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rsurvival-analysiscox-regressionsurvivalhazard
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Reputation: 31

Cox regression model with a time-dependent covariate, in R

I want to study which variables are possible risk factors for the non-relapse mortality event variable in a sample of patients with a hematologic disease that received a stem cell transplant. I have created, first, univariate models with the different variables in order to study the effect separately and, after it, I have included the ones with a p value <= 0.20 in a multivariate cox regression model.

I have studied the residuals of the variables to check for the proportional hazard assumption. I have seen that for chronic GVHD variable the residuals follow a pattern and this is why I decided to consider this variable as time-dependent covariate.

Here the code used, in R, and the plots of the residuals for chronic GVHD:

install.packages(“survival”)
library(survival)

# EICRc: chronic GVHD variable 
# TRM: non-relapse mortality (a dummy variable where 1 represents the event)
# T_seguimiento: time until the event (in months)

# here the univariate cox regression model, with the EICRc variable as non-time-dependent variable.
TRM_cGVHD <- coxph(Surv(T_seguimiento, TRM) ~ EICRc, data = dat)
test.ph <- cox.zph(TRM_cGVHD)
test.ph

# I check for the proportional hazard assumption:
plot(test.ph)

enter image description here

I can see that residuals follow a pattern, are not randomly distributed, and for this reason I decided to create a cox regression model with EICRc as a time-dependent covariate. Here the code:

##I use the tt() function of the survival package:

dat$EICRc <- relevel(as.factor(dat$EICRc), ref = "no")
TRM_cGVHD <- coxph(Surv(T_seguimiento, TRM) ~ tt(EICRc), data = dat)  
summary(TRM_cGVHD)

Call:
coxph(formula = Surv(T_seguimiento, TRM) ~ EICRc, data = dat)

  n= 226, number of events= 40 
   (1 observation deleted due to missingness)

           coef exp(coef) se(coef)     z Pr(>|z|)   
EICRcsi -0.8917    0.4100   0.3416 -2.61  0.00905 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

        exp(coef) exp(-coef) lower .95 upper .95
EICRcsi      0.41      2.439    0.2099    0.8008

Concordance= 0.651  (se = 0.028 )
Likelihood ratio test= 7.14  on 1 df,   p=0.008
Wald test            = 6.81  on 1 df,   p=0.009
Score (logrank) test = 7.19  on 1 df,   p=0.007

I want to know if I have created the time-dependent cox regression model correctly and which would be the possibles causes of this result. Chronic GVHD should be a risk factor for non-relapse mortality, but nevertheless, this result shows that is a favorable factor (HR= 0.41, pvalue <0.001).

Can someone help me?

Thank you very much :)

EI_Stats

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