OSTE {OSTE}

Optimal Survival Tree Ensemble

Description

Optimal survival trees ensemble is the main function of OSTE package that grows a sufficiently large number, t.initial, of survival trees and selects optimal survival trees from the total trees grown by random survival forest. Number of survival trees in the initial set, t.initial, is chosen by the user. If not chosen, then the default t.initial = 500 is used. Based on empirical investigation, t.initial =1000 is recommended.

Usage

OSTE(formula = NULL, data, t.initial = NULL, v.size = NULL, mtry = NULL, M = NULL,
minimum.node.size = NULL, always.split.features = NULL, replace = TRUE,
splitting.rule = NULL, info = TRUE)

Arguments

formula

Object of class formula describing the required model to be fitted. Interaction terms are not supported in the current version.

data

A nxd matrix or data frame of n observations on d features along with response variables that are described by the formula.

t.initial

Number of survival trees to be grown initially. If equal to NULL then the defalut of t.initial = 500 is taken. A recommended value is t.initial = 1000.

v.size

Portion of data used for validation in the second phase i.e. for assessing survival trees performance in the ensemble. If equal to NULL then the defalut v.size=0.1

mtry

Number of features selected at random at each node of the survival trees for splitting. If equal to NULL then the default sqrt(d) is taken.

M

Percent of the best t.initial survival trees to be selected on the basis of their performance on out-of-bag observations. For selecting 20% of trees, take M=0.2.

minimum.node.size

Minimal node size. If equal to NULL then the default minimum.node.size = 3 is executed.

always.split.features

Vector of variable names if desired to be always selected in addition to the mtry variables tried for splitting.

replace

Whether sampling should be done with or without replacement.

splitting.rule

Splitting rule."logrank", "C" or "maxstat" are suported with default "logrank".

info

If TRUE, displays process status .

Details

Large values are recommended for t.initial for better performance as possible under the available computational resources. The log-rank test statistic is used as defalut, A C-index based splitting rule (Schmid et al. 2015) and maximally selected rank statistics (Wright et al. 2016) are available. The C-index shows better predictive performance in case of high censoring rate, where logrank is best for situations where the data are noisy (Schmid et al. 2015).

Value

unique.death.times

Unique death times.

CHF

Estimated cumulative hazard function for each observation.

Survival_Prob

Estimated survival probability for each observation.

trees_selected

Number of trees selected.

mtry

Value of mtry used.

forest

Saved forest for prediction purposes.

Note

In the case of missing values in any dataset prior action needs to be taken as the fuction can not handle them at the current version. Moreover, the status/delta variable in the data must be code as 0, 1.

Author(s)

Naz Gul, Nosheen Faiz, Zardad Khan and Berthold Lausen.

References

Marvin N. Wright, Andreas Ziegler (2017). ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R. Journal of Statistical Software, 77(1), 1-17. doi:10.18637/jss.v077.i01

Terry Therneau, Beth Atkinson and Brian Ripley (2015) rpart: Recursive Partitioning and Regression Trees. R package version 4.1-10. https://CRAN.R-project.org/package=rpart

Ulla B. Mogensen, Hemant Ishwaran, Thomas A. Gerds (2012). Evaluating Random Forests for Survival Analysis Using Prediction Error Curves. Journal of Statistical Software, 50(11), 1-23. URL http://www.jstatsoft.org/v50/i11/.

Schmid, M., Wright, M. N. & Ziegler, A. (2016). On the use of Harrell's C for clinical risk prediction via random survival forests. Expert Syst Appl 63:450-459. http://dx.doi.org/10.1016/j.eswa.2016.07.018.

Wright, M. N., Dankowski, T. & Ziegler, A. (2017). Unbiased split variable selection for random survival forests using maximally selected rank statistics. Stat Med. http://dx.doi.org/10.1002/sim.7212.

Zardad Khan, Asma Gul, Aris Perperoglou, Osama Mahmoud, Werner Adler, Miftahuddin and Berthold Lausen (2015). OTE: Optimal Trees Ensembles for Regression, Classification and Class Membership Probability Estimation. R package version 1.0. https://CRAN.R-project.org/package=OTE

Gul, N., Faiz, N., Brawn, D., Kulakowski, R., Khan, Z., & Lausen, B. (2020). Optimal survival trees ensemble. arXiv preprint arXiv:2005.09043.

See Also

VETERAN

Examples

#Load the data
data(VETERAN)
library(survival)
library(prodlim)
library(ranger)
library(pec)
#Divide the data into training and test parts



 predictSurvProb.ranger <- function (object, newdata, times, ...) {

    ptemp <- ranger:::predict.ranger(object, data = newdata, importance = "none")$survival
    pos <- sindex(jump.times = object$unique.death.times,
                           eval.times = times)
    p <- cbind(1, ptemp)[, pos + 1, drop = FALSE]
    if (NROW(p) != NROW(newdata) || NCOL(p) != length(times))
      stop(paste("\nPrediction matrix has wrong dimensions:\nRequested newdata x times: ",
                 NROW(dts[trainind,]), " x ", length(1), "\nProvided prediction matrix: ",
                 NROW(p), " x ", NCOL(p), "\n\n", sep = ""))
    p
  }

n <- nrow(VETERAN)
trainind <- sample(1:n,n*0.7)
testind <- (1:n)[-trainind]

# Grow OSTE on the training data

OSTE.fit <- OSTE(Surv(time,status)~.,data=VETERAN[trainind,],t.initial=100)

# Predict on the test data

pred <- ranger:::predict.ranger(OSTE.fit$forest,data=VETERAN[testind,])

# Index various values

pred$survival
pred$survival

#etc.

# To calculate IBS
# Create formula
frm <- as.formula(Surv(time, status) ~ trt + celltype + karno + diagtime + age + prior)

PredError <- pec(object=OSTE.fit$forest, exact==TRUE,
                   formula = frm, cens.model="marginal",
                   data=VETERAN[testind,], verbose=F)
IBS <- crps(object = PredError, times =100, start = PredError$start)[2,1]
IBS