Percentile75th
## 1 69.000
## 2 90.000
## 3 90.000
## 4 1150.000
## 5 15.750##################################
# Identifying potential data quality issues for response variables (numeric)
##################################
##################################
# Checking for zero or near-zero variance predictors
##################################
if (length(names(DQA.Predictors.Numeric))==0) {
print("No numeric predictors noted.")
} else if (nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$First.Second.Mode.Ratio))>5,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$First.Second.Mode.Ratio))>5,])),
" numeric variable(s) with First.Second.Mode.Ratio>5."))
DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$First.Second.Mode.Ratio))>5,]
} else {
print("No low variance numeric predictors due to high first-second mode ratio noted.")
}## [1] "No low variance numeric predictors due to high first-second mode ratio noted."if (length(names(DQA.Predictors.Numeric))==0) {
print("No numeric predictors noted.")
} else if (nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Unique.Count.Ratio))<0.01,])>0){
print(paste0("Low variance observed for ",
(nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Unique.Count.Ratio))<0.01,])),
" numeric variable(s) with Unique.Count.Ratio<0.01."))
DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Unique.Count.Ratio))<0.01,]
} else {
print("No low variance numeric predictors due to low unique count ratio noted.")
}## [1] "No low variance numeric predictors due to low unique count ratio noted."##################################
# Checking for skewed response variables
##################################
if (length(names(DQA.Predictors.Numeric))==0) {
print("No response variables noted.")
} else if (nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))<(-3),])>0){
print(paste0("High skewness observed for ",
(nrow(DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))<(-3),])),
" response variable(s) with Skewness>3 or Skewness<(-3)."))
DQA.Predictors.Numeric.Summary[as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))>3 |
as.numeric(as.character(DQA.Predictors.Numeric.Summary$Skewness))<(-3),]
} else {
print("No skewed response variables noted.")
}## [1] "No skewed response variables noted."##################################
# Applying data filtering
##################################
DBP.ColumnFiltered <- DBP.Analysis[,!names(DBP.Analysis) %in% c("ph.karno","pat.karno","meal.cal","wt.loss")]
DBP.RowFiltered <- DBP.ColumnFiltered[complete.cases(DBP.ColumnFiltered),]
DBP.Analysis.Filtered <- DBP.RowFiltered
##################################
# Loading filtered dataset
##################################
DQA.Filtered <- DBP.Analysis.Filtered
##################################
# Formulating an overall data quality assessment summary
##################################
(DQA.Filtered.Summary <- data.frame(
Column.Index=c(1:length(names(DQA.Filtered))),
Column.Name= names(DQA.Filtered),
Column.Type=sapply(DQA.Filtered, function(x) class(x)),
Row.Count=sapply(DQA.Filtered, function(x) nrow(DQA.Filtered)),
NA.Count=sapply(DQA.Filtered,function(x)sum(is.na(x))),
Fill.Rate=sapply(DQA.Filtered,function(x)format(round((sum(!is.na(x))/nrow(DQA.Filtered)),3),nsmall=3)),
row.names=NULL)
)## Column.Index Column.Name Column.Type Row.Count NA.Count Fill.Rate
## 1 1 time numeric 227 0 1.000
## 2 2 status numeric 227 0 1.000
## 3 3 age numeric 227 0 1.000
## 4 4 sex factor 227 0 1.000
## 5 5 ph.ecog factor 227 0 1.000
## 6 6 statuslevel factor 227 0 1.0001.3 Research Question
Using the cancer dataset, survival analysis and modelling will be conducted to investigate the following :
[A] Research Question : What is the probability that an advanced lung cancer patient under the Asymptomatic, Ambulatory and Bedridden groups will survive (stay alive) after a specified number of days?
[A.1] Factor variable = ph.ecog
[A.1.1] Asymptomatic = ECOG performance score 0 (asymptomatic)
[A.1.2] Ambulatory = ECOG performance score 1 (symptomatic but completely ambulatory)
[A.1.3] Bedridden = ECOG performance score 2 (symptomatic but <50% in bed) or ECOG performance score 3 (symptomatic but >50% in bed)
[A.2] Response variable = time (numeric)
[A.3] Censoring variable = status (factor)
[A.3.1] 1 = event, patient died before the end of the study
[A.3.2] 0 = censored or non-event, patient remains alive until until the end of the study, lost to follow-up, experiences a different event that makes further follow-up impossible or withdraws before the end of the study
[B] Research Question : Are there differences in survival between advanced lung cancer patients under the Asymptomatic, Ambulatory and Bedridden groups?
[B.1] Factor variable = ph.ecog
[B.1.1] Asymptomatic = ECOG performance score 0 (asymptomatic)
[B.1.2] Ambulatory = ECOG performance score 1 (symptomatic but completely ambulatory)
[B.1.3] Bedridden = ECOG performance score 2 (symptomatic but <50% in bed) or ECOG performance score 3 (symptomatic but >50% in bed)
[B.2] Response variable = time (numeric)
[B.3] Censoring variable = status (factor)
[B.3.1] 1 = event, patient died before the end of the study
[B.3.2] 0 = censored or non-event, patient remains alive until the end of the study, lost to follow-up, experiences a different event that makes further follow-up impossible or withdraws before the end of the study
[C] Research Question : What is the impact of the clinical characteristicS age and sex on the survival of advanced lung cancer patients under the Asymptomatic, Ambulatory and Bedridden groups?
[C.1] Factor variable = ph.ecog (factor) referring to the ECOG performance score (0=best, 3=worst) which describes the level of functioning of patients in terms of their ability to care for themselves, daily activity, and physical ability.
[C.1.1] Asymptomatic = ECOG performance score 0 (asymptomatic)
[C.1.2] Ambulatory = ECOG performance score 1 (symptomatic but completely ambulatory)
[C.1.3] Bedridden = ECOG performance score 2 (symptomatic but <50% in bed) or ECOG performance score 3 (symptomatic but >50% in bed)
[C.2] 1/5 Censoring variable = status (factor)
[C.2.1] 1 = event, patient died before the end of the study
[C.2.2] 0 = censored or non-event, patient remains alive until the end of the study, lost to follow-up, experiences a different event that makes further follow-up impossible or withdraws before the end of the study
[C.3] Response variables = time (numeric)
[C.3.1] time = time in days a patient stays alive up to the point of the patient’s death or being censored
[C.4] Covariate variable = age (numeric)
[C.4.1] age = patient’s age in years during the conduct of the study
[C.5] Covariate variable = sex (factor)
[C.5.1] sex = patient’s sex at birth
1.4 Data Exploration
Exploratory and comparative analyses of the response variable time by factor variable ph.ecog showed that :
[A] Differences in the proportion of censored and uncensored data (p=0.002, Pearson’s Chi-squared Test) observed between ph.ecog=Asymptomatic (censored=41%, uncensored=59%), ph.ecog=Ambulatory (censored=27%, uncensored=73%) and ph.ecog=Bedridden (censored=12%, uncensored=88%).
[B] With both censored and uncensored data considered, differences in median survival time time (p=0.001, Wilcoxon Rank Sum Test) was observed for ph.ecog=Asymptomatic (303), ph.ecog=Ambulatory (243) and compared to ph.ecog=Bedridden (180). Differences in the age of patients age (p=0.002, Wilcoxon Rank Sum Test) was also noted for ph.ecog=Asymptomatic (61), ph.ecog=Ambulatory (61) and compared to ph.ecog=Bedridden (66).
[C] With only the uncensored considered, decreasing mean survival time time observed ph.ecog=Asymptomatic (331), ph.ecog=Ambulatory (296) and ph.ecog=Bedridden (223). Increasing mean hazard rate was also noted for ph.ecog=Asymptomatic (0.17), ph.ecog=Ambulatory (0.23) and ph.ecog=Bedridden (0.38).
Kaplan-Meier survival curve analysis of the response variable time by factor variable ph.ecog (with censoring variable status considered) showed that :
[A] Differences in the Kaplan-Meier survival curves (p<0.0001, Log Rank Test) were noted between ph.ecog=Asymptomatic (median survival time=394), ph.ecog=Ambulatory (median survival time=306) and ph.ecog=Bedridden (median survival time=103). Post-hoc pairwise log rank test showed that differences in the Kaplan-Meier survival curves were observed between ph.ecog=Ambulatory (median survival time=306) and ph.ecog=Bedridden (median survival time=103) (p<0.0001, Log Rank Test) and ph.ecog=Asymptomatic (median survival time=394), and ph.ecog=Bedridden (median survival time=103) (p=0.0039, Log Rank Test) only. Difference in the Kaplan-Meier survival curves between ph.ecog=Asymptomatic (median survival time=394) and ph.ecog=Ambulatory (median survival time=306) was not statistically significant (p=0.0630, Log Rank Test).
[B] Decreasing survival times were consistently observed for advanced lung cancer patients under ph.ecog=Asymptomatic, ph.ecog=Ambulatory and ph.ecog=Bedridden at various sampled durations including time=183 days (6 months) (Asymptomatic=84%, Ambulatory=72%, Bedridden=50%), time=365 days (12 months) (Asymptomatic=54%, Ambulatory=43%, Bedridden=21%), time=548 days (18 months) (Asymptomatic=37%, Ambulatory=26%, Bedridden=11%), time=730 days (24 months) (Asymptomatic=19%, Ambulatory=11%, Bedridden=4%), and time=913 days (32 months) (Asymptomatic=8%, Ambulatory=6%, Bedridden=0%), except for time=1022 days (last recorded follow-up time) where ph.ecog=Ambulatory showed 6% survival while 0% survival was noted for both ph.ecog=Asymptomatic and ph.ecog=Bedridden groups.
1.4.1 Descriptive Statistics
Code Chunk | Output
##################################
# Reusing the dataset
##################################
head(DBP.Analysis.Filtered)## time status age sex ph.ecog statuslevel
## 1 306 1 74 Male Ambulatory 1
## 2 455 1 68 Male Asymptomatic 1
## 3 1010 0 56 Male Asymptomatic 0
## 4 210 1 57 Male Ambulatory 1
## 5 883 1 60 Male Asymptomatic 1
## 6 1022 0 74 Male Ambulatory 0##################################
# Formulating a preliminary summary
# of descriptive statistics
##################################
DBP.Analysis.Filtered %>%
select(time,statuslevel,ph.ecog,age,sex) %>%
tbl_summary(
by = ph.ecog,
type = all_continuous() ~ "continuous2",
statistic = all_continuous() ~ c("{N_nonmiss}",
"{mean} ({sd})",
"{median} ({p25}, {p75})",
"{min}, {max}"),
missing = "no") %>%
add_overall() %>%
add_p()| Characteristic | Overall N = 2271 |
Bedridden N = 511 |
Ambulatory N = 1131 |
Asymptomatic N = 631 |
p-value2 |
|---|---|---|---|---|---|
| time | 0.001 | ||||
| N Non-missing | 227 | 51 | 113 | 63 | |
| Mean (SD) | 306 (211) | 232 (189) | 314 (207) | 352 (220) | |
| Median (Q1, Q3) | 259 (167, 404) | 180 (95, 310) | 243 (177, 426) | 303 (224, 442) | |
| Min, Max | 5, 1,022 | 11, 814 | 11, 1,022 | 5, 1,010 | |
| statuslevel | 0.002 | ||||
| 0 | 63 (28%) | 6 (12%) | 31 (27%) | 26 (41%) | |
| 1 | 164 (72%) | 45 (88%) | 82 (73%) | 37 (59%) | |
| age | 0.002 | ||||
| N Non-missing | 227 | 51 | 113 | 63 | |
| Mean (SD) | 62 (9) | 66 (8) | 61 (9) | 61 (10) | |
| Median (Q1, Q3) | 63 (56, 69) | 68 (60, 73) | 63 (55, 68) | 61 (56, 68) | |
| Min, Max | 39, 82 | 48, 77 | 40, 80 | 39, 82 | |
| sex | 0.7 | ||||
| Male | 137 (60%) | 30 (59%) | 71 (63%) | 36 (57%) | |
| Female | 90 (40%) | 21 (41%) | 42 (37%) | 27 (43%) | |
| 1 n (%) | |||||
| 2 Kruskal-Wallis rank sum test; Pearson’s Chi-squared test | |||||
##################################
# Computing for the mean uncensored survival time
# and mean hazard rate between asymptomatic, ambulatory and bedridden groups
##################################
DBP.Analysis.Filtered.DescriptiveStatistics <- DBP.Analysis.Filtered %>%
group_by(ph.ecog) %>%
summarise(
Mean.Uncensored.Survival.Time = mean(time[status==1]),
Total.Uncensored.Survival.Time = sum(status==1),
Total.Survival.Time = sum(time),
Mean.Hazard.Rate = (Total.Uncensored.Survival.Time/Total.Survival.Time)*100)
kable(DBP.Analysis.Filtered.DescriptiveStatistics)| ph.ecog | Mean.Uncensored.Survival.Time | Total.Uncensored.Survival.Time | Total.Survival.Time | Mean.Hazard.Rate |
|---|---|---|---|---|
| Bedridden | 223.5556 | 45 | 11822 | 0.3806463 |
| Ambulatory | 296.3902 | 82 | 35532 | 0.2307779 |
| Asymptomatic | 331.3514 | 37 | 22168 | 0.1669073 |
1.4.2 Kaplan-Meier Survival Curve
Kaplan-Meier Survival Curve estimates a survival function which makes no assumptions about how the probability that an observation develops the event changes over time. It is a step function plot obtained from the values of a follow-up table which summarizes the experiences of subjects over a pre-defined follow-up period in a study until the time of the event of interest or the end of the study, whichever comes first. The method involves generating a sequential list of time values corresponding to an event or censoring; determining the counts of event-free observations, event and censored cases for each time value; and computing the survival probabilities based on these counts.
