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rpart: Survival Analysis

# nolint start
library(mlexperiments)
library(mlsurvlrnrs)

See https://github.com/kapsner/mlsurvlrnrs/blob/main/R/learner_surv_rpart_cox.R for implementation details.

Preprocessing

Import and Prepare Data

dataset <- survival::colon |>
  data.table::as.data.table() |>
  na.omit()
dataset <- dataset[get("etype") == 2, ]

surv_cols <- c("status", "time", "rx")
feature_cols <- colnames(dataset)[3:(ncol(dataset) - 1)]
cat_vars <- c("sex", "obstruct", "perfor", "adhere", "differ", "extent",
              "surg", "node4", "rx")

General Configurations

seed <- 123
if (isTRUE(as.logical(Sys.getenv("_R_CHECK_LIMIT_CORES_")))) {
  # on cran
  ncores <- 2L
} else {
  ncores <- ifelse(
    test = parallel::detectCores() > 4,
    yes = 4L,
    no = ifelse(
      test = parallel::detectCores() < 2L,
      yes = 1L,
      no = parallel::detectCores()
    )
  )
}
options("mlexperiments.bayesian.max_init" = 10L)

Generate Training- and Test Data

split_vector <- splitTools::multi_strata(
  df = dataset[, .SD, .SDcols = surv_cols],
  strategy = "kmeans",
  k = 4
)

data_split <- splitTools::partition(
  y = split_vector,
  p = c(train = 0.7, test = 0.3),
  type = "stratified",
  seed = seed
)

train_x <- data.matrix(
  dataset[
    data_split$train, .SD, .SDcols = setdiff(feature_cols, surv_cols[1:2])
  ]
)
train_y <- survival::Surv(
  event = (dataset[data_split$train, get("status")] |>
             as.character() |>
             as.integer()),
  time = dataset[data_split$train, get("time")],
  type = "right"
)
split_vector_train <- splitTools::multi_strata(
  df = dataset[data_split$train, .SD, .SDcols = surv_cols],
  strategy = "kmeans",
  k = 4
)


test_x <- data.matrix(
  dataset[data_split$test, .SD, .SDcols = setdiff(feature_cols, surv_cols[1:2])]
)
test_y <- survival::Surv(
  event = (dataset[data_split$test, get("status")] |>
             as.character() |>
             as.integer()),
  time = dataset[data_split$test, get("time")],
  type = "right"
)

Generate Training Data Folds

fold_list <- splitTools::create_folds(
  y = split_vector_train,
  k = 3,
  type = "stratified",
  seed = seed
)

Experiments

Prepare Experiments

# required learner arguments, not optimized
learner_args <- list(method = "exp")

# set arguments for predict function and performance metric,
# required for mlexperiments::MLCrossValidation and
# mlexperiments::MLNestedCV
predict_args <- NULL
performance_metric <- c_index
performance_metric_args <- NULL
return_models <- FALSE

# required for grid search and initialization of bayesian optimization
parameter_grid <- expand.grid(
  minsplit = seq(2L, 82L, 10L),
  cp = seq(0.01, 0.1, 0.01),
  maxdepth = seq(2L, 30L, 5L)
)

# reduce to a maximum of 10 rows
if (nrow(parameter_grid) > 10) {
  set.seed(123)
  sample_rows <- sample(seq_len(nrow(parameter_grid)), 10, FALSE)
  parameter_grid <- kdry::mlh_subset(parameter_grid, sample_rows)
}

# required for bayesian optimization
parameter_bounds <- list(
  minsplit = c(2L, 100L),
  cp = c(0.01, 0.1),
  maxdepth = c(2L, 30L)
)
optim_args <- list(
  iters.n = ncores,
  kappa = 3.5,
  acq = "ucb"
)

