# R: [R] time dependency of Cox regression

Vito Muggeo vito.muggeo at giustizia.it
Wed Nov 3 10:02:16 CET 2004

```Hi,
in order to fit Cox model with time-dependent coeff, you have to restruct
can use the counting process formulation "(start,stop,status)".
Some years ago I wrote a function (reCox() below) to make the job. It seems
to work if there are not ties, but
if there are ties it works but some problem rises (results do not match
exactly). Let me know if you can fix such problem.

Note that in the restructed dataset, a (linear) time varying effect for the
variable X, say, may be included by the "X:stop" term in the model.

Hope this helps,
regards,
vito

#example taken from ?cph in the Hmisc package
n <- 100
set.seed(731)
age <- 50 + 12*rnorm(n)
sex <- factor(sample(c('Male','Female'), n,rep=TRUE, prob=c(.6, .4)))
cens <- 15*runif(n)
h <- .02*exp(.04*(age-50)+.8*(sex=='Female'))
ttime <- -log(runif(n))/h
status <- ifelse(ttime <= cens,1,0)
ttime <- pmin(ttime, cens)
d<-data.frame(ttime=ttime,status=status,age=age,sex=sex)
#restruct the original dataframe
dd<-reCox(d)
#compare fitted model without ties (minor (negligible?) differences)
coxph(Surv(ttime,status) ~ age + sex,data=d)
coxph(Surv(start,stop,status) ~ age + sex,data=dd)

#data with ties (major differences)
d\$ttime[d\$status==1]<-round(d\$ttime[d\$status==1],1)
dd<-reCox(d,k=1:2,epss=0.01) #here you have to specify epss>0 to allow
coxph() to work
coxph(Surv(ttime,status) ~ age + sex,data=d)
coxph(Surv(start,stop,status) ~ age + sex,data=dd)

reCox<-function(data,k=1:2,epss=0){
#FUNZIONA SOLO SE NON CI SONO TIES :-(
#(Preliminary) function to reshape dataframe according to the
"counting-process" formulation
#       author: <vito.muggeo at giustizia.it>
#data: the data-frame to be transformed
#k: indices of SurvTime and Status variables in data
#epss: if for any new record start==stop, then stop is incremented by epss
if(ncol(data)<=3) data[,"tmp"]<-rep(99,nrow(data))
dati<-data[order(data[,k]),] #order(unique(surv.time))#???
status<-dati[,k]
b<-dati[,-k]
dati[,"start"]<-rep(0,nrow(dati))
names(dati)[k]<-"stop"
n<-nrow(dati)
a<-matrix(-99,(n*(n-1)/2+n),3)
a[1,]<-c(1,as.numeric(as.matrix(dati)[1,c("start","stop")]))
colnames(a)<-c('id.new','start','stop')
a[,"id.new"]<-rep(1:n,1:n)
for(i in 2:nrow(dati)){

a[a[,1]==i,-1]<-rbind(a[a[,1]==(i-1),2:3],c(dati[(i-1),"stop"],dati[i,"stop"
]))
}
a<-cbind(a,status=rep(0,nrow(a)))
a[cumsum(1:n),"status"]<-status
bb<-sapply(b,function(x)rep(x,1:n))#le categorie le trasforma in
numeri....
#bb<-lapply(b,function(x)rep(x,1:n))
#bb<-apply(b,2,function(x)rep(x,1:n))NO!!!
A<-data.frame(cbind(a,bb),row.names=NULL)
#if(!missing(epss))
A[,"stop"]<-A[,"stop"]+ifelse(A[,"stop"]==A[,"start"],epss,0)
if(epss>0)
A[,"stop"]<-A[,"stop"]+ifelse(A[,"stop"]==A[,"start"],epss,0)
A\$tmp<-NULL
return(A)
}

----- Original Message -----
From: array chip <arrayprofile at yahoo.com>
To: <R-help at stat.math.ethz.ch>
Sent: Wednesday, November 03, 2004 12:41 AM
Subject: [R] time dependency of Cox regression

> Hi,
>
> How can I specify a Cox proportional hazards model
> with a covariate which i believe its strength on
> survival changes/diminishes with time? The value of
> the covariate was only recorded once at the beginning
> of the study for each individual (e.g. at the
> diagnosis of the disease), so I do not have the time
> course data of the covariate for any given individual.
> For example, I want to state at the end of the
> analysis that the hazard ratio of the covariate is 6
> at the beginning, decrease to 3 after 2 years and
> decrease to 1.5 after 5 years.
>
> Is this co-called time-dependent covariate? I guess
> not, because it's really about the influence of the
> covariate (which was measured once at the beginning)
> on survival changing over time.
>
> Thanks for any input.
>
>
>
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