# [R] Competing risks Kalbfleisch & Prentice method

Eleni Rapsomaniki er339 at medschl.cam.ac.uk
Thu Mar 26 18:17:16 CET 2009

```Ravi,

I agree with you, that the Fine & Gray method does much more than
calculating the cumulative incidence. The Kalbfleisch & Prentice formula
relies on the strong assumption that the coefficients for the cause
specific hazard models are valid in the presence of competing risks. You
will find my code below, but it may be wrong (I'm not really a
statistician!). And no, it doesn't even calculate confidence
intervals...

Thank you for pointing out these papers.
Please let me know (nicely) if you find bugs!!!

#####
#Method to calculate Cumulative Incidence adjusting for competing risks,
based on the Kalbfleisch & Prentice formula, 1980, p.169
#create data
ftime <- rexp(200, 0.3)
fstatus <- sample(0:2,200,replace=TRUE)
cov <- matrix(runif(600),nrow=200)
dimnames(cov)[[2]] <- c('x1','x2','x3')
dat=data.frame(ftime, fstatus, cov)

diffrHaz=function(x){
hazard=x\$hazard
time=x\$time

hz.v=NULL

for(e in 1:(length(hazard)-1)){
hz=hazard[e+1]-hazard[e]
hz.v=c(hz.v,hz)
}
dhz=data.frame(hazard=hz.v, time=x\$time[-length(x\$time)])
return(dhz)
}

#build cause specific cox models
library(Design)
a.f=cph(Surv(ftime, fstatus==1) ~ x1+x2+x3, data=dat, surv=T, x=T, y=T)
b.f=cph(Surv(ftime, fstatus==2) ~ x1+x2+x3, data=dat, surv=T, x=T, y=T)

#get unique event times - up till the time of interest, eg. time=10
uts=unique(dat\$ftime[dat\$fstatus>0] )
uts=uts[uts<=10]  # the times up till 10 years
uts=uts[order(uts)]  #order them

#get baseline hazard rate (cumulative)
a.bz=basehaz(a.f)
b.bz=basehaz(b.f)

#get instanteneous baseline hazard rate, apply above function
a.dhz1=diffrHaz(a.bz)
b.dhz1=diffrHaz(b.bz)

P.t=NULL #intitialize where to store all results
for(i in 1:nrow(dat)){  # i is the individual, iterate through the
number of rows in dat
P.i.t=NULL
all.lambda.i.t=NULL

for(u.i in 1:length(uts)){
u=uts[u.i]
#get the instanteneous baseline hazard from each model
corresponding to this timepoint (if there is no event at that time
return 0)
a.dhz.u=ifelse((u %in%
a.dhz1\$time)==F,0,a.dhz1\$hazard[a.dhz1\$time==u])
b.dhz.u=ifelse((u %in%
b.dhz1\$time)==F,0,b.dhz1\$hazard[b.dhz1\$time==u])

#multiply by the linear predictors to get the actual hazard at
that point
a.lambda.i.u=a.dhz.u*exp(a.f\$linear.predictors[i])
b.lambda.i.u=b.dhz.u*exp(b.f\$linear.predictors[i])
all.lambda.i.u=a.lambda.i.u+b.lambda.i.u
#store in a vector
all.lambda.i.t=c(all.lambda.i.t, all.lambda.i.u) #build a vector
with all previous all.lambda.i.u's
S.i.u=exp(-sum(all.lambda.i.t))     #this is the probability of
surviving till time u

p.i.u=S.i.u*a.lambda.i.u

P.i.t=c(P.i.t, p.i.u)

}
P.t[i]=sum(P.i.t)
}

a.risk   = 1-survest(a.f, linear.predictors=a.f\$linear.predictors,
times=10)\$surv
plot(a.risk ~ P.t) #P.t is the CR adjusted, should always be lower
mean(a.risk)
mean(P.t)

Eleni Rapsomaniki

Research Associate
Tel:     +44 (0) 1223 740273
Strangeways Research Laboratory
Department of Public Health and Primary Care
University of Cambridge

-----Original Message-----
Sent: 26 March 2009 14:36
To: Eleni Rapsomaniki; 'Arthur Allignol'
Cc: r-help at r-project.org
Subject: RE: [R] Competing risks Kalbfleisch & Prentice method

Hi Eleni,

I would like to take a look at your R function for obtaining the
cumulative
incidence function (CIF) from individual Cox models for cause-specific
hazards (CSH).  Does your code predict the CIF (with pointwise
confidence
intervals and global confidence bands) for different sub-groups?  Have
you
seen the paper by Cheng, Fine, and Wei (Biometrics 1998) that does this?