Code Chunk | Output
##################################
# Reusing the dataset
##################################
head(DBP.Analysis.Filtered)## time status age sex ph.ecog statuslevel
## 1 306 1 74 Male Ambulatory 1
## 2 455 1 68 Male Asymptomatic 1
## 3 1010 0 56 Male Asymptomatic 0
## 4 210 1 57 Male Ambulatory 1
## 5 883 1 60 Male Asymptomatic 1
## 6 1022 0 74 Male Ambulatory 0##################################
# Computing the Kaplan-Meier survival estimates
# using the Baseline data
##################################
DBP.Analysis.Filtered.Baseline.KaplanMeierEstimates <- survfit(Surv(time, status) ~ 1, data = DBP.Analysis.Filtered)
print(DBP.Analysis.Filtered.Baseline.KaplanMeierEstimates)## Call: survfit(formula = Surv(time, status) ~ 1, data = DBP.Analysis.Filtered)
##
## n events median 0.95LCL 0.95UCL
## [1,] 227 164 310 285 363tbl_survfit(DBP.Analysis.Filtered.Baseline.KaplanMeierEstimates,
times = c(183,365,548,730,913,1022),
label_header = "**Day {time}**"
)| Characteristic | Day 183 | Day 365 | Day 548 | Day 730 | Day 913 | Day 1022 |
|---|---|---|---|---|---|---|
| Overall | 71% (65%, 77%) | 41% (35%, 49%) | 26% (20%, 33%) | 12% (7.2%, 19%) | 5.1% (2.1%, 12%) | 5.1% (2.1%, 12%) |
##################################
# Formulating a summary of the Kaplan-Meier survival estimates
# using the Baseline data
##################################
summary(DBP.Analysis.Filtered.Baseline.KaplanMeierEstimates)## Call: survfit(formula = Surv(time, status) ~ 1, data = DBP.Analysis.Filtered)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 5 227 1 0.9956 0.00440 0.9870 1.000
## 11 226 3 0.9824 0.00873 0.9654 1.000
## 12 223 1 0.9780 0.00974 0.9591 0.997
## 13 222 2 0.9692 0.01147 0.9469 0.992
## 15 220 1 0.9648 0.01224 0.9411 0.989
## 26 219 1 0.9604 0.01295 0.9353 0.986
## 30 218 1 0.9559 0.01362 0.9296 0.983
## 31 217 1 0.9515 0.01425 0.9240 0.980
## 53 216 2 0.9427 0.01542 0.9130 0.973
## 54 214 1 0.9383 0.01597 0.9075 0.970
## 59 213 1 0.9339 0.01649 0.9022 0.967
## 60 212 2 0.9251 0.01747 0.8915 0.960
## 61 210 1 0.9207 0.01793 0.8862 0.957
## 62 209 1 0.9163 0.01838 0.8810 0.953
## 65 208 2 0.9075 0.01923 0.8706 0.946
## 79 206 1 0.9031 0.01964 0.8654 0.942
## 81 205 2 0.8943 0.02041 0.8552 0.935
## 88 203 2 0.8855 0.02114 0.8450 0.928
## 92 201 1 0.8811 0.02149 0.8399 0.924
## 93 199 1 0.8766 0.02183 0.8349 0.920
## 95 198 2 0.8678 0.02249 0.8248 0.913
## 105 196 1 0.8633 0.02281 0.8198 0.909
## 107 194 2 0.8544 0.02342 0.8097 0.902
## 110 192 1 0.8500 0.02372 0.8048 0.898
## 116 191 1 0.8455 0.02401 0.7998 0.894
## 118 190 1 0.8411 0.02429 0.7948 0.890
## 122 189 1 0.8366 0.02457 0.7899 0.886
## 131 188 1 0.8322 0.02484 0.7849 0.882
## 132 187 2 0.8233 0.02536 0.7751 0.875
## 135 185 1 0.8188 0.02561 0.7702 0.871
## 142 184 1 0.8144 0.02585 0.7653 0.867
## 144 183 1 0.8099 0.02609 0.7604 0.863
## 145 182 2 0.8010 0.02655 0.7507 0.855
## 147 180 1 0.7966 0.02677 0.7458 0.851
## 153 179 1 0.7921 0.02699 0.7410 0.847
## 156 178 2 0.7832 0.02741 0.7313 0.839
## 163 176 3 0.7699 0.02801 0.7169 0.827
## 166 173 2 0.7610 0.02838 0.7073 0.819
## 167 171 1 0.7565 0.02856 0.7026 0.815
## 170 170 1 0.7521 0.02874 0.6978 0.811
## 175 167 1 0.7476 0.02892 0.6930 0.806
## 176 165 1 0.7431 0.02910 0.6882 0.802
## 177 164 1 0.7385 0.02927 0.6833 0.798
## 179 162 2 0.7294 0.02961 0.6736 0.790
## 180 160 1 0.7248 0.02977 0.6688 0.786
## 181 159 2 0.7157 0.03009 0.6591 0.777
## 182 157 1 0.7112 0.03024 0.6543 0.773
## 183 156 1 0.7066 0.03039 0.6495 0.769
## 186 154 1 0.7020 0.03054 0.6447 0.765
## 189 152 1 0.6974 0.03068 0.6398 0.760
## 194 149 1 0.6927 0.03083 0.6349 0.756
## 197 147 1 0.6880 0.03098 0.6299 0.751
## 199 145 1 0.6833 0.03113 0.6249 0.747
## 201 144 2 0.6738 0.03141 0.6149 0.738
## 202 142 1 0.6690 0.03154 0.6100 0.734
## 207 139 1 0.6642 0.03168 0.6049 0.729
## 208 138 1 0.6594 0.03182 0.5999 0.725
## 210 137 1 0.6546 0.03195 0.5949 0.720
## 212 135 1 0.6497 0.03208 0.5898 0.716
## 218 134 1 0.6449 0.03220 0.5848 0.711
## 222 132 1 0.6400 0.03233 0.5797 0.707
## 223 130 1 0.6351 0.03245 0.5746 0.702
## 226 126 1 0.6300 0.03258 0.5693 0.697
## 229 125 1 0.6250 0.03271 0.5641 0.693
## 230 124 1 0.6200 0.03283 0.5588 0.688
## 239 121 2 0.6097 0.03308 0.5482 0.678
## 245 117 1 0.6045 0.03320 0.5428 0.673
## 246 116 1 0.5993 0.03332 0.5374 0.668
## 267 112 1 0.5939 0.03345 0.5319 0.663
## 268 111 1 0.5886 0.03358 0.5263 0.658
## 269 110 1 0.5832 0.03369 0.5208 0.653
## 270 108 1 0.5778 0.03381 0.5152 0.648
## 283 104 1 0.5723 0.03394 0.5095 0.643
## 284 103 1 0.5667 0.03406 0.5038 0.638
## 285 101 2 0.5555 0.03430 0.4922 0.627
## 286 99 1 0.5499 0.03441 0.4864 0.622
## 288 98 1 0.5443 0.03451 0.4807 0.616
## 291 97 1 0.5387 0.03461 0.4749 0.611
## 293 94 1 0.5329 0.03471 0.4691 0.606
## 301 91 1 0.5271 0.03482 0.4631 0.600
## 303 89 1 0.5212 0.03493 0.4570 0.594
## 305 87 1 0.5152 0.03504 0.4509 0.589
## 306 86 1 0.5092 0.03514 0.4448 0.583
## 310 85 2 0.4972 0.03532 0.4326 0.571
## 320 82 1 0.4911 0.03541 0.4264 0.566
## 329 81 1 0.4851 0.03548 0.4203 0.560
## 337 79 1 0.4789 0.03556 0.4141 0.554
## 340 78 1 0.4728 0.03563 0.4079 0.548
## 345 77 1 0.4667 0.03570 0.4017 0.542
## 348 76 1 0.4605 0.03575 0.3955 0.536
## 350 75 1 0.4544 0.03580 0.3894 0.530
## 351 74 1 0.4482 0.03584 0.3832 0.524
## 353 73 2 0.4360 0.03589 0.3710 0.512
## 361 70 1 0.4297 0.03591 0.3648 0.506
## 363 69 2 0.4173 0.03594 0.3525 0.494
## 364 67 1 0.4110 0.03594 0.3463 0.488
## 371 65 2 0.3984 0.03593 0.3339 0.475
## 387 60 1 0.3918 0.03594 0.3273 0.469
## 390 59 1 0.3851 0.03593 0.3208 0.462
## 394 58 1 0.3785 0.03592 0.3142 0.456
## 426 55 1 0.3716 0.03592 0.3075 0.449
## 428 54 1 0.3647 0.03591 0.3007 0.442
## 429 53 1 0.3578 0.03589 0.2940 0.436
## 433 52 1 0.3510 0.03585 0.2873 0.429
## 442 51 1 0.3441 0.03580 0.2806 0.422
## 444 50 1 0.3372 0.03574 0.2739 0.415
## 450 48 1 0.3302 0.03568 0.2671 0.408
## 455 47 1 0.3231 0.03561 0.2604 0.401
## 457 46 1 0.3161 0.03552 0.2536 0.394
## 460 44 1 0.3089 0.03543 0.2467 0.387
## 473 43 1 0.3017 0.03533 0.2399 0.380
## 477 42 1 0.2946 0.03521 0.2330 0.372
## 519 39 1 0.2870 0.03511 0.2258 0.365
## 520 38 1 0.2795 0.03499 0.2186 0.357
## 524 37 2 0.2643 0.03469 0.2044 0.342
## 533 34 1 0.2566 0.03453 0.1971 0.334
## 550 32 1 0.2486 0.03437 0.1896 0.326
## 558 30 1 0.2403 0.03420 0.1818 0.318
## 567 28 1 0.2317 0.03404 0.1737 0.309
## 574 27 1 0.2231 0.03385 0.1657 0.300
## 583 26 1 0.2145 0.03361 0.1578 0.292
## 613 24 1 0.2056 0.03338 0.1496 0.283
## 624 23 1 0.1967 0.03311 0.1414 0.274
## 641 22 1 0.1877 0.03278 0.1333 0.264
## 643 21 1 0.1788 0.03242 0.1253 0.255
## 654 20 1 0.1698 0.03201 0.1174 0.246
## 655 19 1 0.1609 0.03155 0.1096 0.236
## 687 18 1 0.1520 0.03103 0.1018 0.227
## 689 17 1 0.1430 0.03047 0.0942 0.217
## 705 16 1 0.1341 0.02985 0.0867 0.207
## 707 15 1 0.1251 0.02916 0.0793 0.198
## 728 14 1 0.1162 0.02842 0.0720 0.188
## 731 13 1 0.1073 0.02760 0.0648 0.178
## 735 12 1 0.0983 0.02671 0.0577 0.167
## 765 10 1 0.0885 0.02579 0.0500 0.157
## 791 9 1 0.0787 0.02472 0.0425 0.146
## 814 7 1 0.0674 0.02361 0.0339 0.134
## 883 4 1 0.0506 0.02295 0.0208 0.123(DBP.Analysis.Filtered.Baseline.KaplanMeierEstimates.Summary <- summary(DBP.Analysis.Filtered.Baseline.KaplanMeierEstimates)$table)## records n.max n.start events rmean se(rmean) median 0.95LCL
## 227.00000 227.00000 227.00000 164.00000 377.61957 19.74867 310.00000 285.00000
## 0.95UCL
## 363.00000##################################
# Listing the details of the Kaplan-Meier survival estimates
# using the Baseline data
##################################
(DBP.Analysis.Filtered.Baseline.KaplanMeierEstimates.Details <- surv_summary(DBP.Analysis.Filtered.Baseline.KaplanMeierEstimates))## time n.risk n.event n.censor surv std.err upper lower
## 1 5 227 1 0 0.99559471 0.004415022 1.0000000 0.98701672
## 2 11 226 3 0 0.98237885 0.008889240 0.9996444 0.96541151
## 3 12 223 1 0 0.97797357 0.009960831 0.9972540 0.95906588
## 4 13 222 2 0 0.96916300 0.011839265 0.9919149 0.94693294
## 5 15 220 1 0 0.96475771 0.012685571 0.9890454 0.94106643
## 6 26 219 1 0 0.96035242 0.013485904 0.9860748 0.93530103
## 7 30 218 1 0 0.95594714 0.014248108 0.9830189 0.92962087
## 8 31 217 1 0 0.95154185 0.014978094 0.9798899 0.92401393
## 9 53 216 2 0 0.94273128 0.016358816 0.9734476 0.91298421
## 10 54 214 1 0 0.93832599 0.017016149 0.9701478 0.90754794
## 11 59 213 1 0 0.93392070 0.017654880 0.9668027 0.90215704
## 12 60 212 2 0 0.92511013 0.018884343 0.9599925 0.89149529
## 13 61 210 1 0 0.92070485 0.019478261 0.9565339 0.88621787
## 14 62 209 1 0 0.91629956 0.020060059 0.9530433 0.88097244
## 15 65 208 2 0 0.90748899 0.021191569 0.9459750 0.87056874
## 16 79 206 1 0 0.90308370 0.021743101 0.9424011 0.86540668
## 17 81 205 2 0 0.89427313 0.022821526 0.9351815 0.85515426
## 18 88 203 2 0 0.88546256 0.023871281 0.9278750 0.84498875
## 19 92 201 1 1 0.88105727 0.024386752 0.9241919 0.83993581
## 20 93 199 1 0 0.87662985 0.024901668 0.9204763 0.83487203
## 21 95 198 2 0 0.86777500 0.025915803 0.9129914 0.82479793
## 22 105 196 1 1 0.86334757 0.026415775 0.9092239 0.81978605
## 23 107 194 2 0 0.85444708 0.027413269 0.9016114 0.80975000
## 24 110 192 1 0 0.84999684 0.027906201 0.8977825 0.80475468
## 25 116 191 1 0 0.84554659 0.028395631 0.8939391 0.79977374
## 26 118 190 1 0 0.84109635 0.028881816 0.8900819 0.79480667
## 27 122 189 1 0 0.83664610 0.029364995 0.8862114 0.78985299
## 28 131 188 1 0 0.83219586 0.029845394 0.8823279 0.78491224
## 29 132 187 2 0 0.82329537 0.030798691 0.8745237 0.77506795
## 30 135 185 1 0 0.81884512 0.031271978 0.8706037 0.77016364
## 31 142 184 1 0 0.81439488 0.031743265 0.8666724 0.76527076
## 32 144 183 1 0 0.80994463 0.032212722 0.8627299 0.76038898
## 33 145 182 2 0 0.80104414 0.033146788 0.8548129 0.75065754
## 34 147 180 1 0 0.79659390 0.033611697 0.8508388 0.74580733
## 35 153 179 1 0 0.79214365 0.034075380 0.8468548 0.74096711
## 36 156 178 2 0 0.78324316 0.034999602 0.8388578 0.73131570
## 37 163 176 3 0 0.76989243 0.036379951 0.8267929 0.71690792
## 38 166 173 2 0 0.76099193 0.037297549 0.8187056 0.70734668
## 39 167 171 1 0 0.75654169 0.037755886 0.8146494 0.70257873
## 40 170 170 1 0 0.75209144 0.038214052 0.8105849 0.69781900
## 41 173 169 0 1 0.75209144 0.038214052 0.8105849 0.69781900
## 42 174 168 0 1 0.75209144 0.038214052 0.8105849 0.69781900
## 43 175 167 1 1 0.74758790 0.038683151 0.8064722 0.69300299
## 44 176 165 1 0 0.74305707 0.039157899 0.8023307 0.68816234
## 45 177 164 1 1 0.73852623 0.039632681 0.7981809 0.68333006
## 46 179 162 2 0 0.72940862 0.040594457 0.7898142 0.67362288
## 47 180 160 1 0 0.72484982 0.041075761 0.7856187 0.66878155
## 48 181 159 2 0 0.71573221 0.042039704 0.7772036 0.65912275
## 49 182 157 1 0 0.71117341 0.042522539 0.7729845 0.65430503
## 50 183 156 1 0 0.70661460 0.043006079 0.7687576 0.64949493
## 51 185 155 0 1 0.70661460 0.043006079 0.7687576 0.64949493
## 52 186 154 1 0 0.70202620 0.043496713 0.7645005 0.64465722
## 53 188 153 0 1 0.70202620 0.043496713 0.7645005 0.64465722
## 54 189 152 1 0 0.69740760 0.043994696 0.7602125 0.63979129
## 55 191 151 0 1 0.69740760 0.043994696 0.7602125 0.63979129
## 56 192 150 0 1 0.69740760 0.043994696 0.7602125 0.63979129
## 57 194 149 1 0 0.69272702 0.044507085 0.7558692 0.63485950
## 58 196 148 0 1 0.69272702 0.044507085 0.7558692 0.63485950
## 59 197 147 1 1 0.68801459 0.045027487 0.7514933 0.62989793
## 60 199 145 1 0 0.68326966 0.045556199 0.7470844 0.62490591
## 61 201 144 2 0 0.67377980 0.046617340 0.7382420 0.61494636
## 62 202 142 1 1 0.66903487 0.047149989 0.7338088 0.60997862
## 63 203 140 0 1 0.66903487 0.047149989 0.7338088 0.60997862
## 64 207 139 1 0 0.66422167 0.047699619 0.7293148 0.60493826
## 65 208 138 1 0 0.65940847 0.048250875 0.7248126 0.59990614
## 66 210 137 1 0 0.65459527 0.048803873 0.7203023 0.59488214
## 67 211 136 0 1 0.65459527 0.048803873 0.7203023 0.59488214
## 68 212 135 1 0 0.64974642 0.049366964 0.7157562 0.58982430
## 69 218 134 1 0 0.64489757 0.049932030 0.7112020 0.58477462
## 70 221 133 0 1 0.64489757 0.049932030 0.7112020 0.58477462
## 71 222 132 1 1 0.64001198 0.050507800 0.7066110 0.57968997
## 72 223 130 1 0 0.63508881 0.051094697 0.7019826 0.57456951
## 73 224 129 0 1 0.63508881 0.051094697 0.7019826 0.57456951
## 74 225 128 0 2 0.63508881 0.051094697 0.7019826 0.57456951
## 75 226 126 1 0 0.63004842 0.051712283 0.6972548 0.56931988
## 76 229 125 1 0 0.62500803 0.052332364 0.6925179 0.56407936
## 77 230 124 1 0 0.61996765 0.052955089 0.6877720 0.55884783
## 78 235 123 0 1 0.61996765 0.052955089 0.6877720 0.55884783
## 79 237 122 0 1 0.61996765 0.052955089 0.6877720 0.55884783
## 80 239 121 2 0 0.60972025 0.054250714 0.6781237 0.54821678
## 81 240 119 0 1 0.60972025 0.054250714 0.6781237 0.54821678
## 82 243 118 0 1 0.60972025 0.054250714 0.6781237 0.54821678
## 83 245 117 1 0 0.60450896 0.054925596 0.6732177 0.54281269
## 84 246 116 1 0 0.59929768 0.055603809 0.6683018 0.53741842
## 85 252 115 0 1 0.59929768 0.055603809 0.6683018 0.53741842
## 86 259 114 0 1 0.59929768 0.055603809 0.6683018 0.53741842
## 87 266 113 0 1 0.59929768 0.055603809 0.6683018 0.53741842
## 88 267 112 1 0 0.59394681 0.056322475 0.6632684 0.53187034
## 89 268 111 1 0 0.58859593 0.057044906 0.6582244 0.52633293
## 90 269 110 1 1 0.58324506 0.057771309 0.6531698 0.52080608
## 91 270 108 