Fitting ROC-guided ensemble in rocTree package

Sy Han (Steven) Chiou

2020-01-24

Source: vignettes/rocTree-ensemble.Rmd

In this vignette, we demonstrate how to use the rocTree() function in rocTree package to fit the ensemble method.

Simulated data

We will demonstrate fitting ensembles with a simulated data prepared by the simu function.

> library(rocTree)
> set.seed(2019)
> dat <- simu(n = 100, cen = 0.25, sce = 2.1, summary = TRUE)
Summary results:
Number of subjects: 100
Number of subjects experienced death: 77
Number of covariates: 2
Time independent covaraites: z1.
Time dependent covaraites: z2.
Number of unique observation times: 100
Median survival time: 0.3213932

The ensembles

The ensemble method can be easily called by setting ensemble = TRUE (default) when fitting a rocTree(). Ensemble method improve the variance reduction of bagging by reducing the correlation between the trees via random selection of predictors in the tree- growing process. In the following, we apply the ensemble method with fully grown trees with small terminal nodes and without pruning. We first load the survival package to enable Surv. A total of 500 survival trees can be grown as follow:

> library(survival)
> system.time(fit <- rocTree(Surv(Time, death) ~ z1 + z2, id = id, data = dat, 
+     ensemble = TRUE))
   user  system elapsed 
  0.992   0.012   1.015

Some of the important parameters can be printed directly.

> fit
ROC-guided ensembles

Call:
 rocTree(formula = Surv(Time, death) ~ z1 + z2, data = dat, id = id,      ensemble = TRUE) 

Sample size:                                        
Number of independent variables:                    100 
Number of trees:                                    500 
Split rule:                                         dCON 
Number of variables tried at each split:            2 
Number of time points to evaluate CON:              20 
Min. number of baseline obs. in a splittable node:  30 
Min. number of baseline obs. in a terminal node:    15

The function rocTree returns an object of S3 class. The 500 survival trees are stored in fit$trees. These survival trees can be printed and plotted with the generic function print and plot, respectively. For example, the first of the 500 survival trees can be printed/plotted as below.

> print(fit, tree = 1)
 ROC-guided survival tree

 node), split
   * denotes terminal node
  
Root                          
 ¦--2) z1 <= 0.51741          
 ¦   ¦--4) z2 <= 0.60199*     
 ¦   °--5) z2 > 0.60199*      
 °--3) z1 > 0.51741           
     ¦--6) z2 <= 0.85075      
     ¦   ¦--12) z2 <= 0.29851*
     ¦   °--13) z2 > 0.29851* 
     °--7) z2 > 0.85075*      
> plot(fit, tree = 1)

The other trees can be printed/plotted similarly by specifying the tree argument. Users are referred to the Package vignette on fitting time-invariant survival tree for different printing/plotting options.

Prediction

Suppose we have a new data that is generated as below:

> newdat <- dplyr::tibble(Time = sort(unique(dat$Time)), 
+                         z1 = 1 * (Time < median(Time)), 
+                         z2 = runif(1))
> newdat
# A tibble: 100 x 3
     Time    z1    z2
    <dbl> <dbl> <dbl>
 1 0.0168     1 0.640
 2 0.0315     1 0.640
 3 0.0417     1 0.640
 4 0.0606     1 0.640
 5 0.0711     1 0.640
 6 0.0803     1 0.640
 7 0.0872     1 0.640
 8 0.0901     1 0.640
 9 0.102      1 0.640
10 0.105      1 0.640
# … with 90 more rows

The predicted survival curve can be plotted with the following codes.

> pred <- predict(fit, newdat)
> pred
 Fitted survival probabilities:
        Time  Survival
1 0.01676500 1.0000000
2 0.03145121 1.0000000
3 0.04165134 0.9881193
4 0.06056327 0.9576287
5 0.07110612 0.9234714
> plot(pred)