Just as the random forest algorithm may be applied to regression and classification tasks, it can also be extended to survival analysis.

In the example below a survival model is fit and used for prediction, scoring, and performance analysis using the package randomForestSRC from CRAN.

require(randomForestSRC)

set.seed(130948) #Other seeds give similar comparative results
x1   <- runif(1000)
y    <- rnorm(1000, mean = x1, sd = .3)
data <- data.frame(x1 = x1, y = y)
head(data)

         x1          y
1 0.9604353  1.3549648
2 0.3771234  0.2961592
3 0.7844242  0.6942191
4 0.9860443  1.5348900
5 0.1942237  0.4629535
6 0.7442532 -0.0672639

(modRFSRC <- rfsrc(y ~ x1, data = data, ntree=500, nodesize = 5))

                             Sample size: 1000
                     Number of trees: 500
          Minimum terminal node size: 5
       Average no. of terminal nodes: 208.258
No. of variables tried at each split: 1
              Total no. of variables: 1
                            Analysis: RF-R
                              Family: regr
                      Splitting rule: mse
                % variance explained: 32.08
                          Error rate: 0.11

x1new   <- runif(10000)
ynew    <- rnorm(10000, mean = x1new, sd = .3)
newdata <- data.frame(x1 = x1new, y = ynew)

survival.results <- predict(modRFSRC, newdata = newdata)
survival.results

  Sample size of test (predict) data: 10000
                Number of grow trees: 500
  Average no. of grow terminal nodes: 208.258
         Total no. of grow variables: 1
                            Analysis: RF-R
                              Family: regr
                % variance explained: 34.97
                 Test set error rate: 0.11

survival is the most commonly used package for survival analysis in R. Using the built-in lung dataset we can get started with Survival Analysis by fitting a regression model with the survreg() function, creating a curve with survfit(), and plotting predicted survival curves by calling the predict method for this package with new data.

In the example below we plot 2 predicted curves and vary sex between the 2 sets of new data, to visualize its effect:

require(survival)
s <- with(lung,Surv(time,status))

sWei  <- survreg(s ~ as.factor(sex)+age+ph.ecog+wt.loss+ph.karno,dist='weibull',data=lung)

fitKM <- survfit(s ~ sex,data=lung)
plot(fitKM)

lines(predict(sWei, newdata = list(sex      = 1, 
                                   age      = 1, 
                                   ph.ecog  = 1, 
                                   ph.karno = 90,
                                   wt.loss  = 2),
                                 type = "quantile",
                                 p    = seq(.01, .99, by = .01)),
                                 seq(.99, .01, by        =-.01),
                                 col = "blue")

lines(predict(sWei, newdata = list(sex      = 2, 
                                   age      = 1, 
                                   ph.ecog  = 1, 
                                   ph.karno = 90,
                                   wt.loss  = 2),
                                 type = "quantile",
                                 p    = seq(.01, .99, by = .01)),
                                 seq(.99, .01, by        =-.01),
                                 col = "red")

Base plot

install.packages('survminer')
source("https://bioconductor.org/biocLite.R")
biocLite("RTCGA.clinical") # data for examples
library(RTCGA.clinical)
survivalTCGA(BRCA.clinical, OV.clinical,
             extract.cols = "admin.disease_code") -> BRCAOV.survInfo
library(survival)
fit <- survfit(Surv(times, patient.vital_status) ~ admin.disease_code,
               data = BRCAOV.survInfo)
library(survminer)
ggsurvplot(fit, risk.table = TRUE)

More advanced

ggsurvplot(
   fit,                     # survfit object with calculated statistics.
   risk.table = TRUE,       # show risk table.
   pval = TRUE,             # show p-value of log-rank test.
   conf.int = TRUE,         # show confidence intervals for 
                            # point estimaes of survival curves.
   xlim = c(0,2000),        # present narrower X axis, but not affect
                            # survival estimates.
   break.time.by = 500,     # break X axis in time intervals by 500.
   ggtheme = theme_RTCGA(), # customize plot and risk table with a theme.
 risk.table.y.text.col = T, # colour risk table text annotations.
  risk.table.y.text = FALSE # show bars instead of names in text annotations
                            # in legend of risk table
)

Based on

http://r-addict.com/2016/05/23/Informative-Survival-Plots.html