Hyperparameter Tuning

tuner <- mlexperiments::MLTuneParameters$new(
  learner = LearnerSurvRpartCox$new(),
  strategy = "grid",
  ncores = ncores,
  seed = seed
)

tuner$parameter_grid <- parameter_grid
tuner$learner_args <- learner_args
tuner$split_type <- "stratified"
tuner$split_vector <- split_vector_train

tuner$set_data(
  x = train_x,
  y = train_y,
  cat_vars = cat_vars
)

tuner_results_grid <- tuner$execute(k = 3)
#> 
#> Parameter settings [=====================================================================>---------------------------------------------------------------------] 5/10 ( 50%)
#> Parameter settings [==================================================================================>--------------------------------------------------------] 6/10 ( 60%)
#> Parameter settings [================================================================================================>------------------------------------------] 7/10 ( 70%)
#> Parameter settings [==============================================================================================================>----------------------------] 8/10 ( 80%)
#> Parameter settings [============================================================================================================================>--------------] 9/10 ( 90%)
#> Parameter settings [==========================================================================================================================================] 10/10 (100%)                                                                                                                                                                             

head(tuner_results_grid)
#>    setting_id metric_optim_mean minsplit   cp maxdepth method
#> 1:          1         0.6218275        2 0.07       22    exp
#> 2:          1         0.6218275        2 0.07       22    exp
#> 3:          1         0.6218275        2 0.07       22    exp
#> 4:          1         0.6218275        2 0.07       22    exp
#> 5:          1         0.6218275        2 0.07       22    exp
#> 6:          1         0.6218275        2 0.07       22    exp

Bayesian Optimization

tuner <- mlexperiments::MLTuneParameters$new(
  learner = LearnerSurvRpartCox$new(),
  strategy = "bayesian",
  ncores = ncores,
  seed = seed
)

tuner$parameter_grid <- parameter_grid
tuner$parameter_bounds <- parameter_bounds

tuner$learner_args <- learner_args
tuner$optim_args <- optim_args

tuner$split_type <- "stratified"
tuner$split_vector <- split_vector_train

tuner$set_data(
  x = train_x,
  y = train_y,
  cat_vars = cat_vars
)

tuner_results_bayesian <- tuner$execute(k = 3)
#> 
#> Registering parallel backend using 4 cores.

head(tuner_results_bayesian)
#>    Epoch setting_id minsplit   cp maxdepth gpUtility acqOptimum inBounds Elapsed     Score metric_optim_mean errorMessage method
#> 1:     0          1        2 0.07       22        NA      FALSE     TRUE   0.991 0.6218275         0.6218275           NA    exp
#> 2:     0          2       32 0.02       27        NA      FALSE     TRUE   1.009 0.6218275         0.6218275           NA    exp
#> 3:     0          3       72 0.10        7        NA      FALSE     TRUE   0.999 0.6218275         0.6218275           NA    exp
#> 4:     0          4       32 0.09       27        NA      FALSE     TRUE   1.010 0.6218275         0.6218275           NA    exp
#> 5:     0          5       52 0.02       12        NA      FALSE     TRUE   0.071 0.6218275         0.6218275           NA    exp
#> 6:     0          6        2 0.04        7        NA      FALSE     TRUE   0.065 0.6218275         0.6218275           NA    exp

k-Fold Cross Validation

validator <- mlexperiments::MLCrossValidation$new(
  learner = LearnerSurvRpartCox$new(),
  fold_list = fold_list,
  ncores = ncores,
  seed = seed
)

validator$learner_args <- tuner$results$best.setting[-1]

validator$predict_args <- predict_args
validator$performance_metric <- performance_metric
validator$performance_metric_args <- performance_metric_args
validator$return_models <- return_models

validator$set_data(
  x = train_x,
  y = train_y,
  cat_vars = cat_vars
)

validator_results <- validator$execute()
#> 
#> CV fold: Fold1
#> 
#> CV fold: Fold2
#> 
#> CV fold: Fold3

head(validator_results)
#>     fold performance minsplit   cp maxdepth method
#> 1: Fold1   0.6202320        2 0.07       22    exp
#> 2: Fold2   0.5903866        2 0.07       22    exp
#> 3: Fold3   0.6548638        2 0.07       22    exp

Nested Cross Validation

validator <- mlexperiments::MLNestedCV$new(
  learner = LearnerSurvRpartCox$new(),
  strategy = "grid",
  fold_list = fold_list,
  k_tuning = 3L,
  ncores = ncores,
  seed = seed
)

validator$parameter_grid <- parameter_grid
validator$learner_args <- learner_args
validator$split_type <- "stratified"
validator$split_vector <- split_vector_train

validator$predict_args <- predict_args
validator$performance_metric <- performance_metric
validator$performance_metric_args <- performance_metric_args
validator$return_models <- return_models

validator$set_data(
  x = train_x,
  y = train_y,
  cat_vars = cat_vars
)