1 0 0.57784465 0.058515462 0.6480665 0.51523178
## 92 272 107 0 1 0.57784465 0.058515462 0.6480665 0.51523178
## 93 276 106 0 1 0.57784465 0.058515462 0.6480665 0.51523178
## 94 279 105 0 1 0.57784465 0.058515462 0.6480665 0.51523178
## 95 283 104 1 0 0.57228845 0.059307778 0.6428325 0.50948583
## 96 284 103 1 1 0.56673225 0.060104877 0.6375868 0.50375174
## 97 285 101 2 0 0.55550983 0.061746386 0.6269752 0.49219039
## 98 286 99 1 0 0.54989862 0.062575456 0.6216515 0.48642770
## 99 288 98 1 0 0.54428741 0.063410444 0.6163159 0.48067686
## 100 291 97 1 0 0.53867620 0.064251636 0.6109686 0.47493775
## 101 292 96 0 2 0.53867620 0.064251636 0.6109686 0.47493775
## 102 293 94 1 0 0.53294560 0.065135728 0.6055172 0.46907172
## 103 296 93 0 1 0.53294560 0.065135728 0.6055172 0.46907172
## 104 300 92 0 1 0.53294560 0.065135728 0.6055172 0.46907172
## 105 301 91 1 1 0.52708905 0.066066355 0.5999565 0.46307167
## 106 303 89 1 1 0.52116670 0.067025700 0.5943319 0.45700851
## 107 305 87 1 0 0.51517628 0.068015429 0.5886413 0.45088005
## 108 306 86 1 0 0.50918586 0.069013749 0.5829361 0.44476615
## 109 310 85 2 0 0.49720502 0.071037908 0.5714827 0.43258148
## 110 315 83 0 1 0.49720502 0.071037908 0.5714827 0.43258148
## 111 320 82 1 0 0.49114154 0.072089815 0.5656784 0.42642603
## 112 329 81 1 0 0.48507807 0.073152324 0.5598594 0.42028536
## 113 332 80 0 1 0.48507807 0.073152324 0.5598594 0.42028536
## 114 337 79 1 0 0.47893784 0.074253265 0.5539667 0.41407085
## 115 340 78 1 0 0.47279761 0.075366090 0.5480586 0.40787167
## 116 345 77 1 0 0.46665738 0.076491368 0.5421353 0.40168773
## 117 348 76 1 0 0.46051715 0.077629685 0.5361969 0.39551895
## 118 350 75 1 0 0.45437692 0.078781648 0.5302435 0.38936526
## 119 351 74 1 0 0.44823669 0.079947888 0.5242750 0.38322659
## 120 353 73 2 0 0.43595624 0.082325826 0.5122934 0.37099412
## 121 356 71 0 1 0.43595624 0.082325826 0.5122934 0.37099412
## 122 361 70 1 0 0.42972829 0.083573806 0.5062116 0.36480081
## 123 363 69 2 0 0.41727240 0.086123171 0.4940010 0.35246133
## 124 364 67 1 1 0.41104445 0.087426212 0.4878722 0.34631513
## 125 371 65 2 0 0.39839693 0.090176178 0.4754163 0.33385500
## 126 376 63 0 1 0.39839693 0.090176178 0.4754163 0.33385500
## 127 382 62 0 1 0.39839693 0.090176178 0.4754163 0.33385500
## 128 384 61 0 1 0.39839693 0.090176178 0.4754163 0.33385500
## 129 387 60 1 0 0.39175698 0.091729106 0.4689178 0.32729305
## 130 390 59 1 0 0.38511703 0.093308390 0.4623991 0.32075134
## 131 394 58 1 0 0.37847708 0.094915415 0.4558603 0.31422985
## 132 404 57 0 1 0.37847708 0.094915415 0.4558603 0.31422985
## 133 413 56 0 1 0.37847708 0.094915415 0.4558603 0.31422985
## 134 426 55 1 0 0.37159568 0.096672831 0.4491162 0.30745573
## 135 428 54 1 0 0.36471428 0.098463406 0.4423489 0.30070494
## 136 429 53 1 0 0.35783288 0.100289018 0.4355584 0.29397749
## 137 433 52 1 0 0.35095148 0.102151657 0.4287447 0.28727341
## 138 442 51 1 0 0.34407008 0.104053437 0.4219076 0.28059276
## 139 444 50 1 1 0.33718867 0.105996609 0.4150472 0.27393562
## 140 450 48 1 0 0.33016391 0.108067310 0.4080531 0.26714222
## 141 455 47 1 0 0.32313915 0.110186561 0.4010334 0.26037459
## 142 457 46 1 0 0.31611438 0.112357332 0.3939880 0.25363286
## 143 458 45 0 1 0.31611438 0.112357332 0.3939880 0.25363286
## 144 460 44 1 0 0.30892996 0.114685270 0.3867945 0.24674011
## 145 473 43 1 0 0.30174555 0.117074425 0.3795726 0.23987608
## 146 477 42 1 0 0.29456113 0.119528830 0.3723219 0.23304099
## 147 511 41 0 2 0.29456113 0.119528830 0.3723219 0.23304099
## 148 519 39 1 0 0.28700828 0.122318866 0.3647644 0.22582729
## 149 520 38 1 0 0.27945543 0.125192422 0.3571713 0.21864954
## 150 524 37 2 0 0.26434973 0.131215640 0.3418770 0.20440331
## 151 529 35 0 1 0.26434973 0.131215640 0.3418770 0.20440331
## 152 533 34 1 0 0.25657474 0.134568977 0.3340098 0.19709181
## 153 543 33 0 1 0.25657474 0.134568977 0.3340098 0.19709181
## 154 550 32 1 0 0.24855678 0.138263785 0.3259237 0.18955501
## 155 551 31 0 1 0.24855678 0.138263785 0.3259237 0.18955501
## 156 558 30 1 0 0.24027155 0.142359754 0.3175991 0.18177138
## 157 559 29 0 1 0.24027155 0.142359754 0.3175991 0.18177138
## 158 567 28 1 0 0.23169043 0.146932130 0.3090131 0.17371576
## 159 574 27 1 0 0.22310930 0.151702183 0.3003633 0.16572519
## 160 583 26 1 0 0.21452817 0.156690822 0.2916485 0.15780068
## 161 588 25 0 1 0.21452817 0.156690822 0.2916485 0.15780068
## 162 613 24 1 0 0.20558950 0.162368741 0.2826243 0.14955206
## 163 624 23 1 0 0.19665082 0.168344565 0.2735212 0.14138411
## 164 641 22 1 0 0.18771215 0.174655074 0.2643377 0.13329864
## 165 643 21 1 0 0.17877348 0.181343175 0.2550719 0.12529781
## 166 654 20 1 0 0.16983480 0.188459348 0.2457217 0.11738424
## 167 655 19 1 0 0.16089613 0.196063517 0.2362845 0.10956101
## 168 687 18 1 0 0.15195745 0.204227512 0.2267570 0.10183176
## 169 689 17 1 0 0.14301878 0.213038370 0.2171359 0.09420078
## 170 705 16 1 0 0.13408011 0.222602816 0.2074169 0.08667313
## 171 707 15 1 0 0.12514143 0.233053467 0.1975953 0.07925481
## 172 728 14 1 0 0.11620276 0.244557609 0.1876654 0.07195295
## 173 731 13 1 0 0.10726409 0.257329906 0.1776209 0.06477609
## 174 735 12 1 0 0.09832541 0.271651317 0.1674541 0.05773455
## 175 740 11 0 1 0.09832541 0.271651317 0.1674541 0.05773455
## 176 765 10 1 0 0.08849287 0.291385568 0.1566521 0.04998969
## 177 791 9 1 0 0.07866033 0.314315825 0.1456471 0.04248246
## 178 806 8 0 1 0.07866033 0.314315825 0.1456471 0.04248246
## 179 814 7 1 0 0.06742314 0.350148485 0.1339232 0.03394392
## 180 821 6 0 1 0.06742314 0.350148485 0.1339232 0.03394392
## 181 840 5 0 1 0.06742314 0.350148485 0.1339232 0.03394392
## 182 883 4 1 0 0.05056735 0.453803146 0.1230689 0.02077745
## 183 965 3 0 1 0.05056735 0.453803146 0.1230689 0.02077745
## 184 1010 2 0 1 0.05056735 0.453803146 0.1230689 0.02077745
## 185 1022 1 0 1 0.05056735 0.453803146 0.1230689 0.02077745##################################
# Plotting the Kaplan-Meier survival curves
# using the Baseline data
##################################
SurvivalTimeInWeek.KaplanMeier.Baseline <- ggsurvplot(DBP.Analysis.Filtered.Baseline.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curve (Baseline)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
palette = c("#000000"))
ggpar(SurvivalTimeInWeek.KaplanMeier.Baseline,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Computing the Kaplan-Meier survival estimates
# using the Factor Variable
##################################
DBP.Analysis.Filtered.KaplanMeierEstimates <- survfit(Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered)
print(DBP.Analysis.Filtered.KaplanMeierEstimates)## Call: survfit(formula = Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered)
##
## n events median 0.95LCL 0.95UCL
## ph.ecog=Bedridden 51 45 183 153 288
## ph.ecog=Ambulatory 113 82 306 268 429
## ph.ecog=Asymptomatic 63 37 394 348 574tbl_survfit(DBP.Analysis.Filtered.KaplanMeierEstimates,
times = c(183,365,548,730,913,1022),
label_header = "**Day {time}**"
)| Characteristic | Day 183 | Day 365 | Day 548 | Day 730 | Day 913 | Day 1022 |
|---|---|---|---|---|---|---|
| ph.ecog | ||||||
| Bedridden | 50% (37%, 66%) | 21% (12%, 37%) | 11% (4.6%, 26%) | 3.6% (0.6%, 22%) | — (—, —) | — (—, —) |
| Ambulatory | 72% (65%, 81%) | 43% (34%, 54%) | 26% (18%, 38%) | 11% (5.8%, 22%) | 6.1% (2.3%, 16%) | 6.1% (2.3%, 16%) |
| Asymptomatic | 84% (76%, 94%) | 54% (41%, 70%) | 37% (25%, 55%) | 19% (9.4%, 40%) | 7.7% (1.5%, 39%) | — (—, —) |
##################################
# Formulating a summary of the Kaplan-Meier survival estimates
# using the Factor Variable
##################################
summary(DBP.Analysis.Filtered.KaplanMeierEstimates)## Call: survfit(formula = Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered)
##
## ph.ecog=Bedridden
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 11 51 1 0.9804 0.0194 0.94307 1.000
## 12 50 1 0.9608 0.0272 0.90896 1.000
## 13 49 1 0.9412 0.0329 0.87877 1.000
## 26 48 1 0.9216 0.0376 0.85066 0.998
## 30 47 1 0.9020 0.0416 0.82393 0.987
## 53 46 1 0.8824 0.0451 0.79821 0.975
## 54 45 1 0.8627 0.0482 0.77329 0.963
## 61 44 1 0.8431 0.0509 0.74901 0.949
## 65 43 1 0.8235 0.0534 0.72528 0.935
## 81 42 1 0.8039 0.0556 0.70202 0.921
## 93 40 1 0.7838 0.0577 0.67847 0.906
## 95 39 1 0.7637 0.0596 0.65534 0.890
## 105 38 1 0.7436 0.0614 0.63258 0.874
## 107 36 1 0.7230 0.0630 0.60940 0.858
## 118 35 1 0.7023 0.0645 0.58657 0.841
## 122 34 1 0.6817 0.0659 0.56406 0.824
## 132 33 1 0.6610 0.0670 0.54187 0.806
## 145 32 1 0.6403 0.0680 0.51996 0.789
## 153 31 1 0.6197 0.0689 0.49834 0.771
## 156 30 1 0.5990 0.0696 0.47698 0.752
## 163 29 1 0.5784 0.0702 0.45588 0.734
## 166 28 1 0.5577 0.0707 0.43503 0.715
## 177 27 1 0.5371 0.0710 0.41442 0.696
## 180 26 1 0.5164 0.0712 0.39406 0.677
## 183 25 1 0.4958 0.0713 0.37394 0.657
## 199 24 1 0.4751 0.0713 0.35406 0.638
## 201 23 1 0.4544 0.0711 0.33441 0.618
## 208 22 1 0.4338 0.0708 0.31500 0.597
## 212 20 1 0.4121 0.0705 0.29467 0.576
## 222 19 1 0.3904 0.0701 0.27464 0.555
## 239 18 1 0.3687 0.0694 0.25490 0.533
## 285 17 1 0.3470 0.0687 0.23547 0.511
## 288 16 1 0.3253 0.0677 0.21636 0.489
## 291 15 1 0.3036 0.0666 0.19757 0.467
## 310 13 1 0.2803 0.0654 0.17738 0.443
## 329 12 1 0.2569 0.0640 0.15767 0.419
## 351 11 1 0.2336 0.0623 0.13847 0.394
## 361 10 1 0.2102 0.0603 0.11982 0.369
## 387 9 1 0.1869 0.0579 0.10176 0.343
## 444 8 1 0.1635 0.0552 0.08435 0.317
## 524 6 1 0.1363 0.0523 0.06421 0.289
## 533 5 1 0.1090 0.0484 0.04564 0.260
## 654 3 1 0.0727 0.0438 0.02227 0.237
## 707 2 1 0.0363 0.0338 0.00588 0.225
## 814 1 1 0.0000 NaN NA NA
##
## ph.ecog=Ambulatory
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 11 113 1 0.9912 0.00881 0.9740 1.000
## 13 112 1 0.9823 0.01240 0.9583 1.000
## 59 111 1 0.9735 0.01512 0.9443 1.000
## 60 110 2 0.9558 0.01935 0.9186 0.994
## 62 108 1 0.9469 0.02109 0.9064 0.989
## 79 107 1 0.9381 0.02268 0.8946 0.984
## 88 106 2 0.9204 0.02547 0.8718 0.972
## 92 104 1 0.9115 0.02672 0.8606 0.965
## 95 103 1 0.9027 0.02789 0.8496 0.959
## 107 102 1 0.8938 0.02898 0.8388 0.952
## 110 101 1 0.8850 0.03002 0.8280 0.946
## 116 100 1 0.8761 0.03099 0.8174 0.939
## 131 99 1 0.8673 0.03192 0.8069 0.932
## 132 98 1 0.8584 0.03280 0.7965 0.925
## 135 97 1 0.8496 0.03363 0.7861 0.918
## 142 96 1 0.8407 0.03443 0.7759 0.911
## 144 95 1 0.8319 0.03518 0.7657 0.904
## 145 94 1 0.8230 0.03590 0.7556 0.896
## 156 93 1 0.8142 0.03659 0.7455 0.889
## 163 92 2 0.7965 0.03788 0.7256 0.874
## 167 90 1 0.7876 0.03848 0.7157 0.867
## 170 89 1 0.7788 0.03905 0.7059 0.859
## 175 86 1 0.7697 0.03963 0.6958 0.851
## 179 84 2 0.7514 0.04075 0.6756 0.836
## 181 82 2 0.7331 0.04177 0.6556 0.820
## 182 80 1 0.7239 0.04224 0.6457 0.812
## 186 78 1 0.7146 0.04270 0.6356 0.803
## 194 75 1 0.7051 0.04318 0.6253 0.795
## 197 73 1 0.6954 0.04366 0.6149 0.786
## 202 71 1 0.6856 0.04413 0.6044 0.778
## 207 69 1 0.6757 0.04459 0.5937 0.769
## 210 68 1 0.6658 0.04503 0.5831 0.760
## 218 67 1 0.6558 0.04544 0.5725 0.751
## 223 64 1 0.6456 0.04587 0.5616 0.742
## 226 62 1 0.6352 0.04630 0.5506 0.733
## 229 61 1 0.6247 0.04670 0.5396 0.723
## 230 60 1 0.6143 0.04707 0.5287 0.714
## 239 58 1 0.6037 0.04743 0.5176 0.704
## 245 56 1 0.5930 0.04779 0.5063 0.694
## 268 55 1 0.5822 0.04812 0.4951 0.685
## 269 54 1 0.5714 0.04843 0.4839 0.675
## 270 53 1 0.5606 0.04870 0.4729 0.665
## 283 50 1 0.5494 0.04900 0.4613 0.654
## 284 49 1 0.5382 0.04926 0.4498 0.644
## 293 48 1 0.5270 0.04950 0.4384 0.633
## 301 46 1 0.5155 0.04973 0.4267 0.623
## 305 43 1 0.5035 0.05000 0.4145 0.612
## 306 42 1 0.4915 0.05022 0.4023 0.601
## 310 41 1 0.4796 0.05041 0.3903 0.589
## 345 40 1 0.4676 0.05055 0.3783 0.578
## 363 38 2 0.4430 0.05080 0.3538 0.555
## 364 36 1 0.4307 0.05086 0.3417 0.543
## 371 34 1 0.4180 0.05091 0.3292 0.531
## 390 32 1 0.4049 0.05097 0.3164 0.518
## 426 29 1 0.3910 0.05109 0.3026 0.505
## 429 28 1 0.3770 0.05114 0.2890 0.492
## 450 27 1 0.3630 0.05112 0.2755 0.478
## 457 26 1 0.3491 0.05102 0.2621 0.465
## 460 24 1 0.3345 0.05093 0.2482 0.451
## 473 23 1 0.3200 0.05075 0.2345 0.437
## 477 22 1 0.3054 0.05048 0.2209 0.422
## 519 20 1 0.2902 0.05021 0.2067 0.407
## 520 19 1 0.2749 0.04984 0.1927 0.392
## 524 18 1 0.2596 0.04935 0.1789 0.377
## 550 16 1 0.2434 0.04886 0.1642 0.361
## 567 15 1 0.2272 0.04823 0.1498 0.344
## 583 14 1 0.2109 0.04743 0.1358 0.328
## 613 13 1 0.1947 0.04648 0.1220 0.311
## 624 12 1 0.1785 0.04535 0.1085 0.294
## 641 11 1 0.1623 0.04403 0.0953 0.276
## 687 10 1 0.1460 0.04251 0.0825 0.258
## 689 9 1 0.1298 0.04077 0.0701 0.240
## 728 8 1 0.1136 0.03877 0.0582 0.222
## 731 7 1 0.0974 0.03647 0.0467 0.203
## 735 6 1 0.0811 0.03381 0.0359 0.184
## 765 4 1 0.0608 0.03085 0.0225 0.164
##
## ph.ecog=Asymptomatic
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 5 63 1 0.9841 0.0157 0.9537 1.000
