06. Machine Learning with Random Survival Forests

Introduction

While classical models like the Cox Proportional Hazards model are highly interpretable, they rely on strict assumptions of linear, additive effects. Random Survival Forests (RSF) overcome this by building a non-linear ensemble of decision trees.

In this tutorial, we will demonstrate how to run a standalone RSF using SuperSurv’s unified wrappers, evaluate its individual performance, and finally include it in a Super Learner ensemble.

1. Prepare the Data

This teaching example uses 200 sampled patients, 50 trees, and three cross-validation folds to keep it quick to run. These settings illustrate the workflow rather than provide a full-data performance comparison.

library(SuperSurv)
library(survival)

data("metabric", package = "SuperSurv")
set.seed(123)
metabric <- metabric[sample(seq_len(nrow(metabric)), 200), ]

train_idx <- sample(1:nrow(metabric), 0.7 * nrow(metabric))
train <- metabric[train_idx, ]
test  <- metabric[-train_idx, ]

X_tr <- train[, grep("^x", names(metabric))]
X_te <- test[, grep("^x", names(metabric))]

new.times <- seq(50, 200, by = 25) 

2. Standalone Machine Learning

SuperSurv provides unified wrappers that automatically handle the training and standardization of survival probabilities. You can use these completely independent of the Super Learner ensemble.

# 1. Fit the standalone wrapper
rf_standalone <- surv.rfsrc(
  time = train$duration,
  event = train$event,
  X = X_tr,
  new.times = new.times,
  ntree = 50
)

# 2. Extract the fitted model object and prediction matrix
rf_fit <- rf_standalone[["fit"]]
rf_pred_matrix <- rf_standalone[["pred"]]

Because our plotting functions are universally compatible, we can plot individual patient curves directly from this standalone matrix:

Plotting examples run only when both randomForestSRC and the optional ggplot2 package are installed.

# Plot the first 3 patients in our training set
plot_predict(preds = rf_pred_matrix, eval_times = new.times, patient_idx = 1:3)

3. Evaluating the Standalone Model

We can also pass this standalone model directly into our evaluation suite to test its performance on new data.

# The function automatically detects this is a single model and plots it!
plot_benchmark(
  object = rf_fit,
  newdata = X_te,
  time = test$duration,
  event = test$event,
  eval_times = new.times
)

# plot_calibration(
#   object   = rf_fit,
#   newdata  = X_te,
#   time     = test$duration,
#   event    = test$event,
#   eval_time = 150,
#   bins     = 2
# )

4. Train the Benchmark Ensemble

While the standalone RSF is powerful, we can objectively evaluate if it outperforms classical models by putting them together in a SuperSurv ensemble.

rf_library <- create_grid("surv.rfsrc", list(ntree = 50))
my_library <- c("surv.coxph", "surv.weibull", rf_library)

fit_supersurv <- SuperSurv(
  time = train$duration,
  event = train$event,
  X = X_tr,
  newdata = X_te,
  new.times = new.times,
  event.library = my_library,
  cens.library = c("surv.coxph"), 
  control = list(
    saveFitLibrary = TRUE,
    event.t.grid = seq(0, max(train$duration[train$event == 1]), length.out = 30),
    cens.t.grid = seq(0, max(train$duration[train$event == 0]), length.out = 30)
  ),
  verbose = FALSE,
  nFolds = 3
)

5. Visualizing Ensemble vs. Base Learners

When we pass the SuperSurv ensemble into the exact same benchmark function, it automatically unpacks the library and plots the ensemble against all its constituent models.

plot_benchmark(
  object = fit_supersurv,
  newdata = X_te,
  time = test$duration,
  event = test$event,
  eval_times = new.times
)

Including flexible learners broadens the candidate library and may improve adaptation to nonlinear or non-proportional-hazards structure. Their contribution is determined by the selected cross-validated objective and should be evaluated on held-out data.