Cox model, coxph(), control treatment with no event, seed germination - r

Question

I am performing survival analysis and I´m not sure if I am doing it correctly. My dataset is a result of a seed germination experiment. The main variable of interest is the "treat" one (categorical with 3 levels). In my script I am trying to figure out if there is a difference in between treatments, which one is the best, and at what extent, by comparing the PH coeff percentages. Could anyone help me with some of the problems that I'm dealing with?
1) Do I need to declare my variables as.factor() to use them? Or integer is interpreted equally?
2) If proportionality of hazards assumption (PH) is violated, what should I do with my data to proceed to a cox model building? I've intensely researched but haven't been able to understand the programming to add covariate*time interaction
or stratification to my model.
3) How to include frailty terms to cox model and detect random effect (e.g. plate in which seeds were germinated, categorical variable with 4 levels, representing repetition).
4) I also wasn't able to interpret the print(summary(cox.fra)).*
*see below
See below my two whole scripts with comments.
SCRIPT 1
rd01 <- read.table("sa_kb01.txt", header = T) # raw dataset, seed
survival
rd01
str(rd01)
rd01$begin <- as.factor(rd01$begin) # integers to factors
rd01$spp <- as.factor(rd01$spp)
rd01$cit <- as.factor(rd01$cit)
rd01$treat <- as.factor(rd01$treat)
rd01$plate <- as.factor(rd01$plate)
str(rd01)
summary(rd01)
names(rd01) # headers
### Survival analysis
# install.packages("survival")
library(survival)
library (survminer)
?survfit
?survfit.formula
?survfit.coxph
?ggsurvplot
## Fit Kaplan-Meier survivor function
km.fit <- survfit(Surv(day, status) ~ treat, data= rd01, type="kaplan-meier")
km.fit
print(summary(km.fit))
plot(km.fit, conf.int= T, fun = "event", mark.time = c(140), pch = c("S", "W", "A"), col = c("darkred","darkblue","darkgreen"), lty = c("solid","dotted","longdash"),lwd = 1.5, xlab = "time [days]", ylab = "germination probability [%]")
print(summary(km.fit))
## Comparison of Survivor Functions
# Log-rank tests
?survdiff
# Log-rank or Mantel-Haenszel test in "rho = 0" OR
# Peto & Peto modification of the Gehan-Wilcoxon test in "rho = 1"
# ... Assess all groups for heterogeneity
lrmh.123 <- survdiff(Surv(day,status) ~ treat, data= rd01, rho= 0)
print(lrmh.123) # If p<0.05 there are difference between all groups!
# ... Comparing groups pairwise
lrmh.120 <- survdiff(Surv(day,status) ~ treat, data= rd01, subset= {treat!=3}, rho= 0)
lrmh.103 <- survdiff(Surv(day,status) ~ treat, data= rd01, subset= {treat!=2}, rho= 0)
lrmh.023 <- survdiff(Surv(day,status) ~ treat, data= rd01, subset= {treat!=1}, rho= 0)
print(lrmh.120)
print(lrmh.103)
print(lrmh.023) # If p<0.05 there are difference pairwised groups!
## Checking Proportional Hazard (PH) assumption
# Define function mlogmlog() to calculate -log(-log(S(t)))
mlogmlog <- function(y){-log(-log(y))}
# Use estimated Kaplan-Meier survivor functions
km.fit
# ... to plot -log(-log(S(t))) versus log(t)
plot(km.fit, fun= mlogmlog, log="x", mark.time= c(140), pch = c("S", "W", "A"), col = c("darkred","darkblue","darkgreen"), lty = c("solid","dotted","longdash"), lwd = 1.5, xlab="time [days]", ylab= "-log(-log(S(t)))") # If lines do not cross, PH assumption is plausible!
# Interpretarion: http://www.sthda.com/english/wiki/cox-model-assumptions#testing-proportional-hazards-assumption
## Checking for multicollinearity
# install.packages("HH")
library(HH)
# Fit a generalized linear model predicting days from treatment
?glm
mc.glm <- glm(day ~ treat, data=rd01)
print(mc.glm) # doesn't need interpretation, only used to create object to VIF function
# Check for multicollinearity among covariates throught variance inflation factor (VIF)
?vif
mc.vif <- vif(mc.glm)
print(mc.vif) # VIF can determine what proportion of the variation in each covariate
# is explained by the other covariates:
# VIF > 10, serious multicollinearity; VIF = 5, evidence of multicollinearity;
# VIF < 1, no evidence of multicollinearity
## Adding covariates to the Cox model
# Create a Cox model
cox.mod <- coxph(Surv(day, status) ~ treat, data= rd01)
print(summary(cox.mod))
# Interpretation: http://www.sthda.com/english/wiki/cox-proportional-hazards-model
# Double check for PH assumption now with Cox model built
dc.ph <- cox.zph(cox.mod)
dc.ph
ggcoxzph(dc.ph) # if global and individual p-vale > 0.05, PH assumption is plausible!
## Including random effects
?frailty
# Adding plate variable as frailty term
cox.fra <- coxph(Surv(day, status) ~ treat + frailty(plate), data= rd01)
print(summary(cox.fra)) # if global and individual p-vale < 0.05,
# maintain frailty term while adding covariates 1 at a time in cox model!`
SCRIPT 2 - the same, but different dataset, control treat1 with no event!