## 11 62 1 0.9683 0.0221 0.9259 1.000
## 15 61 1 0.9524 0.0268 0.9012 1.000
## 31 60 1 0.9365 0.0307 0.8782 0.999
## 53 59 1 0.9206 0.0341 0.8562 0.990
## 65 58 1 0.9048 0.0370 0.8351 0.980
## 81 57 1 0.8889 0.0396 0.8146 0.970
## 147 56 1 0.8730 0.0419 0.7946 0.959
## 166 55 1 0.8571 0.0441 0.7749 0.948
## 176 53 1 0.8410 0.0461 0.7553 0.936
## 189 52 1 0.8248 0.0480 0.7359 0.924
## 201 50 1 0.8083 0.0498 0.7164 0.912
## 246 44 1 0.7899 0.0519 0.6944 0.899
## 267 40 1 0.7702 0.0543 0.6709 0.884
## 285 36 1 0.7488 0.0568 0.6453 0.869
## 286 35 1 0.7274 0.0591 0.6203 0.853
## 303 32 1 0.7047 0.0615 0.5940 0.836
## 320 30 1 0.6812 0.0637 0.5670 0.818
## 337 28 1 0.6568 0.0659 0.5395 0.800
## 340 27 1 0.6325 0.0678 0.5126 0.780
## 348 26 1 0.6082 0.0695 0.4862 0.761
## 350 25 1 0.5839 0.0708 0.4603 0.741
## 353 24 2 0.5352 0.0728 0.4100 0.699
## 371 22 1 0.5109 0.0734 0.3855 0.677
## 394 19 1 0.4840 0.0743 0.3582 0.654
## 428 18 1 0.4571 0.0749 0.3315 0.630
## 433 17 1 0.4302 0.0752 0.3055 0.606
## 442 16 1 0.4033 0.0751 0.2800 0.581
## 455 14 1 0.3745 0.0751 0.2528 0.555
## 558 12 1 0.3433 0.0750 0.2237 0.527
## 574 10 1 0.3090 0.0750 0.1920 0.497
## 643 8 1 0.2704 0.0749 0.1571 0.465
## 655 7 1 0.2317 0.0735 0.1245 0.431
## 705 6 1 0.1931 0.0707 0.0943 0.396
## 791 5 1 0.1545 0.0662 0.0667 0.358
## 883 2 1 0.0772 0.0639 0.0153 0.391(DBP.Analysis.Filtered.KaplanMeierEstimates.Summary <- summary(DBP.Analysis.Filtered.KaplanMeierEstimates)$table)## records n.max n.start events rmean se(rmean) median
## ph.ecog=Bedridden 51 51 51 45 255.7636 30.74032 183
## ph.ecog=Ambulatory 113 113 113 82 384.8410 27.28943 306
## ph.ecog=Asymptomatic 63 63 63 37 465.3131 42.88835 394
## 0.95LCL 0.95UCL
## ph.ecog=Bedridden 153 288
## ph.ecog=Ambulatory 268 429
## ph.ecog=Asymptomatic 348 574##################################
# Listing the details of the Kaplan-Meier survival estimates
# using the Factor Variable
##################################
(DBP.Analysis.Filtered.KaplanMeierEstimates.Details <- surv_summary(DBP.Analysis.Filtered.KaplanMeierEstimates))## time n.risk n.event n.censor surv std.err upper lower
## 1 11 51 1 0 0.98039216 0.019802951 1.0000000 0.943069123
## 2 12 50 1 0 0.96078431 0.028289930 1.0000000 0.908961465
## 3 13 49 1 0 0.94117647 0.035007002 1.0000000 0.878765599
## 4 26 48 1 0 0.92156863 0.040850369 0.9983885 0.850659556
## 5 30 47 1 0 0.90196078 0.046165867 0.9873795 0.823931673
## 6 53 46 1 0 0.88235294 0.051130999 0.9753604 0.798214389
## 7 54 45 1 0 0.86274510 0.055851854 0.9625509 0.773288081
## 8 61 44 1 0 0.84313725 0.060398434 0.9490946 0.749009005
## 9 65 43 1 0 0.82352941 0.064820372 0.9350919 0.725277013
## 10 81 42 1 0 0.80392157 0.069154904 0.9206158 0.702019086
## 11 92 41 0 1 0.80392157 0.069154904 0.9206158 0.702019086
## 12 93 40 1 0 0.78382353 0.073643916 0.9055326 0.678472862
## 13 95 39 1 0 0.76372549 0.078090910 0.8900377 0.655339254
## 14 105 38 1 1 0.74362745 0.082519257 0.8741701 0.632579181
## 15 107 36 1 0 0.72297113 0.087195634 0.8577130 0.609396420
## 16 118 35 1 0 0.70231481 0.091888055 0.8409053 0.586565580
## 17 122 34 1 0 0.68165850 0.096616149 0.8237713 0.564062252
## 18 132 33 1 0 0.66100218 0.101398471 0.8063311 0.541866566
## 19 145 32 1 0 0.64034586 0.106253068 0.7886011 0.519962270
## 20 153 31 1 0 0.61968954 0.111197947 0.7705947 0.498336048
## 21 156 30 1 0 0.59903322 0.116251489 0.7523230 0.476977029
## 22 163 29 1 0 0.57837691 0.121432845 0.7337950 0.455876410
## 23 166 28 1 0 0.55772059 0.126762325 0.7150180 0.435027178
## 24 177 27 1 0 0.53706427 0.132261818 0.6959976 0.414423903
## 25 180 26 1 0 0.51640795 0.137955246 0.6767381 0.394062586
## 26 183 25 1 0 0.49575163 0.143869096 0.6572427 0.373940546
## 27 199 24 1 0 0.47509532 0.150033033 0.6375131 0.354056360
## 28 201 23 1 0 0.45443900 0.156480655 0.6175501 0.334409817
## 29 208 22 1 0 0.43378268 0.163250414 0.5973532 0.315001922
## 30 211 21 0 1 0.43378268 0.163250414 0.5973532 0.315001922
## 31 212 20 1 0 0.41209355 0.171120649 0.5763071 0.294671173
## 32 222 19 1 0 0.39040441 0.179461007 0.5549734 0.274635852
## 33 239 18 1 0 0.36871528 0.188346030 0.5333491 0.254900508
## 34 285 17 1 0 0.34702614 0.197865352 0.5114292 0.235471799
## 35 288 16 1 0 0.32533701 0.208128240 0.4892069 0.216358714
## 36 291 15 1 0 0.30364788 0.219269854 0.4666734 0.197572916
## 37 292 14 0 1 0.30364788 0.219269854 0.4666734 0.197572916
## 38 310 13 1 0 0.28029035 0.233429916 0.4428983 0.177383098
## 39 329 12 1 0 0.25693282 0.249129049 0.4186765 0.157674168
## 40 351 11 1 0 0.23357529 0.266751180 0.3939906 0.138473886
## 41 361 10 1 0 0.21021776 0.286822773 0.3688191 0.119818925
## 42 387 9 1 0 0.18686023 0.310090619 0.3431362 0.101757697
## 43 444 8 1 0 0.16350270 0.337658607 0.3169133 0.084354724
## 44 511 7 0 1 0.16350270 0.337658607 0.3169133 0.084354724
## 45 524 6 1 0 0.13625225 0.383857615 0.2891238 0.064210122
## 46 533 5 1 0 0.10900180 0.444237176 0.2603569 0.045635026
## 47 551 4 0 1 0.10900180 0.444237176 0.2603569 0.045635026
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## 49 707 2 1 0 0.03633393 0.929523176 0.2246591 0.005876258
## 50 814 1 1 0 0.00000000 Inf NA NA
## 51 11 113 1 0 0.99115044 0.008888977 1.0000000 0.974032097
## 52 13 112 1 0 0.98230088 0.012627410 1.0000000 0.958288032
## 53 59 111 1 0 0.97345133 0.015535494 1.0000000 0.944257418
## 54 60 110 2 0 0.95575221 0.020241090 0.9944308 0.918578053
## 55 62 108 1 0 0.94690265 0.022276375 0.9891611 0.906449575
## 56 79 107 1 0 0.93805310 0.024174465 0.9835688 0.894643643
## 57 88 106 2 0 0.92035398 0.027673581 0.9716519 0.871764342
## 58 92 104 1 0 0.91150442 0.029311778 0.9654038 0.860614285
## 59 95 103 1 0 0.90265487 0.030892783 0.9589980 0.849621989
## 60 107 102 1 0 0.89380531 0.032425801 0.9524536 0.838768358
## 61 110 101 1 0 0.88495575 0.033918173 0.9457857 0.828038167
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## 64 132 98 1 0 0.85840708 0.038206293 0.9251551 0.796474792
## 65 135 97 1 0 0.84955752 0.039586729 0.9180981 0.786133864
## 66 142 96 1 0 0.84070796 0.040948239 0.9109622 0.775871783
## 67 144 95 1 0 0.83185841 0.042293502 0.9037529 0.765683195
## 68 145 94 1 0 0.82300885 0.043624886 0.8964748 0.755563440
## 69 156 93 1 0 0.81415929 0.044944496 0.8891319 0.745508432
## 70 163 92 2 0 0.79646018 0.047555794 0.8742661 0.725578658
## 71 167 90 1 0 0.78761062 0.048850768 0.8667491 0.715697852
## 72 170 89 1 0 0.77876106 0.050140591 0.8591796 0.705869603
## 73 173 88 0 1 0.77876106 0.050140591 0.8591796 0.705869603
## 74 174 87 0 1 0.77876106 0.050140591 0.8591796 0.705869603
## 75 175 86 1 0 0.76970570 0.051486675 0.8514325 0.695823618
## 76 177 85 0 1 0.76970570 0.051486675 0.8514325 0.695823618
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## 78 181 82 2 0 0.73305305 0.056974695 0.8196574 0.655599262
## 79 182 80 1 0 0.72388989 0.058346754 0.8115912 0.645665619
## 80 185 79 0 1 0.72388989 0.058346754 0.8115912 0.645665619
## 81 186 78 1 0 0.71460925 0.059756538 0.8034031 0.635629103
## 82 188 77 0 1 0.71460925 0.059756538 0.8034031 0.635629103
## 83 192 76 0 1 0.71460925 0.059756538 0.8034031 0.635629103
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## 85 196 74 0 1 0.70508112 0.061245604 0.7950079 0.625326357
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## 87 202 71 1 0 0.68562779 0.064362179 0.7778101 0.604370460
## 88 203 70 0 1 0.68562779 0.064362179 0.7778101 0.604370460
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## 91 218 67 1 0 0.65581789 0.069291064 0.7512144 0.572535736
## 92 221 66 0 1 0.65581789 0.069291064 0.7512144 0.572535736
## 93 222 65 0 1 0.65581789 0.069291064 0.7512144 0.572535736
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## 95 225 63 0 1 0.64557074 0.071058198 0.7420423 0.561641238
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## 99 237 59 0 1 0.61433344 0.076611929 0.7138654 0.528678884
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## 101 243 57 0 1 0.60374149 0.078561238 0.7042429 0.517582486
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## 103 268 55 1 0 0.58217929 0.082663436 0.6845734 0.495100663
## 104 269 54 1 0 0.57139819 0.084750515 0.6746502 0.483948439
## 105 270 53 1 0 0.56061709 0.086864805 0.6646696 0.472853796
## 106 272 52 0 1 0.56061709 0.086864805 0.6646696 0.472853796
## 107 279 51 0 1 0.56061709 0.086864805 0.6646696 0.472853796
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## 109 284 49 1 0 0.53819241 0.091535937 0.6439514 0.449802679
## 110 293 48 1 0 0.52698007 0.093925982 0.6334964 0.438373455
## 111 296 47 0 1 0.52698007 0.093925982 0.6334964 0.438373455
## 112 301 46 1 1 0.51552398 0.096463371 0.6228144 0.426716171
## 113 303 44 0 1 0.51552398 0.096463371 0.6228144 0.426716171
## 114 305 43 1 0 0.50353505 0.099291952 0.6117122 0.414488269
## 115 306 42 1 0 0.49154612 0.102174419 0.6005308 0.402340035
## 116 310 41 1 0 0.47955719 0.105115974 0.5892713 0.390270323
## 117 345 40 1 0 0.46756826 0.108122124 0.5779347 0.378278192
## 118 356 39 0 1 0.46756826 0.108122124 0.5779347 0.378278192
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## 120 364 36 1 1 0.43065498 0.118093322 0.5428136 0.341671105
## 121 371 34 1 0 0.41798865 0.121808449 0.5306987 0.329216015
## 122 376 33 0 1 0.41798865 0.121808449 0.5306987 0.329216015
## 123 390 32 1 0 0.40492651 0.125878365 0.5182318 0.316394081
## 124 404 31 0 1 0.40492651 0.125878365 0.5182318 0.316394081
## 125 413 30 0 1 0.40492651 0.125878365 0.5182318 0.316394081
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## 128 450 27 1 0 0.36303756 0.140798234 0.4784089 0.275488761
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## 130 458 25 0 1 0.34907458 0.146159516 0.4648678 0.262124137
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## 132 473 23 1 0 0.31998503 0.158589038 0.4366374 0.234497612
## 133 477 22 1 0 0.30544025 0.165272457 0.4222858 0.220925630
## 134 511 21 0 1 0.30544025 0.165272457 0.4222858 0.220925630
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## 137 524 18 1 0 0.25962422 0.190101327 0.3768424 0.178867178
## 138 529 17 0 1 0.25962422 0.190101327 0.3768424 0.178867178
## 139 550 16 1 0 0.24339770 0.200761503 0.3607489 0.164220728
## 140 567 15 1 0 0.22717119 0.212290099 0.3443935 0.149848221
## 141 583 14 1 0 0.21094468 0.224859048 0.3277698 0.135758865
## 142 613 13 1 0 0.19471816 0.238687762 0.3108693 0.121964958
## 143 624 12 1 0 0.17849165 0.254062208 0.2936811 0.108482518
## 144 641 11 1 0 0.16226514 0.271364173 0.2761918 0.095332199
## 145 687 10 1 0 0.14603862 0.291117890 0.2583853 0.082540620
## 146 689 9 1 0 0.12981211 0.314067691 0.2402426 0.070142348
## 147 728 8 1 0 0.11358559 0.341314602 0.2217434 0.058182950
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## 149 735 6 1 0 0.08113257 0.416699550 0.1836075 0.035850888
## 150 740 5 0 1 0.08113257 0.416699550 0.1836075 0.035850888
## 151 765 4 1 0 0.06084943 0.506923907 0.1643429 0.022530046
## 152 806 3 0 1 0.06084943 0.506923907 0.1643429 0.022530046
## 153 965 2 0 1 0.06084943 0.506923907 0.1643429 0.022530046
## 154 1022 1 0 1 0.06084943 0.506923907 0.1643429 0.022530046
## 155 5 63 1 0 0.98412698 0.016000512 1.0000000 0.953743255
## 156 11 62 1 0 0.96825397 0.022812864 1.0000000 0.925914618
## 157 15 61 1 0 0.95238095 0.028171808 1.0000000 0.901219985
## 158 31 60 1 0 0.93650794 0.032804522 0.9986992 0.878189424
## 159 53 59 1 0 0.92063492 0.036991397 0.9898618 0.856249459
## 160 65 58 1 0 0.90476190 0.040875956 0.9802300 0.835104126
## 161 81 57 1 0 0.88888889 0.044543540 0.9699805 0.814576632
## 162 147 56 1 0 0.87301587 0.048049998 0.9592292 0.794551236
## 163 166 55 1 0 0.85714286 0.051434450 0.9480567 0.774947224
## 164 175 54 0 1 0.85714286 0.051434450 0.9480567 0.774947224
## 165 176 53 1 0 0.84097035 0.054848403 0.9364136 0.755255052
## 166 189 52 1 0 0.82479784 0.058184373 0.9244302 0.735903535
## 167 191 51 0 1 0.82479784 0.058184373 0.9244302 0.735903535
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## 169 202 49 0 1 0.80830189 0.061592082 0.9120127 0.716384726
## 170 224 48 0 1 0.80830189 0.061592082 0.9120127 0.716384726
## 171 225 47 0 1 0.80830189 0.061592082 0.9120127 0.716384726
## 172 235 46 0 1 0.80830189 0.061592082 0.9120127 0.716384726
## 173 240 45 0 1 0.80830189 0.061592082 0.9120127 0.716384726
## 174 246 44 1 0 0.78993139 0.065742876 0.8985656 0.694430735
## 175 252 43 0 1 0.78993139 0.065742876 0.8985656 0.694430735
## 176 259 42 0 1 0.78993139 0.065742876 0.8985656 0.694430735
## 177 266 41 0 1 0.78993139 0.065742876 0.8985656 0.694430735
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## 179 269 39 0 1 0.77018310 0.070449637 0.8842210 0.670852662
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## 181 284 37 0 1 0.77018310 0.070449637 0.8842210 0.670852662
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## 183 286 35 1 0 0.72739515 0.081222770 0.8529181 0.620345244
## 184 292 34 0 1 0.72739515 0.081222770 0.8529181 0.620345244
## 185 300 33 0 1 0.72739515 0.081222770 0.8529181 0.620345244
## 186 303 32 1 0 0.70466406 0.087207814 0.8360140 0.593951103
## 187 315 31 0 1 0.70466406 0.087207814 0.8360140 0.593951103
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## 189 332 29 0 1 0.68117525 0.093566170 0.8182811 0.567041956
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## 196 382 21 0 1 0.51088144 0.143733747 0.6771214 0.385455049
## 197 384 20 0 1 0.51088144 0.143733747 0.6771214 0.385455049
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## 202 444 15 0 1 0.40332745 0.186264537 0.5810406 0.279968469
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## 204 543 13 0 1 0.37451835 0.200471901 0.5547727 0.252831458
## 205 558 12 1 0 0.34330849 0.218551460 0.5268851 0.223693415
## 206 559 11 0 1 0.34330849 0.218551460 0.5268851 0.223693415
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## 208 588 9 0 1 0.30897764 0.242643467 0.4971249 0.192038611