A major advantage of the F&G model is that you can get a direct,
numerical
measure of the effect of a covariate on the CIF.  This cannot be
obtained by
modeling all the CSHs and then combining them.  The idiosyncratic
assumption
concerning risk set in F&G model is made mainly for mathematical
purposes so
that a proportional hazards form may be obtained for the CIF.  You can
test
this assumption by plotting schonefeld-type residuals (this is available
in
cmprsk).  Fine (Biostatistics 2006) provides a different approach that
relaxes this assumption (it also uses a different estimation approach),
but
I don't know if there is an R implementation for that.

Thanks,
Ravi.

------------------------------------------------------------------------
----
-------

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Webpage:

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--------

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
Behalf Of Eleni Rapsomaniki
Sent: Thursday, March 26, 2009 10:18 AM
To: Arthur Allignol
Cc: r-help at r-project.org
Subject: Re: [R] Competing risks Kalbfleisch & Prentice method

It wasn't too hard to code actually, which is probably why it doesn't
have a
special package dedicated to it. The results are almost identical to
Fine &
Gray regression model. The problem with the latter is that my colleagues
are
not convinced that the model assumptions (people who die from competing
causes remaining in the risk set) are theoretically sound.

If anybody is interested in the Kalbfleisch & Prentice based cumulative
incidence adjusting for competing risks with covariates, I'm happy to
supply
the code.

Eleni Rapsomaniki

Research Associate
Tel:     +44 (0) 1223 740273
Strangeways Research Laboratory
Department of Public Health and Primary Care University of Cambridge

-----Original Message-----
From: Arthur Allignol [mailto:arthur.allignol at fdm.uni-freiburg.de]
Sent: 26 March 2009 10:36
To: Eleni Rapsomaniki
Cc: r-help at r-project.org
Subject: Re: [R] Competing risks Kalbfleisch & Prentice method

I don't think there is a package to do that.

But you could have a look at ?predict.crr.

Best regards,
Arthur Allignol

Eleni Rapsomaniki wrote:
>
>
> Dear R users
>
>
>
> I would like to calculate the Cumulative incidence for an event
> adjusting for competing risks and adjusting for covariates. One way to

> do this in R is to use the cmprsk package, function crr. This uses the

> Fine & Gray regression model. However, a simpler and more classical
> approach would be to implement the Kalbfleisch & Prentice method
(1980,
> p 169), where one fits cause specific cox models for the event of
> interest and each type of competing risk, and then calculates
incidence
> based on the overall survival.  I believe that this is what the cuminc

> function in the aforementioned package does, but it does not allow to
> adjust for a vector of covariates.
>
>
>
> My question is, is there an R package that implements the Kalbfleisch
&
> Prentice method for competing risks with covariates?
>
>
>
> for example, if k1 is the cause of interest among k competing causes:
>
> P_k1(t; x)=P(T<=t, cause=k1|x)=Sum(u=0, ..., u=t)
{hazard_k(u;x)*S(u;x)}
>
> where S(u;x) = exp{-sum_of_k(sum(hazard_k(u))}
>
>
>
> I have searched extensively for an implementation of this in many
> packages, but it appears that more complex approaches are more
commonly
> implemented, such as timereg package.
>
>
>
> Eleni Rapsomaniki
>
>
>
> Research Associate
>
> Strangeways Research Laboratory
>
> Department of Public Health and Primary Care
>
>
>
> University of Cambridge
>
>
>
>
>
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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