# Survival trees with competing risk

I'm looking for a way to fit survival trees with competing risk.

Can I use the function LTRCART in the LTRCtrees package in R to fit a survival tree using the dataset obtained from the finegray function in survival R package.

Here a reproducible example using mgus2 data in survival package:

library(survival)
data("mgus2")

etime <- with(mgus2, ifelse(pstat==0, futime, ptime))
event <- with(mgus2, ifelse(pstat==0, 2*death, 1))
event <- factor(event, 0:2, labels=c("censor", "pcm", "death"))

ds_finegray <- finegray(Surv(etime, event) ~  age + sex + mspike,
data = mgus2, etype = "pcm")

library(LTRCtrees)

survTree_LTRC <- LTRCART(Surv(fgstart,fgstop, fgstatus) ~ age + sex + mspike,
data = ds_finegray, weights = ds_finegray$fgweights) survTree_LTRC library(partykit) survTree_LTRC_party <- as.party(survTree_LTRC) survTree_LTRC_party$fitted[["(response)"]] <-
Surv(ds_finegray$fgstart, ds_finegray$fgstop, ds_finegray\$fgstatus)
plot(survTree_LTRC_party)


A shown in the example there are no issues with the R programming. My question is about the consistency of the split method used in the rpartfunction. This uses a splitting criterion based on a node deviance measure between a saturated model log–likelihood and a maximized log–likelihood, approximating the full likelihood by replacing the baseline cumulative hazard function by the Nelson–Aalen estimator (8.4 section in rpart vignette).

Since finegray applies a Fine-Gray model to competing risk (multi-state) data, giving as result a dataset with interval censoring time and weights <1 for observations with competing events, I'm not able to understand whether the assumption made by the rpart routine are still valid for this kind of data.

• There is a risk this might be closed as off-topic as you seem to be asking for R help. There does seem to be a possible statistical issue here about fitting trees when you have competing risks - is it possible? Perhaps edit your question to stress the statistical part? – mdewey Nov 22 '17 at 12:51
• I submitted a question on this topic in asked this question at r-help@r-project.org (see R-help Digest, Vol 182, Issue 25) on April 25 2018: "Dear all, I'm interested in fitting survival trees with competing risk analysis. The tree should show the cumulative incidence function for each terminal node I read several paper illustrating this possibility, but to the best of my knowledge no R code are reported. There is any R package for this fit? Thank you very much in advance." However, at this time the query remained unanswered. Any progress on this interesting topic? Mario Petretta – Mario Petretta May 14 '18 at 16:09