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## 210 655 7 1 0 0.23173323 0.317084403 0.4314108 0.124475987
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## 212 791 5 1 0 0.15448882 0.428807477 0.3580129 0.066664629
## 213 821 4 0 1 0.15448882 0.428807477 0.3580129 0.066664629
## 214 840 3 0 1 0.15448882 0.428807477 0.3580129 0.066664629
## 215 883 2 1 0 0.07724441 0.826967866 0.3906460 0.015273928
## 216 1010 1 0 1 0.07724441 0.826967866 0.3906460 0.015273928
## strata ph.ecog
## 1 ph.ecog=Bedridden Bedridden
## 2 ph.ecog=Bedridden Bedridden
## 3 ph.ecog=Bedridden Bedridden
## 4 ph.ecog=Bedridden Bedridden
## 5 ph.ecog=Bedridden Bedridden
## 6 ph.ecog=Bedridden Bedridden
## 7 ph.ecog=Bedridden Bedridden
## 8 ph.ecog=Bedridden Bedridden
## 9 ph.ecog=Bedridden Bedridden
## 10 ph.ecog=Bedridden Bedridden
## 11 ph.ecog=Bedridden Bedridden
## 12 ph.ecog=Bedridden Bedridden
## 13 ph.ecog=Bedridden Bedridden
## 14 ph.ecog=Bedridden Bedridden
## 15 ph.ecog=Bedridden Bedridden
## 16 ph.ecog=Bedridden Bedridden
## 17 ph.ecog=Bedridden Bedridden
## 18 ph.ecog=Bedridden Bedridden
## 19 ph.ecog=Bedridden Bedridden
## 20 ph.ecog=Bedridden Bedridden
## 21 ph.ecog=Bedridden Bedridden
## 22 ph.ecog=Bedridden Bedridden
## 23 ph.ecog=Bedridden Bedridden
## 24 ph.ecog=Bedridden Bedridden
## 25 ph.ecog=Bedridden Bedridden
## 26 ph.ecog=Bedridden Bedridden
## 27 ph.ecog=Bedridden Bedridden
## 28 ph.ecog=Bedridden Bedridden
## 29 ph.ecog=Bedridden Bedridden
## 30 ph.ecog=Bedridden Bedridden
## 31 ph.ecog=Bedridden Bedridden
## 32 ph.ecog=Bedridden Bedridden
## 33 ph.ecog=Bedridden Bedridden
## 34 ph.ecog=Bedridden Bedridden
## 35 ph.ecog=Bedridden Bedridden
## 36 ph.ecog=Bedridden Bedridden
## 37 ph.ecog=Bedridden Bedridden
## 38 ph.ecog=Bedridden Bedridden
## 39 ph.ecog=Bedridden Bedridden
## 40 ph.ecog=Bedridden Bedridden
## 41 ph.ecog=Bedridden Bedridden
## 42 ph.ecog=Bedridden Bedridden
## 43 ph.ecog=Bedridden Bedridden
## 44 ph.ecog=Bedridden Bedridden
## 45 ph.ecog=Bedridden Bedridden
## 46 ph.ecog=Bedridden Bedridden
## 47 ph.ecog=Bedridden Bedridden
## 48 ph.ecog=Bedridden Bedridden
## 49 ph.ecog=Bedridden Bedridden
## 50 ph.ecog=Bedridden Bedridden
## 51 ph.ecog=Ambulatory Ambulatory
## 52 ph.ecog=Ambulatory Ambulatory
## 53 ph.ecog=Ambulatory Ambulatory
## 54 ph.ecog=Ambulatory Ambulatory
## 55 ph.ecog=Ambulatory Ambulatory
## 56 ph.ecog=Ambulatory Ambulatory
## 57 ph.ecog=Ambulatory Ambulatory
## 58 ph.ecog=Ambulatory Ambulatory
## 59 ph.ecog=Ambulatory Ambulatory
## 60 ph.ecog=Ambulatory Ambulatory
## 61 ph.ecog=Ambulatory Ambulatory
## 62 ph.ecog=Ambulatory Ambulatory
## 63 ph.ecog=Ambulatory Ambulatory
## 64 ph.ecog=Ambulatory Ambulatory
## 65 ph.ecog=Ambulatory Ambulatory
## 66 ph.ecog=Ambulatory Ambulatory
## 67 ph.ecog=Ambulatory Ambulatory
## 68 ph.ecog=Ambulatory Ambulatory
## 69 ph.ecog=Ambulatory Ambulatory
## 70 ph.ecog=Ambulatory Ambulatory
## 71 ph.ecog=Ambulatory Ambulatory
## 72 ph.ecog=Ambulatory Ambulatory
## 73 ph.ecog=Ambulatory Ambulatory
## 74 ph.ecog=Ambulatory Ambulatory
## 75 ph.ecog=Ambulatory Ambulatory
## 76 ph.ecog=Ambulatory Ambulatory
## 77 ph.ecog=Ambulatory Ambulatory
## 78 ph.ecog=Ambulatory Ambulatory
## 79 ph.ecog=Ambulatory Ambulatory
## 80 ph.ecog=Ambulatory Ambulatory
## 81 ph.ecog=Ambulatory Ambulatory
## 82 ph.ecog=Ambulatory Ambulatory
## 83 ph.ecog=Ambulatory Ambulatory
## 84 ph.ecog=Ambulatory Ambulatory
## 85 ph.ecog=Ambulatory Ambulatory
## 86 ph.ecog=Ambulatory Ambulatory
## 87 ph.ecog=Ambulatory Ambulatory
## 88 ph.ecog=Ambulatory Ambulatory
## 89 ph.ecog=Ambulatory Ambulatory
## 90 ph.ecog=Ambulatory Ambulatory
## 91 ph.ecog=Ambulatory Ambulatory
## 92 ph.ecog=Ambulatory Ambulatory
## 93 ph.ecog=Ambulatory Ambulatory
## 94 ph.ecog=Ambulatory Ambulatory
## 95 ph.ecog=Ambulatory Ambulatory
## 96 ph.ecog=Ambulatory Ambulatory
## 97 ph.ecog=Ambulatory Ambulatory
## 98 ph.ecog=Ambulatory Ambulatory
## 99 ph.ecog=Ambulatory Ambulatory
## 100 ph.ecog=Ambulatory Ambulatory
## 101 ph.ecog=Ambulatory Ambulatory
## 102 ph.ecog=Ambulatory Ambulatory
## 103 ph.ecog=Ambulatory Ambulatory
## 104 ph.ecog=Ambulatory Ambulatory
## 105 ph.ecog=Ambulatory Ambulatory
## 106 ph.ecog=Ambulatory Ambulatory
## 107 ph.ecog=Ambulatory Ambulatory
## 108 ph.ecog=Ambulatory Ambulatory
## 109 ph.ecog=Ambulatory Ambulatory
## 110 ph.ecog=Ambulatory Ambulatory
## 111 ph.ecog=Ambulatory Ambulatory
## 112 ph.ecog=Ambulatory Ambulatory
## 113 ph.ecog=Ambulatory Ambulatory
## 114 ph.ecog=Ambulatory Ambulatory
## 115 ph.ecog=Ambulatory Ambulatory
## 116 ph.ecog=Ambulatory Ambulatory
## 117 ph.ecog=Ambulatory Ambulatory
## 118 ph.ecog=Ambulatory Ambulatory
## 119 ph.ecog=Ambulatory Ambulatory
## 120 ph.ecog=Ambulatory Ambulatory
## 121 ph.ecog=Ambulatory Ambulatory
## 122 ph.ecog=Ambulatory Ambulatory
## 123 ph.ecog=Ambulatory Ambulatory
## 124 ph.ecog=Ambulatory Ambulatory
## 125 ph.ecog=Ambulatory Ambulatory
## 126 ph.ecog=Ambulatory Ambulatory
## 127 ph.ecog=Ambulatory Ambulatory
## 128 ph.ecog=Ambulatory Ambulatory
## 129 ph.ecog=Ambulatory Ambulatory
## 130 ph.ecog=Ambulatory Ambulatory
## 131 ph.ecog=Ambulatory Ambulatory
## 132 ph.ecog=Ambulatory Ambulatory
## 133 ph.ecog=Ambulatory Ambulatory
## 134 ph.ecog=Ambulatory Ambulatory
## 135 ph.ecog=Ambulatory Ambulatory
## 136 ph.ecog=Ambulatory Ambulatory
## 137 ph.ecog=Ambulatory Ambulatory
## 138 ph.ecog=Ambulatory Ambulatory
## 139 ph.ecog=Ambulatory Ambulatory
## 140 ph.ecog=Ambulatory Ambulatory
## 141 ph.ecog=Ambulatory Ambulatory
## 142 ph.ecog=Ambulatory Ambulatory
## 143 ph.ecog=Ambulatory Ambulatory
## 144 ph.ecog=Ambulatory Ambulatory
## 145 ph.ecog=Ambulatory Ambulatory
## 146 ph.ecog=Ambulatory Ambulatory
## 147 ph.ecog=Ambulatory Ambulatory
## 148 ph.ecog=Ambulatory Ambulatory
## 149 ph.ecog=Ambulatory Ambulatory
## 150 ph.ecog=Ambulatory Ambulatory
## 151 ph.ecog=Ambulatory Ambulatory
## 152 ph.ecog=Ambulatory Ambulatory
## 153 ph.ecog=Ambulatory Ambulatory
## 154 ph.ecog=Ambulatory Ambulatory
## 155 ph.ecog=Asymptomatic Asymptomatic
## 156 ph.ecog=Asymptomatic Asymptomatic
## 157 ph.ecog=Asymptomatic Asymptomatic
## 158 ph.ecog=Asymptomatic Asymptomatic
## 159 ph.ecog=Asymptomatic Asymptomatic
## 160 ph.ecog=Asymptomatic Asymptomatic
## 161 ph.ecog=Asymptomatic Asymptomatic
## 162 ph.ecog=Asymptomatic Asymptomatic
## 163 ph.ecog=Asymptomatic Asymptomatic
## 164 ph.ecog=Asymptomatic Asymptomatic
## 165 ph.ecog=Asymptomatic Asymptomatic
## 166 ph.ecog=Asymptomatic Asymptomatic
## 167 ph.ecog=Asymptomatic Asymptomatic
## 168 ph.ecog=Asymptomatic Asymptomatic
## 169 ph.ecog=Asymptomatic Asymptomatic
## 170 ph.ecog=Asymptomatic Asymptomatic
## 171 ph.ecog=Asymptomatic Asymptomatic
## 172 ph.ecog=Asymptomatic Asymptomatic
## 173 ph.ecog=Asymptomatic Asymptomatic
## 174 ph.ecog=Asymptomatic Asymptomatic
## 175 ph.ecog=Asymptomatic Asymptomatic
## 176 ph.ecog=Asymptomatic Asymptomatic
## 177 ph.ecog=Asymptomatic Asymptomatic
## 178 ph.ecog=Asymptomatic Asymptomatic
## 179 ph.ecog=Asymptomatic Asymptomatic
## 180 ph.ecog=Asymptomatic Asymptomatic
## 181 ph.ecog=Asymptomatic Asymptomatic
## 182 ph.ecog=Asymptomatic Asymptomatic
## 183 ph.ecog=Asymptomatic Asymptomatic
## 184 ph.ecog=Asymptomatic Asymptomatic
## 185 ph.ecog=Asymptomatic Asymptomatic
## 186 ph.ecog=Asymptomatic Asymptomatic
## 187 ph.ecog=Asymptomatic Asymptomatic
## 188 ph.ecog=Asymptomatic Asymptomatic
## 189 ph.ecog=Asymptomatic Asymptomatic
## 190 ph.ecog=Asymptomatic Asymptomatic
## 191 ph.ecog=Asymptomatic Asymptomatic
## 192 ph.ecog=Asymptomatic Asymptomatic
## 193 ph.ecog=Asymptomatic Asymptomatic
## 194 ph.ecog=Asymptomatic Asymptomatic
## 195 ph.ecog=Asymptomatic Asymptomatic
## 196 ph.ecog=Asymptomatic Asymptomatic
## 197 ph.ecog=Asymptomatic Asymptomatic
## 198 ph.ecog=Asymptomatic Asymptomatic
## 199 ph.ecog=Asymptomatic Asymptomatic
## 200 ph.ecog=Asymptomatic Asymptomatic
## 201 ph.ecog=Asymptomatic Asymptomatic
## 202 ph.ecog=Asymptomatic Asymptomatic
## 203 ph.ecog=Asymptomatic Asymptomatic
## 204 ph.ecog=Asymptomatic Asymptomatic
## 205 ph.ecog=Asymptomatic Asymptomatic
## 206 ph.ecog=Asymptomatic Asymptomatic
## 207 ph.ecog=Asymptomatic Asymptomatic
## 208 ph.ecog=Asymptomatic Asymptomatic
## 209 ph.ecog=Asymptomatic Asymptomatic
## 210 ph.ecog=Asymptomatic Asymptomatic
## 211 ph.ecog=Asymptomatic Asymptomatic
## 212 ph.ecog=Asymptomatic Asymptomatic
## 213 ph.ecog=Asymptomatic Asymptomatic
## 214 ph.ecog=Asymptomatic Asymptomatic
## 215 ph.ecog=Asymptomatic Asymptomatic
## 216 ph.ecog=Asymptomatic Asymptomatic##################################
# Plotting the Kaplan-Meier survival curves
# using the Factor Variable
##################################
SurvivalTimeInWeek.KaplanMeier.ByGroup <- ggsurvplot(DBP.Analysis.Filtered.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curve (ECOG Score)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
legend.labs = c("Bedridden", "Ambulatory", "Asymptomatic"),
palette = c("#00CC66","#3259A0","#FF5050"))
ggpar(SurvivalTimeInWeek.KaplanMeier.ByGroup,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
1.4.3 Log Rank Test
Log Rank Test evaluates the null hypothesis of no difference in survival between two or more independent groups by comparing the entire survival experience. The method involves generating a sequential list of time values corresponding to an event or censoring from two or more independent groups; determining the counts of event-free observations, event and expected events for each time value; calculating the Chi-Square test statistic based on these counts; and evaluating the determined test statistic against the rejection region.
Code Chunk | Output
##################################
# Conducting the Log Rank Test
# between the Kaplan-Meier survival estimates
# using the Factor Variable
##################################
(DBP.Analysis.Filtered.LogRankTest <- survdiff(Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered))## Call:
## survdiff(formula = Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## ph.ecog=Bedridden 51 45 26.3 13.2582 15.9641
## ph.ecog=Ambulatory 113 82 83.5 0.0279 0.0573
## ph.ecog=Asymptomatic 63 37 54.2 5.4331 8.2119
##
## Chisq= 19 on 2 degrees of freedom, p= 8e-05##################################
# Conducting the Post-Hoc Test
# between the Kaplan-Meier survival estimates
# using the Factor Variable
#################################
(DBP.Analysis.Filtered.LogRankTest.PosthocTest <- survminer::pairwise_survdiff(Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered))##
## Pairwise comparisons using Log-Rank test
##
## data: DBP.Analysis.Filtered and ph.ecog
##
## Bedridden Ambulatory
## Ambulatory 0.0039 -
## Asymptomatic 9e-05 0.0630
##
## P value adjustment method: BH##################################
# Plotting the Kaplan-Meier survival curves
# using the Factor Variable
##################################
SurvivalTimeInWeek.KaplanMeier.ByGroup <- ggsurvplot(DBP.Analysis.Filtered.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curve (ECOG Score)",
pval = TRUE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
legend.labs = c("Bedridden", "Ambulatory", "Asymptomatic"),
palette = c("#00CC66","#3259A0","#FF5050"))
ggpar(SurvivalTimeInWeek.KaplanMeier.ByGroup,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
1.5 Model Development Summary
Cox Proportional Hazards Regression examines the relationship between a hazard function and a set of covariates by assuming that predictors act multiplicatively on the hazard function without any explicit assumption of its distributional form. The model is semi-parametric because while the baseline hazard can take any form, the covariates enter the model linearly.
Concordance Index is a rank correlation measure between a predictor and a possibly censored outcome with an event or censoring indicator. In survival analysis, a pair of patients is called concordant if the risk of the event predicted by a model is lower for the patient who experiences the event at a later time point. The concordance probability (C-index) is the frequency of concordant pairs among all pairs of subjects which can be used to measure and compare the discrimination power of risk prediction models.
Residual Analysis for Model Assumption Diagnostics assesses whether a fitted Cox Proportional Hazards Regression model adequately describes the data using various residuals to test the proportional hazards assumption, examine influential observations (or outliers) and detect nonlinearity in the relationship between the log hazard and the covariates. Schoenfeld residuals are calculated by regressing the scaled and weighted Martingale residuals on the model covariates. These help evaluate the proportional hazards assumption by examining the relationship between the residuals and time for each covariate. A significant correlation between Schoenfeld residuals and time suggests a violation of the model assumptions. Deviance residuals are derived from the log partial likelihood estimation during regression. These measure the difference between the observed event status and the predicted event probability. Deviance residuals are more sensitive to the shape of the hazard function and can help identify departures from the model assumptions.