rd01 <- read.table("sa_hal01.txt", header = T) # raw dataset, seed survival
rd01
str(rd01)
rd01$begin <- as.factor(rd01$begin) # integers to factors
rd01$spp <- as.factor(rd01$spp)
rd01$cit <- as.factor(rd01$cit)
rd01$treat <- as.factor(rd01$treat)
rd01$plate <- as.factor(rd01$plate)
str(rd01)
summary(rd01)
names(rd01) # headers
### Survival analysis
# install.packages("survival")
library(survival)
library (survminer)
?survfit
?survfit.formula
?survfit.coxph
?ggsurvplot
## Fit Kaplan-Meier survivor function
km.fit <- survfit(Surv(day, status) ~ treat, data= rd01, type="kaplan-meier")
km.fit
print(summary(km.fit))
plot(km.fit, conf.int= T, fun = "event", mark.time = c(140), pch = c("S", "W", "A"), col = c("darkred","darkblue","darkgreen"), lty = c("solid","dotted","longdash"),lwd = 1.5, xlab = "time [days]", ylab = "germination probability [%]")
print(summary(km.fit))
## Comparison of Survivor Functions
# Log-rank tests
?survdiff
# Log-rank or Mantel-Haenszel test in "rho = 0" OR
# Peto & Peto modification of the Gehan-Wilcoxon test in "rho = 1"
# ... Assess all groups for heterogeneity
lrmh.123 <- survdiff(Surv(day,status) ~ treat, data= rd01, rho= 0)
print(lrmh.123) # If p<0.05 there are difference between all groups!
# ... Comparing groups pairwise
lrmh.120 <- survdiff(Surv(day,status) ~ treat, data= rd01, subset= {treat!=3}, rho= 0)
lrmh.103 <- survdiff(Surv(day,status) ~ treat, data= rd01, subset= {treat!=2}, rho= 0)
lrmh.023 <- survdiff(Surv(day,status) ~ treat, data= rd01, subset= {treat!=1}, rho= 0)
print(lrmh.120)
print(lrmh.103)
print(lrmh.023) # If p<0.05 there are difference pairwised groups!
## Checking Proportional Hazard (PH) assumption
# Define function mlogmlog() to calculate -log(-log(S(t)))
mlogmlog <- function(y){-log(-log(y))}
# Use estimated Kaplan-Meier survivor functions
km.fit
# ... to plot -log(-log(S(t))) versus log(t)
plot(km.fit, fun= mlogmlog, log="x", mark.time= c(140), pch = c("S", "W", "A"), col = c("darkred","darkblue","darkgreen"), lty = c("solid","dotted","longdash"), lwd = 1.5, xlab="time [days]", ylab= "- log(-log(S(t)))") # If lines do not cross, PH assumption is plausible!
# Interpretarion: http://www.sthda.com/english/wiki/cox-model- assumptions#testing-proportional-hazards-assumption
## Checking for multicollinearity
# install.packages("HH")
library(HH)
# Fit a generalized linear model predicting days from treatment
?glm
mc.glm <- glm(day ~ treat, data=rd01)
print(mc.glm) # doesn't need interpretation, only used to create object to VIF function
# Check for multicollinearity among covariates throught variance inflation factor (VIF)
?vif
mc.vif <- vif(mc.glm)
print(mc.vif) # VIF can determine what proportion of the variation in each covariate
# is explained by the other covariates:
# VIF > 10, serious multicollinearity; VIF = 5, evidence of multicollinearity;
# VIF < 1, no evidence of multicollinearity
## Adding covariates to the Cox model
# Create a Cox model
cox.mod <- coxph(Surv(day, status) ~ treat, data= rd01)
print(summary(cox.mod))
# Interpretation: http://www.sthda.com/english/wiki/cox-proportional-hazards-model
# Double check for PH assumption now with Cox model built
dc.ph <- cox.zph(cox.mod)
dc.ph
ggcoxzph(dc.ph) # if global and individual p-vale > 0.05, PH assumption is plausible!
## Including random effects
?frailty
# Adding plate variable as frailty term
cox.fra <- coxph(Surv(day, status) ~ treat + frailty(plate), data= rd01)
print(summary(cox.fra)) # if global and individual p-vale < 0.05,
# maintain frailty term while adding covariates 1 at a time in cox model!
There seems to be a statistically significant difference and treat3 differs from the other groups in both scripts. In script 1 PH is violated and I don´t now what to do. Apart from that, Cox model in script 1 seems to work fine and the interpretation of hazard ratios are OK, but in script 2, no idea how to interpret or solve that (there was no event in control treat1).

Answer 1

1) Do I need to declare my variables as.factor() to use them? Or integer is interpreted equally?
I think in your case as.factor is correct. You can use integers if you have continuous numeric variables - for example if you would have time seeds have been stored before the experiment, you could use as.numeric for time variable.
2) If PH is violated, what should I do with my data to proceed to a cox model building? I've intensely researched but haven't been able to understand the programming to add covariate x time interaction or stratification to my model.
Cox regression, aka Cox proportional hazards model, is based on the assumption of proportional hazards. If that assumption is violated, you won´t get reliable results. You probably could try some data transformations to see if it would help. Or if it is violated in some subexperiment/group, you could just leave it out.