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xgboost: Survival Analysis, Cox Regression

# nolint start
library(mlexperiments)
library(mlsurvlrnrs)

See https://github.com/kapsner/mlsurvlrnrs/blob/main/R/learner_surv_xgboost_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)]

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)
options("mlexperiments.optim.xgb.nrounds" = 100L)
options("mlexperiments.optim.xgb.early_stopping_rounds" = 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 <- model.matrix(
  ~ -1 + .,
  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 <- model.matrix(
  ~ -1 + .,
  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(
  objective = "survival:cox",
  eval_metric = "cox-nloglik"
)

# 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(
  subsample = seq(0.6, 1, .2),
  colsample_bytree = seq(0.6, 1, .2),
  min_child_weight = seq(1, 5, 4),
  learning_rate = seq(0.1, 0.2, 0.1),
  max_depth = seq(1, 5, 4)
)
# 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(
  subsample = c(0.2, 1),
  colsample_bytree = c(0.2, 1),
  min_child_weight = c(1L, 10L),
  learning_rate = c(0.1, 0.2),
  max_depth =  c(1L, 10L)
)
optim_args <- list(
  iters.n = ncores,
  kappa = 3.5,
  acq = "ucb"
)

Hyperparameter Tuning

tuner <- mlexperiments::MLTuneParameters$new(
  learner = LearnerSurvXgboostCox$new(
    metric_optimization_higher_better = FALSE
  ),
  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
)

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

head(tuner_results_grid)
#>    setting_id metric_optim_mean nrounds subsample colsample_bytree min_child_weight learning_rate
#>         <int>             <num>   <int>     <num>            <num>            <num>         <num>
#> 1:          1          4.846400      37       0.6              0.8                5           0.2
#> 2:          2          4.862686      10       1.0              0.8                5           0.1
#> 3:          3          4.852380      41       0.8              0.8                5           0.1
#> 4:          4          4.875127       7       0.6              0.8                5           0.2
#> 5:          5          4.897189       7       1.0              0.8                1           0.1
#> 6:          6          4.854463      10       0.8              0.8                5           0.1
#>    max_depth    objective eval_metric
#>        <num>       <char>      <char>
#> 1:         1 survival:cox cox-nloglik
#> 2:         5 survival:cox cox-nloglik
#> 3:         1 survival:cox cox-nloglik
#> 4:         5 survival:cox cox-nloglik
#> 5:         5 survival:cox cox-nloglik
#> 6:         5 survival:cox cox-nloglik

Bayesian Optimization

tuner <- mlexperiments::MLTuneParameters$new(
  learner = LearnerSurvXgboostCox$new(
    metric_optimization_higher_better = FALSE
  ),
  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
)

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

head(tuner_results_bayesian)
#>    Epoch setting_id subsample colsample_bytree min_child_weight learning_rate max_depth gpUtility
#>    <num>      <int>     <num>            <num>            <num>         <num>     <num>     <num>
#> 1:     0          1       0.6              0.8                5           0.2         1        NA
#> 2:     0          2       1.0              0.8                5           0.1         5        NA
#> 3:     0          3       0.8              0.8                5           0.1         1        NA
#> 4:     0          4       0.6              0.8                5           0.2         5        NA
#> 5:     0          5       1.0              0.8                1           0.1         5        NA
#> 6:     0          6       0.8              0.8                5           0.1         5        NA
#>    acqOptimum inBounds Elapsed     Score metric_optim_mean nrounds errorMessage    objective
#>        <lgcl>   <lgcl>   <num>     <num>             <num>   <int>       <lgcl>       <char>
#> 1:      FALSE     TRUE   0.947 -4.846400          4.846400      37           NA survival:cox
#> 2:      FALSE     TRUE   0.945 -4.862686          4.862686      10           NA survival:cox
#> 3:      FALSE     TRUE   0.925 -4.852380          4.852380      41           NA survival:cox
#> 4:      FALSE     TRUE   0.817 -4.875127          4.875127       7           NA survival:cox
#> 5:      FALSE     TRUE   0.081 -4.897189          4.897189       7           NA survival:cox
#> 6:      FALSE     TRUE   0.124 -4.854463          4.854463      10           NA survival:cox
#>    eval_metric
#>         <char>
#> 1: cox-nloglik
#> 2: cox-nloglik
#> 3: cox-nloglik
#> 4: cox-nloglik
#> 5: cox-nloglik
#> 6: cox-nloglik

k-Fold Cross Validation

validator <- mlexperiments::MLCrossValidation$new(
  learner = LearnerSurvXgboostCox$new(
    metric_optimization_higher_better = FALSE
  ),
  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
)

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

head(validator_results)
#>      fold performance subsample colsample_bytree min_child_weight learning_rate max_depth nrounds
#>    <char>       <num>     <num>            <num>            <num>         <num>     <num>   <int>
#> 1:  Fold1   0.6581185       0.6              0.8                5           0.2         1      37
#> 2:  Fold2   0.6584779       0.6              0.8                5           0.2         1      37
#> 3:  Fold3   0.6291327       0.6              0.8                5           0.2         1      37
#>       objective eval_metric
#>          <char>      <char>
#> 1: survival:cox cox-nloglik
#> 2: survival:cox cox-nloglik
#> 3: survival:cox cox-nloglik

Nested Cross Validation

validator <- mlexperiments::MLNestedCV$new(
  learner = LearnerSurvXgboostCox$new(
    metric_optimization_higher_better = FALSE
  ),
  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
)

validator_results <- validator$execute()
#>
#> CV fold: Fold1
#>
#> 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 [=======================================================>-----------------------------------------------------------------------------------] 4/10 ( 40%)
#> 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(validator_results)
#>      fold performance nrounds subsample colsample_bytree min_child_weight learning_rate max_depth
#>    <char>       <num>   <int>     <num>            <num>            <num>         <num>     <num>
#> 1:  Fold1   0.6519473      23       0.6              0.8                5           0.2         1
#> 2:  Fold2   0.6227989      11       0.6              1.0                1           0.2         1
#> 3:  Fold3   0.6508312      54       0.8              0.8                5           0.1         1
#>       objective eval_metric
#>          <char>      <char>
#> 1: survival:cox cox-nloglik
#> 2: survival:cox cox-nloglik
#> 3: survival:cox cox-nloglik

Inner Bayesian Optimization

validator <- mlexperiments::MLNestedCV$new(
  learner = LearnerSurvXgboostCox$new(
    metric_optimization_higher_better = FALSE
  ),
  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
)

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 subsample colsample_bytree min_child_weight learning_rate max_depth nrounds
#>    <char>       <num>     <num>            <num>            <num>         <num>     <num>   <int>
#> 1:  Fold1   0.6491018       0.6              1.0                1     0.2000000         1      24
#> 2:  Fold2   0.6473323       0.6              0.8                5     0.2000000         1      17
#> 3:  Fold3   0.6295374       1.0              0.8                6     0.1592348         5       8
#>       objective eval_metric
#>          <char>      <char>
#> 1: survival:cox cox-nloglik
#> 2: survival:cox cox-nloglik
#> 3: survival:cox cox-nloglik

Holdout Test Dataset Performance

Predict Outcome in Holdout Test Dataset

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

Evaluate Performance on Holdout Test Dataset

perf_xgboost <- mlexperiments::performance(
  object = validator,
  prediction_results = preds_xgboost,
  y_ground_truth = test_y
)
perf_xgboost
#>     model performance
#>    <char>       <num>
#> 1:  Fold1   0.6531627
#> 2:  Fold2   0.6421748
#> 3:  Fold3   0.6318355

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