Cox proportional hazards regression analysis involving the response variable time, factor variable ph.ecog and covariate variables sex and age showed that :
[A] A cox proportional hazards regression model applied on the response variable time and factor variable ph.ecog which includes the covariate variable sex but excludes the covariate variable age was determined with the most optimal fit during stepwise variable selection. Furthermore, the aforementioned model was considered the most appropriate as the final survival model since the addition of the covariate variable sex significantly improved model fit (p<0.001, Likelihood Ratio Test). However, the further inclusion of an interaction term ph.ecog * sex into the model did not show any significant improvement to model fit (p=0.789, Likelihood Ratio Test).
[B] Using the final survival model controlled for sex, association between ph.ecog and survival time time was statistically significant with:
[B.1] An estimated hazard ratio of 0.58 (95% CI 0.40, 0.84; p=0.004, Cox Proportional Hazards Model Wald Test) for ph.ecog=Ambulatory (lower hazard and higher survival rate for advanced lung cancer patients with physician-rated ECOG score = 1) relative to ph.ecog=Bedridden (higher hazard and lower survival rate for advanced lung cancer patients with physician-rated ECOG score = 2 or 3)
[B.2] An estimated hazard ratio of 0.38 (95% CI 0.25, 0.59; p<0.001, Cox Proportional Hazards Model Wald Test) for ph.ecog=Asymptomatic (lower hazard and higher survival rate for advanced lung cancer patients with physician-rated ECOG score = 0) relative to ph.ecog=Bedridden (higher hazard and lower survival rate for advanced lung cancer patients with physician-rated ECOG score = 2 or 3)
[C] Using the final survival model controlled for ph.ecog, association between sex and survival time time was statistically significant with an estimated hazard ratio of 0.58 (95% CI 0.42, 0.80; p=0.001, Cox Proportional Hazards Model Wald Test) for sex=Female (lower hazard and higher survival rate for advanced lung cancer patients who are females) relative to sex=Male (higher hazard and lower survival rate for advanced lung cancer patients who are males).
[D] The estimated Harrel’s concordance index (proportion of advanced lung cancer patients that the model can correctly order in terms of survival times when adjusted for censoring) for the final survival model was determined to be relatively satisfactory at 0.64 (optimistic) and 0.63 (optimism-corrected after a 500-cycle internal bootstrap validation).
[E] The scaled Schoenfield residuals showed random patterns when plotted against time indicating no violation of the proportional hazards assumption. The proportional hazards assumption was further supported by the non-significant relationship between the scaled Schoenfield residuals and time based from the global (p=0.1514) and individual (p=0.2188 for ph.ecpg, 0.1001 for sex ) statistical test results.
[F] The deviance residuals did not show any severely influential observations when plotted against the observations and the dfbeta residuals were reasonably symmetrical when plotted against the observations - all indicating a fairly good model fit for the final survival model. Due to the absence of a numeric covariate, no fitted line with lowess function of the martingale residuals obtained for the null cox model was obtained.
1.5.1 Univariate Cox Proportional Hazards Model
Code Chunk | Output
##################################
# Formulating a Univariate Cox Proportional Hazards Model
# independently for the Factor Variable
##################################
(DBP.Analysis.UnivariateCoxPH.PhEcog <- coxph(Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered))## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered)
##
## coef exp(coef) se(coef) z p
## ph.ecogAmbulatory -0.5628 0.5696 0.1863 -3.021 0.00252
## ph.ecogAsymptomatic -0.9309 0.3942 0.2235 -4.166 3.11e-05
##
## Likelihood ratio test=17.33 on 2 df, p=0.0001722
## n= 227, number of events= 164summary(DBP.Analysis.UnivariateCoxPH.PhEcog)## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ph.ecogAmbulatory -0.5628 0.5696 0.1863 -3.021 0.00252 **
## ph.ecogAsymptomatic -0.9309 0.3942 0.2235 -4.166 3.11e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ph.ecogAmbulatory 0.5696 1.755 0.3954 0.8207
## ph.ecogAsymptomatic 0.3942 2.537 0.2544 0.6108
##
## Concordance= 0.604 (se = 0.024 )
## Likelihood ratio test= 17.33 on 2 df, p=2e-04
## Wald test = 18.17 on 2 df, p=1e-04
## Score (logrank) test = 19 on 2 df, p=7e-05tbl_regression(DBP.Analysis.UnivariateCoxPH.PhEcog,
exponentiate = TRUE)| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| ph.ecog | |||
| Bedridden | — | — | |
| Ambulatory | 0.57 | 0.40, 0.82 | 0.003 |
| Asymptomatic | 0.39 | 0.25, 0.61 | <0.001 |
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
(ggforest(DBP.Analysis.UnivariateCoxPH.PhEcog,
data=DBP.Analysis.Filtered,
main = "",
fontsize = 0.9))
##################################
# Plotting the Kaplan-Meier survival curves
# for the formulated Univariate Cox Proportional Hazards Model
# involving the Factor Variable
##################################
DBP.Analysis.UnivariateCoxPH.PhEcog.KaplanMeierEstimates <- survfit(DBP.Analysis.UnivariateCoxPH.PhEcog, data = DBP.Analysis.Filtered)
SurvivalTimeInWeek.KaplanMeier.UnivariateCoxPH.PhEcog <- ggsurvplot(DBP.Analysis.UnivariateCoxPH.PhEcog.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curves (CoxPH Model : Survival ~ ECOG Score)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
palette = c("#000000"))
ggpar(SurvivalTimeInWeek.KaplanMeier.UnivariateCoxPH.PhEcog,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Formulating a Univariate Cox Proportional Hazards Model
# independently for the Covariate Variable
##################################
(DBP.Analysis.UnivariateCoxPH.Sex <- coxph(Surv(time, status) ~ sex, data = DBP.Analysis.Filtered))## Call:
## coxph(formula = Surv(time, status) ~ sex, data = DBP.Analysis.Filtered)
##
## coef exp(coef) se(coef) z p
## sexFemale -0.5237 0.5923 0.1674 -3.128 0.00176
##
## Likelihood ratio test=10.3 on 1 df, p=0.001331
## n= 227, number of events= 164summary(DBP.Analysis.UnivariateCoxPH.Sex)## Call:
## coxph(formula = Surv(time, status) ~ sex, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## sexFemale -0.5237 0.5923 0.1674 -3.128 0.00176 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## sexFemale 0.5923 1.688 0.4266 0.8224
##
## Concordance= 0.577 (se = 0.021 )
## Likelihood ratio test= 10.3 on 1 df, p=0.001
## Wald test = 9.78 on 1 df, p=0.002
## Score (logrank) test = 10.01 on 1 df, p=0.002tbl_regression(DBP.Analysis.UnivariateCoxPH.Sex,
exponentiate = TRUE)| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| sex | |||
| Male | — | — | |
| Female | 0.59 | 0.43, 0.82 | 0.002 |
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
(ggforest(DBP.Analysis.UnivariateCoxPH.Sex,
data=DBP.Analysis.Filtered,
main = "",
fontsize = 0.9))
##################################
# Plotting the Kaplan-Meier survival curves
# for the formulated Univariate Cox Proportional Hazards Model
# involving the Covariate Variable
##################################
DBP.Analysis.UnivariateCoxPH.Sex.KaplanMeierEstimates <- survfit(DBP.Analysis.UnivariateCoxPH.Sex, data = DBP.Analysis.Filtered)
SurvivalTimeInWeek.KaplanMeier.UnivariateCoxPH.Sex <- ggsurvplot(DBP.Analysis.UnivariateCoxPH.Sex.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curves (CoxPH Model : Survival ~ Sex)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
palette = c("#000000"))
ggpar(SurvivalTimeInWeek.KaplanMeier.UnivariateCoxPH.Sex,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Formulating a Univariate Cox Proportional Hazards Model
# independently for the Covariate Variable
##################################
(DBP.Analysis.UnivariateCoxPH.Age <- coxph(Surv(time, status) ~ age, data = DBP.Analysis.Filtered))## Call:
## coxph(formula = Surv(time, status) ~ age, data = DBP.Analysis.Filtered)
##
## coef exp(coef) se(coef) z p
## age 0.018969 1.019150 0.009231 2.055 0.0399
##
## Likelihood ratio test=4.33 on 1 df, p=0.03754
## n= 227, number of events= 164summary(DBP.Analysis.UnivariateCoxPH.Age)## Call:
## coxph(formula = Surv(time, status) ~ age, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age 0.018969 1.019150 0.009231 2.055 0.0399 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## age 1.019 0.9812 1.001 1.038
##
## Concordance= 0.551 (se = 0.025 )
## Likelihood ratio test= 4.33 on 1 df, p=0.04
## Wald test = 4.22 on 1 df, p=0.04
## Score (logrank) test = 4.24 on 1 df, p=0.04tbl_regression(DBP.Analysis.UnivariateCoxPH.Age,
exponentiate = TRUE)| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| age | 1.02 | 1.00, 1.04 | 0.040 |
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
(ggforest(DBP.Analysis.UnivariateCoxPH.Age,
data=DBP.Analysis.Filtered,
main = "",
fontsize = 0.9))
##################################
# Plotting the Kaplan-Meier survival curves
# for the formulated Univariate Cox Proportional Hazards Model
# involving the Covariate Variable
##################################
DBP.Analysis.UnivariateCoxPH.Age.KaplanMeierEstimates <- survfit(DBP.Analysis.UnivariateCoxPH.Age, data = DBP.Analysis.Filtered)
SurvivalTimeInWeek.KaplanMeier.UnivariateCoxPH.Age <- ggsurvplot(DBP.Analysis.UnivariateCoxPH.Age.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curves (CoxPH Model : Survival ~ Age)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
palette = c("#000000"))
ggpar(SurvivalTimeInWeek.KaplanMeier.UnivariateCoxPH.Age,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Formulating a Univariate Cox Proportional Hazards Model
# individually for the Factor and Covariate Variables
##################################
tbl_survfit(
list(survfit(Surv(time, status) ~ 1, data = DBP.Analysis.Filtered),
survfit(Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered),
survfit(Surv(time, status) ~ sex, data = DBP.Analysis.Filtered),
survfit(Surv(time, status) ~ age, data = DBP.Analysis.Filtered)),
probs = 0.5,
label_header = "**Median Survival**") %>%
add_n() %>%
add_nevent()| Characteristic | N | Event N | Median Survival |
|---|---|---|---|
| Overall | 227 | 164 | 310 (285, 363) |
| ph.ecog | 227 | 164 | |
| Bedridden | 183 (153, 288) | ||
| Ambulatory | 306 (268, 429) | ||
| Asymptomatic | 394 (348, 574) | ||
| sex | 227 | 164 | |
| Male | 270 (218, 320) | ||
| Female | 426 (348, 550) | ||
| age | 227 | 164 | |
| 39 | — (—, —) | ||
| 40 | 132 (—, —) | ||
| 41 | — (—, —) | ||
| 42 | — (—, —) | ||
| 43 | — (—, —) | ||
| 44 | 268 (181, —) | ||
| 45 | — (—, —) | ||
| 46 | 320 (—, —) | ||
| 47 | 353 (—, —) | ||
| 48 | 419 (223, —) | ||
| 49 | 147 (81, —) | ||
| 50 | 239 (131, —) | ||
| 51 | 705 (—, —) | ||
| 52 | 179 (81, —) | ||
| 53 | 226 (202, —) | ||
| 54 | 491 (163, —) | ||
| 55 | 308 (156, —) | ||
| 56 | 363 (197, —) | ||
| 57 | 245 (170, —) | ||
| 58 | 371 (348, —) | ||
| 59 | 433 (293, —) | ||
| 60 | 387 (145, —) | ||
| 61 | 166 (147, —) | ||
| 62 | 291 (105, —) | ||
| 63 | 519 (189, —) | ||
| 64 | 477 (110, —) | ||
| 65 | 174 (60, —) | ||
| 66 | 288 (156, —) | ||
| 67 | 230 (208, —) | ||
| 68 | 455 (310, —) | ||
| 69 | 450 (329, —) | ||
| 70 | 460 (229, —) | ||
| 71 | 332 (284, —) | ||
| 72 | 270 (54, —) | ||
| 73 | 164 (59, —) | ||
| 74 | 306 (93, —) | ||
| 75 | 397 (201, —) | ||
| 76 | 116 (95, —) | ||
| 77 | — (—, —) | ||
| 80 | 323 (283, —) | ||
| 81 | 11 (—, —) | ||
| 82 | 31 (—, —) |
1.5.2 Multivariate Cox Proportional Hazards Model
Code Chunk | Output
##################################
# Formulating a Multivariate Cox Proportional Hazards Model
# with both the Factor and Covariate Variables
##################################
(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge <- coxph(Surv(time, status) ~ ph.ecog + sex + age, data = DBP.Analysis.Filtered))## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex + age, data = DBP.Analysis.Filtered)
##
## coef exp(coef) se(coef) z p
## ph.ecogAmbulatory -0.506291 0.602727 0.188454 -2.687 0.00722
## ph.ecogAsymptomatic -0.915752 0.400215 0.227042 -4.033 5.5e-05
## sexFemale -0.551322 0.576188 0.167987 -3.282 0.00103
## age 0.011031 1.011092 0.009297 1.186 0.23544
##
## Likelihood ratio test=30.08 on 4 df, p=4.704e-06
## n= 227, number of events= 164summary(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge)## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex + age, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ph.ecogAmbulatory -0.506291 0.602727 0.188454 -2.687 0.00722 **
## ph.ecogAsymptomatic -0.915752 0.400215 0.227042 -4.033 5.5e-05 ***
## sexFemale -0.551322 0.576188 0.167987 -3.282 0.00103 **
## age 0.011031 1.011092 0.009297 1.186 0.23544
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ph.ecogAmbulatory 0.6027 1.659 0.4166 0.8720
## ph.ecogAsymptomatic 0.4002 2.499 0.2565 0.6245
## sexFemale 0.5762 1.736 0.4145 0.8009
## age 1.0111 0.989 0.9928 1.0297
##
## Concordance= 0.637 (se = 0.025 )
## Likelihood ratio test= 30.08 on 4 df, p=5e-06
## Wald test = 29.77 on 4 df, p=5e-06
## Score (logrank) test = 30.94 on 4 df, p=3e-06tbl_regression(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge,
exponentiate = TRUE)| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| ph.ecog | |||
| Bedridden | — | — | |
| Ambulatory | 0.60 | 0.42, 0.87 | 0.007 |
| Asymptomatic | 0.40 | 0.26, 0.62 | <0.001 |
| sex | |||
| Male | — | — | |
| Female | 0.58 | 0.41, 0.80 | 0.001 |
| age | 1.01 | 0.99, 1.03 | 0.2 |
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
(DBP.Analysis.MultivariateCoxPH.DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.ForestPlot <- ggforest(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge,
data=DBP.Analysis.Filtered,
main = "",
fontsize = 0.9))
##################################
# Plotting the Kaplan-Meier survival curves
# for the formulated Multivariate Cox Proportional Hazards Model
# involving the Factor and Covariate variables
##################################
DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.KaplanMeierEstimates <- survfit(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge , data = DBP.Analysis.Filtered)
SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSexAge <- ggsurvplot(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curves (CoxPH Model : Survival ~ ECOG Score + Sex + Age)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
palette = c("#000000"))
ggpar(SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSexAge,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Formulating a Multivariate Cox Proportional Hazards Model
# with both the Factor and Covariate Variables
# including their interaction
##################################
(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.WithInteraction <- coxph(Surv(time, status) ~ ph.ecog + sex + age + ph.ecog*sex*age, data = DBP.Analysis.Filtered))## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex + age + ph.ecog *
## sex * age, data = DBP.Analysis.Filtered)
##
## coef exp(coef) se(coef) z
## ph.ecogAmbulatory 2.430e+00 1.136e+01 2.064e+00 1.177
## ph.ecogAsymptomatic -1.392e+00 2.486e-01 2.547e+00 -0.546
## sexFemale 7.319e+00 1.509e+03 2.746e+00 2.665
## age 4.669e-02 1.048e+00 2.842e-02 1.643
## ph.ecogAmbulatory:sexFemale -7.406e+00 6.073e-04 3.180e+00 -2.329
## ph.ecogAsymptomatic:sexFemale -7.486e+00 5.610e-04 4.250e+00 -1.761
## ph.ecogAmbulatory:age -4.524e-02 9.558e-01 3.178e-02 -1.424
## ph.ecogAsymptomatic:age 8.315e-03 1.008e+00 3.895e-02 0.213
## sexFemale:age -1.151e-01 8.912e-01 4.139e-02 -2.782
## ph.ecogAmbulatory:sexFemale:age 1.065e-01 1.112e+00 4.896e-02 2.176
## ph.ecogAsymptomatic:sexFemale:age 1.102e-01 1.116e+00 6.622e-02 1.664
## p
## ph.ecogAmbulatory 0.2390
## ph.ecogAsymptomatic 0.5848
## sexFemale 0.0077
## age 0.1004
## ph.ecogAmbulatory:sexFemale 0.0199
## ph.ecogAsymptomatic:sexFemale 0.0782
## ph.ecogAmbulatory:age 0.1545
## ph.ecogAsymptomatic:age 0.8309
## sexFemale:age 0.0054
## ph.ecogAmbulatory:sexFemale:age 0.0295
## ph.ecogAsymptomatic:sexFemale:age 0.0961
##
## Likelihood ratio test=42.43 on 11 df, p=1.362e-05
## n= 227, number of events= 164summary(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.WithInteraction)## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex + age + ph.ecog *
