# # Survival analysis

## # Random Forest Survival Analysis with randomForestSRC

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
```

## # Introduction - basic fitting and plotting of parametric survival models with the survival package

`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")
```

## # Kaplan Meier estimates of survival curves and risk set tables with survminer

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