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" = 20L)
    options("mlexperiments.optim.xgb.early_stopping_rounds" = 5L)

## 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(
      n_iter = ncores,
      kappa = 3.5,
      acq = "ucb"
    )

## Hyperparameter Tuning

### Grid Search

    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

### Inner Grid Search

    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