# Fit a relative risk survival tree for LTRC data `LTRCART` returns an rpart object. This function extends the survival tree algorithm in `rpart` to fit left-truncated and right censored (LTRC) data. ```r LTRCART( formula, data, weights = NULL, subset = NULL, no.SE = 0, control = rpart::rpart.control(cp = 0.001) ) ``` ## Arguments - `formula`: A formula object specifies the regression function, with the response be a Surv object, with form Surv(time1, time2, event) - `data`: An optional data frame which contains the variables named in the formula. - `weights`: Optional case weights, same as in `rpart` - `subset`: Optional expression saying that only a subset of the rows of the data should be used in the fit, same as in `rpart` - `no.SE`: Number of standard errors used in pruning, with default value 0. - `control`: A list of control values used to control the `rpart` algorithm, with default cp = 0.001. See rpart.control for details. ## Returns An object of class rpart. See rpart.object . ## Examples ```r ## The Assay of serum free light chain data in survival package ## Adjust data & clean data library(survival) library(LTRCtrees) Data <- flchain Data <- Data[!is.na(Data$creatinine),] Data$End <- Data$age + Data$futime/365 DATA <- Data[Data$End > Data$age,] names(DATA)[6] <- "FLC" ## Setup training set and test set Train = DATA[1:500,] Test = DATA[1000:1020,] ## Fit LTRCART survival tree ## make sure to attach survival package (by library(survival) ) before using Surv function LTRCART.obj <- LTRCART(Surv(age, End, death) ~ sex + FLC + creatinine, Train) ## Putting Surv(End, death) in formula would result an error message ## since LTRCART is expecting Surv(time1, time2, event) ## Plot the fitted tree library(rpart.plot) rpart.plot(LTRCART.obj) ## Plot as partykit::party object library(partykit) plot(as.party(LTRCART.obj)) ## Plot as partykit::party object with survival curves on terminal nodes LTRCART.obj.party <- as.party(LTRCART.obj) LTRCART.obj.party$fitted[["(response)"]]<- Surv(Train$age, Train$End, Train$death) plot(LTRCART.obj.party) ## Predict relative risk on test set LTRCART.pred <- predict(LTRCART.obj, newdata = Test) #################################################################### ####### Survival tree with time-varying covariates ################## #################################################################### ## The pbcseq dataset of survival package library(survival) ## Create the start-stop-event triplet needed for coxph and LTRC trees first <- with(pbcseq, c(TRUE, diff(id) !=0)) #first id for each subject last <- c(first[-1], TRUE) #last id time1 <- with(pbcseq, ifelse(first, 0, day)) time2 <- with(pbcseq, ifelse(last, futime, c(day[-1], 0))) event <- with(pbcseq, ifelse(last, status, 0)) event <- 1*(event==2) pbcseq$time1 <- time1 pbcseq$time2 <- time2 pbcseq$event <- event ## Fit the Cox model and LTRCART tree with time-varying covariates fit.cox <- coxph(Surv(time1, time2, event) ~ age + sex + log(bili), pbcseq) LTRCART.fit <- LTRCART(Surv(time1, time2, event) ~ age + sex + log(bili), pbcseq) rpart.plot(LTRCART.fit) ### transform the wide format data into long format data using tmerge function ### from survival function ## Stanford Heart Transplant data jasa$subject <- 1:nrow(jasa) tdata <- with(jasa, data.frame(subject = subject, futime= pmax(.5, fu.date - accept.dt), txtime= ifelse(tx.date== fu.date, (tx.date -accept.dt) -.5, (tx.date - accept.dt)), fustat = fustat)) sdata <- tmerge(jasa, tdata, id=subject,death = event(futime, fustat), trt = tdc(txtime), options= list(idname="subject")) sdata$age <- sdata$age - 48 sdata$year <- as.numeric(sdata$accept.dt - as.Date("1967-10-01"))/365.25 Cox.fit <- coxph(Surv(tstart, tstop, death) ~ age+ surgery, data= sdata) LTRCART.fit <- LTRCART(Surv(tstart, tstop, death) ~ age + transplant, data = sdata) rpart.plot(LTRCART.fit) ``` ## References Fu, W. and Simonoff, J.S. (2017). Survival trees for left-truncated and right-censored data, with application to time-varying covariate data. Biostatistics 18 (2), 352-369.

LTRCART function