## sex * age, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z
## ph.ecogAmbulatory 2.430e+00 1.136e+01 2.064e+00 1.177
## ph.ecogAsymptomatic -1.392e+00 2.486e-01 2.547e+00 -0.546
## sexFemale 7.319e+00 1.509e+03 2.746e+00 2.665
## age 4.669e-02 1.048e+00 2.842e-02 1.643
## ph.ecogAmbulatory:sexFemale -7.406e+00 6.073e-04 3.180e+00 -2.329
## ph.ecogAsymptomatic:sexFemale -7.486e+00 5.610e-04 4.250e+00 -1.761
## ph.ecogAmbulatory:age -4.524e-02 9.558e-01 3.178e-02 -1.424
## ph.ecogAsymptomatic:age 8.315e-03 1.008e+00 3.895e-02 0.213
## sexFemale:age -1.151e-01 8.912e-01 4.139e-02 -2.782
## ph.ecogAmbulatory:sexFemale:age 1.065e-01 1.112e+00 4.896e-02 2.176
## ph.ecogAsymptomatic:sexFemale:age 1.102e-01 1.116e+00 6.622e-02 1.664
## Pr(>|z|)
## ph.ecogAmbulatory 0.2390
## ph.ecogAsymptomatic 0.5848
## sexFemale 0.0077 **
## age 0.1004
## ph.ecogAmbulatory:sexFemale 0.0199 *
## ph.ecogAsymptomatic:sexFemale 0.0782 .
## ph.ecogAmbulatory:age 0.1545
## ph.ecogAsymptomatic:age 0.8309
## sexFemale:age 0.0054 **
## ph.ecogAmbulatory:sexFemale:age 0.0295 *
## ph.ecogAsymptomatic:sexFemale:age 0.0961 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ph.ecogAmbulatory 1.136e+01 8.804e-02 1.989e-01 6.488e+02
## ph.ecogAsymptomatic 2.486e-01 4.022e+00 1.688e-03 3.663e+01
## sexFemale 1.509e+03 6.627e-04 6.935e+00 3.284e+05
## age 1.048e+00 9.544e-01 9.910e-01 1.108e+00
## ph.ecogAmbulatory:sexFemale 6.073e-04 1.647e+03 1.192e-06 3.095e-01
## ph.ecogAsymptomatic:sexFemale 5.610e-04 1.782e+03 1.352e-07 2.327e+00
## ph.ecogAmbulatory:age 9.558e-01 1.046e+00 8.981e-01 1.017e+00
## ph.ecogAsymptomatic:age 1.008e+00 9.917e-01 9.342e-01 1.088e+00
## sexFemale:age 8.912e-01 1.122e+00 8.218e-01 9.665e-01
## ph.ecogAmbulatory:sexFemale:age 1.112e+00 8.989e-01 1.011e+00 1.224e+00
## ph.ecogAsymptomatic:sexFemale:age 1.116e+00 8.957e-01 9.806e-01 1.271e+00
##
## Concordance= 0.662 (se = 0.024 )
## Likelihood ratio test= 42.43 on 11 df, p=1e-05
## Wald test = 41.85 on 11 df, p=2e-05
## Score (logrank) test = 47.09 on 11 df, p=2e-06tbl_regression(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.WithInteraction,
exponentiate = TRUE)| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| ph.ecog | |||
| Bedridden | — | — | |
| Ambulatory | 11.4 | 0.20, 649 | 0.2 |
| Asymptomatic | 0.25 | 0.00, 36.6 | 0.6 |
| sex | |||
| Male | — | — | |
| Female | 1,509 | 6.93, 328,387 | 0.008 |
| age | 1.05 | 0.99, 1.11 | 0.10 |
| ph.ecog * sex | |||
| Ambulatory * Female | 0.00 | 0.00, 0.31 | 0.020 |
| Asymptomatic * Female | 0.00 | 0.00, 2.33 | 0.078 |
| ph.ecog * age | |||
| Ambulatory * age | 0.96 | 0.90, 1.02 | 0.2 |
| Asymptomatic * age | 1.01 | 0.93, 1.09 | 0.8 |
| sex * age | |||
| Female * age | 0.89 | 0.82, 0.97 | 0.005 |
| ph.ecog * sex * age | |||
| Ambulatory * Female * age | 1.11 | 1.01, 1.22 | 0.030 |
| Asymptomatic * Female * age | 1.12 | 0.98, 1.27 | 0.10 |
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.WithInteraction.ForestPlot <- ggforest(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.WithInteraction,
data=DBP.Analysis.Filtered,
main = "",
fontsize = 0.9))
##################################
# Plotting the Kaplan-Meier survival curves
# for the formulated Multivariate Cox Proportional Hazards Model
# involving the Factor and Covariate variables
# including their interaction
##################################
DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.WithInteraction.KaplanMeierEstimates <- survfit(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.WithInteraction, data = DBP.Analysis.Filtered)
SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSexAge.WithInteraction <- ggsurvplot(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge.WithInteraction.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curves (CoxPH Model : Survival ~ ECOG Score * Sex * Age)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
palette = c("#000000"))
ggpar(SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSexAge.WithInteraction,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Formulating a Multivariate Cox Proportional Hazards Model
# with both the Factor and Covariate Variables
##################################
(DBP.Analysis.MultivariateCoxPH.PhEcogSex <- coxph(Surv(time, status) ~ ph.ecog + sex , data = DBP.Analysis.Filtered))## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex, data = DBP.Analysis.Filtered)
##
## coef exp(coef) se(coef) z p
## ph.ecogAmbulatory -0.5433 0.5808 0.1861 -2.919 0.00351
## ph.ecogAsymptomatic -0.9611 0.3825 0.2237 -4.297 1.73e-05
## sexFemale -0.5503 0.5768 0.1679 -3.277 0.00105
##
## Likelihood ratio test=28.66 on 3 df, p=2.643e-06
## n= 227, number of events= 164summary(DBP.Analysis.MultivariateCoxPH.PhEcogSex)## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ph.ecogAmbulatory -0.5433 0.5808 0.1861 -2.919 0.00351 **
## ph.ecogAsymptomatic -0.9611 0.3825 0.2237 -4.297 1.73e-05 ***
## sexFemale -0.5503 0.5768 0.1679 -3.277 0.00105 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ph.ecogAmbulatory 0.5808 1.722 0.4033 0.8365
## ph.ecogAsymptomatic 0.3825 2.615 0.2467 0.5929
## sexFemale 0.5768 1.734 0.4151 0.8016
##
## Concordance= 0.642 (se = 0.025 )
## Likelihood ratio test= 28.66 on 3 df, p=3e-06
## Wald test = 28.99 on 3 df, p=2e-06
## Score (logrank) test = 30.04 on 3 df, p=1e-06tbl_regression(DBP.Analysis.MultivariateCoxPH.PhEcogSex,
exponentiate = TRUE)| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| ph.ecog | |||
| Bedridden | — | — | |
| Ambulatory | 0.58 | 0.40, 0.84 | 0.004 |
| Asymptomatic | 0.38 | 0.25, 0.59 | <0.001 |
| sex | |||
| Male | — | — | |
| Female | 0.58 | 0.42, 0.80 | 0.001 |
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
(DBP.Analysis.MultivariateCoxPH.DBP.Analysis.MultivariateCoxPH.PhEcogSex.ForestPlot <- ggforest(DBP.Analysis.MultivariateCoxPH.PhEcogSex,
data=DBP.Analysis.Filtered,
main = "",
fontsize = 0.9))
##################################
# Plotting the Kaplan-Meier survival curves
# for the formulated Multivariate Cox Proportional Hazards Model
# involving the Factor and Covariate variables
##################################
DBP.Analysis.MultivariateCoxPH.PhEcogSex.KaplanMeierEstimates <- survfit(DBP.Analysis.MultivariateCoxPH.PhEcogSex , data = DBP.Analysis.Filtered)
SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSex <- ggsurvplot(DBP.Analysis.MultivariateCoxPH.PhEcogSex.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curves (CoxPH Model : Survival ~ ECOG Score + Sex)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
palette = c("#000000"))
ggpar(SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSex,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Formulating a Multivariate Cox Proportional Hazards Model
# with both the Factor and Covariate Variables
# including their interaction
##################################
(DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction <- coxph(Surv(time, status) ~ ph.ecog + sex + ph.ecog*sex, data = DBP.Analysis.Filtered))## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex + ph.ecog *
## sex, data = DBP.Analysis.Filtered)
##
## coef exp(coef) se(coef) z p
## ph.ecogAmbulatory -0.4669 0.6269 0.2312 -2.020 0.04339
## ph.ecogAsymptomatic -0.8692 0.4193 0.2667 -3.259 0.00112
## sexFemale -0.3724 0.6891 0.3130 -1.190 0.23419
## ph.ecogAmbulatory:sexFemale -0.2258 0.7979 0.3927 -0.575 0.56533
## ph.ecogAsymptomatic:sexFemale -0.3055 0.7367 0.4945 -0.618 0.53670
##
## Likelihood ratio test=29.13 on 5 df, p=2.186e-05
## n= 227, number of events= 164summary(DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction)## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex + ph.ecog *
## sex, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ph.ecogAmbulatory -0.4669 0.6269 0.2312 -2.020 0.04339 *
## ph.ecogAsymptomatic -0.8692 0.4193 0.2667 -3.259 0.00112 **
## sexFemale -0.3724 0.6891 0.3130 -1.190 0.23419
## ph.ecogAmbulatory:sexFemale -0.2258 0.7979 0.3927 -0.575 0.56533
## ph.ecogAsymptomatic:sexFemale -0.3055 0.7367 0.4945 -0.618 0.53670
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ph.ecogAmbulatory 0.6269 1.595 0.3985 0.9862
## ph.ecogAsymptomatic 0.4193 2.385 0.2486 0.7072
## sexFemale 0.6891 1.451 0.3731 1.2727
## ph.ecogAmbulatory:sexFemale 0.7979 1.253 0.3695 1.7228
## ph.ecogAsymptomatic:sexFemale 0.7367 1.357 0.2795 1.9420
##
## Concordance= 0.643 (se = 0.025 )
## Likelihood ratio test= 29.13 on 5 df, p=2e-05
## Wald test = 28.01 on 5 df, p=4e-05
## Score (logrank) test = 30.3 on 5 df, p=1e-05tbl_regression(DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction,
exponentiate = TRUE)| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| ph.ecog | |||
| Bedridden | — | — | |
| Ambulatory | 0.63 | 0.40, 0.99 | 0.043 |
| Asymptomatic | 0.42 | 0.25, 0.71 | 0.001 |
| sex | |||
| Male | — | — | |
| Female | 0.69 | 0.37, 1.27 | 0.2 |
| ph.ecog * sex | |||
| Ambulatory * Female | 0.80 | 0.37, 1.72 | 0.6 |
| Asymptomatic * Female | 0.74 | 0.28, 1.94 | 0.5 |
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
(DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction.ForestPlot <- ggforest(DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction,
data=DBP.Analysis.Filtered,
main = "",
fontsize = 0.9))
##################################
# Plotting the Kaplan-Meier survival curves
# for the formulated Multivariate Cox Proportional Hazards Model
# involving the Factor and Covariate variables
# including their interaction
##################################
DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction.KaplanMeierEstimates <- survfit(DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction, data = DBP.Analysis.Filtered)
SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSex.WithInteraction <- ggsurvplot(DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curves (CoxPH Model : Survival ~ ECOG Score * Sex)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
palette = c("#000000"))
ggpar(SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSex.WithInteraction,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Formulating complete and reduced
# Multivariate Cox Proportional Hazards Models
# involving the Factor and Covariate Variables
##################################
DBP.Analysis.SurvivalResponse <- "Surv(time, status)"
DBP.Analysis.SurvivalPredictorComplete <- c("ph.ecog", "sex", "age")
DBP.Analysis.SurvivalPredictorReduced <- c("ph.ecog", "sex")
DBP.Analysis.CoxPHModelSummary <- DBP.Analysis.Filtered %>%
finalfit(DBP.Analysis.SurvivalResponse,
DBP.Analysis.SurvivalPredictorComplete,
DBP.Analysis.SurvivalPredictorReduced,
keep_models = TRUE,
add_dependent_label = FALSE) %>%
rename("Overall Survival" = label) %>%
rename(" " = levels) %>%
rename(" " = all)
kable(DBP.Analysis.CoxPHModelSummary)| Overall Survival | HR (univariable) | HR (multivariable full) | HR (multivariable) | |||
|---|---|---|---|---|---|---|
| 4 | ph.ecog | Bedridden | 51 (22.5) | - | - | - |
| 2 | Ambulatory | 113 (49.8) | 0.57 (0.40-0.82, p=0.003) | 0.60 (0.42-0.87, p=0.007) | 0.58 (0.40-0.84, p=0.004) | |
| 3 | Asymptomatic | 63 (27.8) | 0.39 (0.25-0.61, p<0.001) | 0.40 (0.26-0.62, p<0.001) | 0.38 (0.25-0.59, p<0.001) | |
| 6 | sex | Male | 137 (60.4) | - | - | - |
| 5 | Female | 90 (39.6) | 0.59 (0.43-0.82, p=0.002) | 0.58 (0.41-0.80, p=0.001) | 0.58 (0.42-0.80, p=0.001) | |
| 1 | age | Mean (SD) | 62.5 (9.1) | 1.02 (1.00-1.04, p=0.040) | 1.01 (0.99-1.03, p=0.235) | - |
1.5.3 Model Selection
Code Chunk | Output
##################################
# Applying Stepwise Variable Selection
##################################
DBP.Analysis.MultivariateCoxPH.StepwiseSelection <- stepAIC(DBP.Analysis.MultivariateCoxPH.PhEcogSexAge,
direction = "both",
trace = TRUE)## Start: AIC=1466.88
## Surv(time, status) ~ ph.ecog + sex + age
##
## Df AIC
## - age 1 1466.3
## <none> 1466.9
## - sex 1 1476.2
## - ph.ecog 2 1479.1
##
## Step: AIC=1466.3
## Surv(time, status) ~ ph.ecog + sex
##
## Df AIC
## <none> 1466.3
## + age 1 1466.9
## - sex 1 1475.6
## - ph.ecog 2 1480.7summary(DBP.Analysis.MultivariateCoxPH.StepwiseSelection)## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ph.ecogAmbulatory -0.5433 0.5808 0.1861 -2.919 0.00351 **
## ph.ecogAsymptomatic -0.9611 0.3825 0.2237 -4.297 1.73e-05 ***
## sexFemale -0.5503 0.5768 0.1679 -3.277 0.00105 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ph.ecogAmbulatory 0.5808 1.722 0.4033 0.8365
## ph.ecogAsymptomatic 0.3825 2.615 0.2467 0.5929
## sexFemale 0.5768 1.734 0.4151 0.8016
##
## Concordance= 0.642 (se = 0.025 )
## Likelihood ratio test= 28.66 on 3 df, p=3e-06
## Wald test = 28.99 on 3 df, p=2e-06
## Score (logrank) test = 30.04 on 3 df, p=1e-06##################################
# Reusing formulated models
##################################
summary(DBP.Analysis.UnivariateCoxPH.PhEcog)## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ph.ecogAmbulatory -0.5628 0.5696 0.1863 -3.021 0.00252 **
## ph.ecogAsymptomatic -0.9309 0.3942 0.2235 -4.166 3.11e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ph.ecogAmbulatory 0.5696 1.755 0.3954 0.8207
## ph.ecogAsymptomatic 0.3942 2.537 0.2544 0.6108
##
## Concordance= 0.604 (se = 0.024 )
## Likelihood ratio test= 17.33 on 2 df, p=2e-04
## Wald test = 18.17 on 2 df, p=1e-04
## Score (logrank) test = 19 on 2 df, p=7e-05summary(DBP.Analysis.MultivariateCoxPH.PhEcogSex)## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ph.ecogAmbulatory -0.5433 0.5808 0.1861 -2.919 0.00351 **
## ph.ecogAsymptomatic -0.9611 0.3825 0.2237 -4.297 1.73e-05 ***
## sexFemale -0.5503 0.5768 0.1679 -3.277 0.00105 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ph.ecogAmbulatory 0.5808 1.722 0.4033 0.8365
## ph.ecogAsymptomatic 0.3825 2.615 0.2467 0.5929
## sexFemale 0.5768 1.734 0.4151 0.8016
##
## Concordance= 0.642 (se = 0.025 )
## Likelihood ratio test= 28.66 on 3 df, p=3e-06
## Wald test = 28.99 on 3 df, p=2e-06
## Score (logrank) test = 30.04 on 3 df, p=1e-06summary(DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction)## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex + ph.ecog *
## sex, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ph.ecogAmbulatory -0.4669 0.6269 0.2312 -2.020 0.04339 *
## ph.ecogAsymptomatic -0.8692 0.4193 0.2667 -3.259 0.00112 **
## sexFemale -0.3724 0.6891 0.3130 -1.190 0.23419
## ph.ecogAmbulatory:sexFemale -0.2258 0.7979 0.3927 -0.575 0.56533
## ph.ecogAsymptomatic:sexFemale -0.3055 0.7367 0.4945 -0.618 0.53670
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ph.ecogAmbulatory 0.6269 1.595 0.3985 0.9862
## ph.ecogAsymptomatic 0.4193 2.385 0.2486 0.7072
## sexFemale 0.6891 1.451 0.3731 1.2727
## ph.ecogAmbulatory:sexFemale 0.7979 1.253 0.3695 1.7228
## ph.ecogAsymptomatic:sexFemale 0.7367 1.357 0.2795 1.9420
##
## Concordance= 0.643 (se = 0.025 )
## Likelihood ratio test= 29.13 on 5 df, p=2e-05
## Wald test = 28.01 on 5 df, p=4e-05
## Score (logrank) test = 30.3 on 5 df, p=1e-05##################################
# Formulating the linear predictors
# for the formulated Univariate Cox Proportional Hazards Models
##################################