validator_results <- validator$execute()
#> 
#> CV fold: Fold1
#> 
#> Parameter settings [=====================================================================>---------------------------------------------------------------------] 5/10 ( 50%)
#> Parameter settings [==================================================================================>--------------------------------------------------------] 6/10 ( 60%)
#> Parameter settings [================================================================================================>------------------------------------------] 7/10 ( 70%)
#> Parameter settings [==============================================================================================================>----------------------------] 8/10 ( 80%)
#> Parameter settings [============================================================================================================================>--------------] 9/10 ( 90%)
#> Parameter settings [==========================================================================================================================================] 10/10 (100%)                                                                                                                                                                             
#> CV fold: Fold2
#> CV progress [=================================================================================================>-------------------------------------------------] 2/3 ( 67%)
#> 
#> Parameter settings [=====================================================================>---------------------------------------------------------------------] 5/10 ( 50%)
#> Parameter settings [==================================================================================>--------------------------------------------------------] 6/10 ( 60%)
#> Parameter settings [================================================================================================>------------------------------------------] 7/10 ( 70%)
#> Parameter settings [==============================================================================================================>----------------------------] 8/10 ( 80%)
#> Parameter settings [============================================================================================================================>--------------] 9/10 ( 90%)
#> Parameter settings [==========================================================================================================================================] 10/10 (100%)                                                                                                                                                                             
#> CV fold: Fold3
#> CV progress [===================================================================================================================================================] 3/3 (100%)
#>                                                                                                                                                                              
#> Parameter settings [==================================================================================>--------------------------------------------------------] 6/10 ( 60%)
#> Parameter settings [================================================================================================>------------------------------------------] 7/10 ( 70%)
#> Parameter settings [==============================================================================================================>----------------------------] 8/10 ( 80%)
#> Parameter settings [============================================================================================================================>--------------] 9/10 ( 90%)
#> Parameter settings [==========================================================================================================================================] 10/10 (100%)                                                                                                                                                                             

head(validator_results)
#>     fold performance minsplit   cp maxdepth method
#> 1: Fold1   0.6202320       42 0.02        2    exp
#> 2: Fold2   0.5903866       42 0.02        2    exp
#> 3: Fold3   0.6343591       42 0.02        2    exp

Inner Bayesian Optimization

validator <- mlexperiments::MLNestedCV$new(
  learner = LearnerSurvRpartCox$new(),
  strategy = "bayesian",
  fold_list = fold_list,
  k_tuning = 3L,
  ncores = ncores,
  seed = 312
)

validator$parameter_grid <- parameter_grid
validator$learner_args <- learner_args
validator$split_type <- "stratified"
validator$split_vector <- split_vector_train


validator$parameter_bounds <- parameter_bounds
validator$optim_args <- optim_args

validator$predict_args <- predict_args
validator$performance_metric <- performance_metric
validator$performance_metric_args <- performance_metric_args
validator$return_models <- TRUE

validator$set_data(
  x = train_x,
  y = train_y,
  cat_vars = cat_vars
)

validator_results <- validator$execute()
#> 
#> CV fold: Fold1
#> 
#> Registering parallel backend using 4 cores.
#> 
#> CV fold: Fold2
#> CV progress [=================================================================================================>-------------------------------------------------] 2/3 ( 67%)
#> 
#> Registering parallel backend using 4 cores.
#> 
#> CV fold: Fold3
#> CV progress [===================================================================================================================================================] 3/3 (100%)
#>                                                                                                                                                                              
#> Registering parallel backend using 4 cores.

head(validator_results)
#>     fold performance minsplit   cp maxdepth method
#> 1: Fold1   0.6202320        2 0.07       22    exp
#> 2: Fold2   0.5903866       42 0.02        2    exp
#> 3: Fold3   0.6548638       72 0.10        7    exp

Holdout Test Dataset Performance

Predict Outcome in Holdout Test Dataset

preds_rpart <- mlexperiments::predictions(
  object = validator,
  newdata = test_x
)

Evaluate Performance on Holdout Test Dataset

perf_rpart <- mlexperiments::performance(
  object = validator,
  prediction_results = preds_rpart,
  y_ground_truth = test_y
)
perf_rpart
#>    model performance
#> 1: Fold1   0.6132183
#> 2: Fold2   0.5931751
#> 3: Fold3   0.6272602

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