DBP.Analysis.Filtered$LP.Univariate.PhEcog <- predict(DBP.Analysis.UnivariateCoxPH.PhEcog, type = "lp")
##################################
# Formulating the linear predictors
# for the formulated Multivariate Cox Proportional Hazards Models
##################################
DBP.Analysis.Filtered$LP.Multivariate.PhEcogSex <- predict(DBP.Analysis.MultivariateCoxPH.PhEcogSex, type = "lp")
DBP.Analysis.Filtered$LP.Multivariate.PhEcogSex.WithInteraction <- predict(DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction, type = "lp")
##################################
# Conducting a likelihood ratio test between nested models
# including the formulated Multivariate Cox Proportional Hazards Models
# involving the Factor variable only
# and both Factor and Covariate variables
##################################
(LikelihoodRatioTest.CoxPHPhEcog.CoxPHPhEcogSex <- anova(DBP.Analysis.UnivariateCoxPH.PhEcog,
DBP.Analysis.MultivariateCoxPH.PhEcogSex,
test="LRT"))## Analysis of Deviance Table
## Cox model: response is Surv(time, status)
## Model 1: ~ ph.ecog
## Model 2: ~ ph.ecog + sex
## loglik Chisq Df Pr(>|Chi|)
## 1 -735.81
## 2 -730.15 11.324 1 0.0007652 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##################################
# Conducting a likelihood ratio test between nested models
# including the formulated Multivariate Cox Proportional Hazards Models
# involving both Factor and Covariate variables only
# and both Factor and Covariate variables including their interaction
##################################
(LikelihoodRatioTest.CoxPHPhEcogSex.CoxPHPhEcogSexWithInteraction <- anova(DBP.Analysis.MultivariateCoxPH.PhEcogSex,
DBP.Analysis.MultivariateCoxPH.PhEcogSex.WithInteraction,
test="LRT"))## Analysis of Deviance Table
## Cox model: response is Surv(time, status)
## Model 1: ~ ph.ecog + sex
## Model 2: ~ ph.ecog + sex + ph.ecog * sex
## loglik Chisq Df Pr(>|Chi|)
## 1 -730.15
## 2 -729.92 0.4727 2 0.78951.5.4 Model Performance Validation
Code Chunk | Output
##################################
# Measuring the Harrel's Concordance Index
# for the formulated Univariate Cox Proportional Hazards Model
# involving the Factor variable
##################################
rcorrcens(formula = Surv(time, status) ~ I(-1 * LP.Univariate.PhEcog), data = DBP.Analysis.Filtered)##
## Somers' Rank Correlation for Censored Data Response variable:Surv(time, status)
##
## C Dxy aDxy SD Z P n
## I(-1 * LP.Univariate.PhEcog) 0.604 0.208 0.208 0.048 4.35 0 227LP.Univariate.PhEcog.Concordance <- survConcordance(Surv(time, status) ~ LP.Univariate.PhEcog,
data = DBP.Analysis.Filtered)
(LP.Univariate.PhEcog.Concordance$concordance)## concordant
## 0.6039571DBP.Analysis.UnivariateCoxPH.PhEcog.Validation <- cph(Surv(time, status) ~ ph.ecog,
x=TRUE,
y=TRUE,
data = DBP.Analysis.Filtered)
set.seed (88888888)
DBP.Analysis.UnivariateCoxPH.PhEcog.Validation.Summary <- validate(DBP.Analysis.UnivariateCoxPH.PhEcog.Validation, B =500)
(DBP.Analysis.UnivariateCoxPH.PhEcog.ConcordanceIndex.Optimistic <- (DBP.Analysis.UnivariateCoxPH.PhEcog.Validation.Summary[1,1]/2)+0.50)## [1] 0.6039571(DBP.Analysis.UnivariateCoxPH.PhEcog.ConcordanceIndex.OptimismCorrected <- (DBP.Analysis.UnivariateCoxPH.PhEcog.Validation.Summary[1,5]/2)+0.50)## [1] 0.6035354##################################
# Measuring the Harrel's Concordance Index
# for the formulated Multivariate Cox Proportional Hazards Model
# involving the Factor and Covariate variables
##################################
rcorrcens(formula = Surv(time, status) ~ I(-1 * LP.Multivariate.PhEcogSex), data = DBP.Analysis.Filtered)##
## Somers' Rank Correlation for Censored Data Response variable:Surv(time, status)
##
## C Dxy aDxy SD Z P n
## I(-1 * LP.Multivariate.PhEcogSex) 0.642 0.284 0.284 0.049 5.74 0 227LP.Multivariate.PhEcogSex.Concordance <- survConcordance(Surv(time, status) ~ LP.Multivariate.PhEcogSex,
data = DBP.Analysis.Filtered)
(LP.Multivariate.PhEcogSex.Concordance$concordance)## concordant
## 0.6418861DBP.Analysis.Multivariate.PhEcogSex.Validation <- cph(Surv(time, status) ~ ph.ecog + sex,
x=TRUE,
y=TRUE,
data = DBP.Analysis.Filtered)
set.seed (88888888)
DBP.Analysis.Multivariate.PhEcogSex.Validation.Summary <- validate(DBP.Analysis.Multivariate.PhEcogSex.Validation, B =500)
(DBP.Analysis.Multivariate.PhEcogSex.ConcordanceIndex.Optimistic <- (DBP.Analysis.Multivariate.PhEcogSex.Validation.Summary[1,1]/2)+0.50)## [1] 0.6418861(DBP.Analysis.Multivariate.PhEcogSex.ConcordanceIndex.OptimismCorrected <- (DBP.Analysis.Multivariate.PhEcogSex.Validation.Summary[1,5]/2)+0.50)## [1] 0.6355095##################################
# Measuring the Harrel's Concordance Index
# for the formulated Multivariate Cox Proportional Hazards Model
# involving the Factor and Covariate variables
# including their interaction
##################################
rcorrcens(formula = Surv(time, status) ~ I(-1 * LP.Multivariate.PhEcogSex.WithInteraction), data = DBP.Analysis.Filtered)##
## Somers' Rank Correlation for Censored Data Response variable:Surv(time, status)
##
## C Dxy aDxy SD Z
## I(-1 * LP.Multivariate.PhEcogSex.WithInteraction) 0.643 0.286 0.286 0.049 5.83
## P n
## I(-1 * LP.Multivariate.PhEcogSex.WithInteraction) 0 227LP.Multivariate.PhEcogSex.WithInteraction.Concordance <- survConcordance(Surv(time, status) ~ LP.Multivariate.PhEcogSex.WithInteraction, data = DBP.Analysis.Filtered)
(LP.Multivariate.PhEcogSex.WithInteraction.Concordance$concordance)## concordant
## 0.6432001DBP.Analysis.Multivariate.PhEcogSex.WithInteraction.Validation <- cph(Surv(time, status) ~ ph.ecog + sex + ph.ecog*sex,
x=TRUE,
y=TRUE,
data = DBP.Analysis.Filtered)
set.seed (88888888)
DBP.Analysis.Multivariate.PhEcogSex.WithInteraction.Validation.Summary <- validate(DBP.Analysis.Multivariate.PhEcogSex.WithInteraction.Validation, B =500)
(DBP.Analysis.Multivariate.PhEcogSex.WithInteraction.ConcordanceIndex.Optimistic <- (DBP.Analysis.Multivariate.PhEcogSex.WithInteraction.Validation.Summary[1,1]/2)+0.50)## [1] 0.6432001(DBP.Analysis.Multivariate.PhEcogSex.WithInteraction.ConcordanceIndex.OptimismCorrected <- (DBP.Analysis.Multivariate.PhEcogSex.WithInteraction.Validation.Summary[1,5]/2)+0.50)## [1] 0.6329231.5.5 Model Diagnostics
Code Chunk | Output
##################################
# Reusing selected model
##################################
summary(DBP.Analysis.MultivariateCoxPH.PhEcogSex)## Call:
## coxph(formula = Surv(time, status) ~ ph.ecog + sex, data = DBP.Analysis.Filtered)
##
## n= 227, number of events= 164
##
## coef exp(coef) se(coef) z Pr(>|z|)
## ph.ecogAmbulatory -0.5433 0.5808 0.1861 -2.919 0.00351 **
## ph.ecogAsymptomatic -0.9611 0.3825 0.2237 -4.297 1.73e-05 ***
## sexFemale -0.5503 0.5768 0.1679 -3.277 0.00105 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## ph.ecogAmbulatory 0.5808 1.722 0.4033 0.8365
## ph.ecogAsymptomatic 0.3825 2.615 0.2467 0.5929
## sexFemale 0.5768 1.734 0.4151 0.8016
##
## Concordance= 0.642 (se = 0.025 )
## Likelihood ratio test= 28.66 on 3 df, p=3e-06
## Wald test = 28.99 on 3 df, p=2e-06
## Score (logrank) test = 30.04 on 3 df, p=1e-06tbl_regression(DBP.Analysis.MultivariateCoxPH.PhEcogSex,
exponentiate = TRUE)| Characteristic | HR1 | 95% CI1 | p-value |
|---|---|---|---|
| ph.ecog | |||
| Bedridden | — | — | |
| Ambulatory | 0.58 | 0.40, 0.84 | 0.004 |
| Asymptomatic | 0.38 | 0.25, 0.59 | <0.001 |
| sex | |||
| Male | — | — | |
| Female | 0.58 | 0.42, 0.80 | 0.001 |
| 1 HR = Hazard Ratio, CI = Confidence Interval | |||
(DBP.Analysis.MultivariateCoxPH.DBP.Analysis.MultivariateCoxPH.PhEcogSex.ForestPlot <- ggforest(DBP.Analysis.MultivariateCoxPH.PhEcogSex,
data=DBP.Analysis.Filtered,
main = "",
fontsize = 0.9))
##################################
# Plotting the Kaplan-Meier survival curves
# for the formulated Multivariate Cox Proportional Hazards Model
# involving the Factor and Covariate variables
##################################
DBP.Analysis.MultivariateCoxPH.PhEcogSex.KaplanMeierEstimates <- survfit(DBP.Analysis.MultivariateCoxPH.PhEcogSex , data = DBP.Analysis.Filtered)
SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSex <- ggsurvplot(DBP.Analysis.MultivariateCoxPH.PhEcogSex.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curves (CoxPH Model : Survival ~ ECOG Score + Sex)",
pval = FALSE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
palette = c("#000000"))
ggpar(SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSex,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Plotting the Kaplan-Meier survival curves
# of the Factor variable adjusted by the Covariate variable
# using the formulated Multivariate Cox Proportional Hazards Model
##################################
(DBP.PhEcogAdjustedBySex <- with(DBP.Analysis.Filtered,
data.frame(ph.ecog = c("Bedridden", "Ambulatory","Asymptomatic"),
sex = c("Male", "Male", "Male"))))## ph.ecog sex
## 1 Bedridden Male
## 2 Ambulatory Male
## 3 Asymptomatic MaleDBP.Analysis.MultivariateCoxPH.PhEcogSex.PhEcogAdjustedBySex.KaplanMeierEstimates <- survfit(DBP.Analysis.MultivariateCoxPH.PhEcogSex,
newdata = DBP.PhEcogAdjustedBySex,
data=DBP.Analysis.Filtered)
SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSex.PhEcogAdjustedBySex <- ggsurvplot(DBP.Analysis.MultivariateCoxPH.PhEcogSex.PhEcogAdjustedBySex.KaplanMeierEstimates,
title = "Kaplan-Meier Survival Curves (CoxPH Model : Survival ~ ECOG Score + Sex)",
pval = TRUE,
conf.int = TRUE,
conf.int.style = "ribbon",
xlab = "Time (Days)",
ylab="Estimated Survival Probability",
break.time.by = 100,
ggtheme = theme_bw(),
risk.table = "abs_pct",
risk.table.title="Number at Risk (Survival Probability)",
risk.table.y.text.col = FALSE,
risk.table.y.text = TRUE,
fontsize = 3,
ncensor.plot = FALSE,
surv.median.line = "hv",
legend.labs = c("Bedridden", "Ambulatory", "Asymptomatic"),
palette = c("#00CC66","#3259A0","#FF5050"))
ggpar(SurvivalTimeInWeek.KaplanMeier.MultivariateCoxPH.PhEcogSex.PhEcogAdjustedBySex,
font.title = c(14,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.legend=c(12),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"))
##################################
# Testing the proportional hazards assumption
# based on the scaled Schoenfield residuals
##################################
(DBP.Analysis.MultivariateCoxPH.PhEcogSex.PHAssumptionCheck <- cox.zph(DBP.Analysis.MultivariateCoxPH.PhEcogSex))## chisq df p
## ph.ecog 3.04 2 0.22
## sex 2.70 1 0.10
## GLOBAL 5.29 3 0.15##################################
# Formulating the graphical verification
# of the proportional hazards assumption test results
# using the scaled Schoenfeld residuals against time
##################################
(DBP.Analysis.MultivariateCoxPH.PhEcogSex.PHAssumptionPlot <- ggcoxzph(DBP.Analysis.MultivariateCoxPH.PhEcogSex.PHAssumptionCheck,
point.col = "red",
point.size = 2,
point.shape = 19,
point.alpha = 0.50,
ggtheme = theme_survminer(),
font.main = c(12,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black")))
##################################
# Formulating the graphical verification
# to evaluate potential influential observations
# using the deviance residuals against observations
##################################
ggcoxdiagnostics(DBP.Analysis.MultivariateCoxPH.PhEcogSex,
type = "deviance",
ox.scale = "observation.id",
point.col = "red",
point.size = 2,
point.shape = 19,
point.alpha = 0.50,
ggtheme = theme_survminer(),
font.main = c(12,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"),
main = "Deviance Residuals by Observation")
##################################
# Formulating the graphical verification
# to evaluate symmetry
# using the dfbeta residuals against observations
##################################
ggcoxdiagnostics(DBP.Analysis.MultivariateCoxPH.PhEcogSex,
type = "dfbeta",
ox.scale = "observation.id",
point.col = "red",
point.size = 2,
point.shape = 19,
point.alpha = 0.50,
ggtheme = theme_survminer(),
font.main = c(12,"bold"),
font.x = c(12,"bold"),
font.y = c(12,"bold"),
font.xtickslab=c(9,"black"),
font.ytickslab=c(9,"black"),
main = "Deviance Residuals by Observation")
##################################
# Formulating the graphical verification
# to evaluate linearity of the numeric covariate
# using the martingale residuals of the null cox proportional hazards model
# and the individual values of the numeric covariate
##################################
# No graphical verification proceeded
# due to the absence of a numeric covariate
# on the final selected model
3. References
[Book] Survival Analysis : A Self-Learning Text by David Kleinbaum and Mitchel Klein
[Book] Applied Survival Analysis Using R by Dirk Moore
[Book] R for Health Data Science by Ewen Harrison and Riinu Pius
[Book] Supervised Machine Learning by Michael Foley
[Book] Data Science for Biological, Medical and Health Research by Thomas Love
[R Package] moments by Lukasz Komsta and Frederick Novomestky
[R Package] car by John Fox and Sanford Weisberg
[R Package] multcomp by Torsten Hothorn, Frank Bretz and Peter Westfall
[R Package] effects by John Fox and Sanford Weisberg
[R Package] psych by William Revelle
[R Package] ggplot2 by Hadley Wickham
[R Package] dplyr by Hadley Wickham
[R Package] ggpubr by Alboukadel Kassambara
[R Package] rstatix by Alboukadel Kassambara
[R Package] ggfortify by Yuan Tang
[R Package] trend by Thorsten Pohlert
[R Package] survival by Terry Therneau
[R Package] rms by Frank Harrell
[R Package] survminer by Alboukadel Kassambara
[R Package] Hmisc by Frank Harrel
[R Package] finalfit by Ewen Harrison
[R Package] knitr by Yihui Xie
[R Package] gtsummary by Daniel Sjoberg
[Article] Survival Analysis by Alboukadel Kassambara
[Article] Survival Analysis in R by Emily Zabor
[Article] Survival Analysis with R by Joseph Rickert
[Article] Assessment of Discrimination in Survival Analysis by R-Studio Team
[Article] Cox Model Assumptions by Alboukadel Kassambara
[Publication] Regression Models and Life-Tables by David Cox (Royal Statistical Society)
[Publication] Evaluating the Yield of Medical Tests by Frank Harrell, Robert Califf, David Pryor, Kerry Lee and Robert Rosati (Journal of the American Medical Association)
[Publication] Survival Analysis Part I: Basic Concepts and First Analyses by Taane Clark (British Journal of Cancer)
[Publication] Survival Analysis Part II: Multivariate Data Analysis – An Introduction to Concepts and Methods by Mike Bradburn (British Journal of Cancer)
[Publication] Survival Analysis Part III: Multivariate Data Analysis – Choosing a Model and Assessing its Adequacy and Fit by Mike Bradburn (British Journal of Cancer)
[Publication] Survival Analysis Part IV: Further Concepts and Methods in Survival Analysis by Taane Clark (British Journal of Cancer)
[Tutorial] Survival Analysis / Time-To-Event Analysis in R by Heidi Seibold (Datacamp)