Bagging for MDTL-Integrated Cox Elastic-Net Models — cox_MDTL_enet

Performs bootstrap aggregation (bagging) for the Mahalanobis-distance–based transfer-learning Cox elastic-net model (cv.cox_MDTL_enet) by repeatedly refitting the model on bootstrap resamples of the internal dataset and averaging the resulting fitted coefficient vectors. This procedure reduces sampling variability and improves robustness relative to a single data split.

Usage

cox_MDTL_enet_bagging(
  z,
  delta,
  time,
  stratum = NULL,
  beta = NULL,
  vcov = NULL,
  etas,
  alpha = 1,
  B = 100,
  lambda = NULL,
  nlambda = 100,
  lambda.min.ratio = ifelse(nrow(z) < ncol(z), 0.01, 1e-04),
  nfolds = 5,
  cv.criteria = c("V&VH", "LinPred", "CIndex_pooled", "CIndex_foldaverage"),
  c_index_stratum = NULL,
  message = FALSE,
  seed = NULL,
  ncores = 1,
  ...
)

Arguments

z: Matrix of predictors of dimension n x p.
delta: Event indicator vector.
time: Survival time vector.
stratum: Optional stratum indicator vector for stratified Cox modeling.
beta: External coefficient vector of length p. Treated as fixed prior information and not resampled across bootstrap replicates.
vcov: Optional weighting matrix (p x p) used in the Mahalanobis distance formulation.
etas: Vector of eta values for transfer-learning shrinkage.
alpha: Elastic-net mixing parameter between 0 and 1. alpha = 1 corresponds to lasso; alpha = 0 to ridge. Default is 1.0.
B: Number of bootstrap replicates. Default is 100.
lambda: Optional user-specified lambda sequence.
nlambda: Number of lambda values to generate if lambda is not supplied.
lambda.min.ratio: Ratio of the smallest to the largest lambda when generating a sequence.
nfolds: Number of folds for inner cross-validation via cv.cox_MDTL_enet.
cv.criteria: Cross-validation criterion used for selecting the optimal (eta, lambda) pair.
c_index_stratum: Optional stratum assignment for stratified C-index evaluation (may differ from model stratification).
message: Logical indicating whether to print progress. Default is FALSE.
seed: Optional integer seed for reproducibility.
ncores: Integer. Number of parallel cores. Default 1 (sequential execution).
...: Additional arguments passed to cv.cox_MDTL_enet.

Value

An object of class "cox_MDTL_bagging" containing:

best_beta — aggregated coefficient estimate obtained by averaging across valid bootstrap replicates.
all_betas — matrix of dimension p x B_valid containing coefficient vectors from each successful bootstrap fit.
B — total number of requested bootstrap replicates.
valid_replicates — number of successful (non-error) fits contributing to aggregation.
seed — seed used for reproducibility (if supplied).

Details

External information is supplied via a fixed coefficient vector (beta) and, optionally, a weighting matrix (vcov). Both represent external prior information and are not resampled across replicates.

Examples

if (FALSE) { # \dontrun{
data(ExampleData_highdim)
train_dat_highdim     <- ExampleData_highdim$train
beta_external_highdim <- ExampleData_highdim$beta_external

etas <- generate_eta(method = "exponential", n = 10, max_eta = 10)

bag.out <- cox_MDTL_enet_bagging(
  z            = train_dat_highdim$z,
  delta        = train_dat_highdim$status,
  time         = train_dat_highdim$time,
  stratum      = train_dat_highdim$stratum,
  beta         = beta_external_highdim,
  vcov         = NULL,
  etas         = etas,
  alpha        = 0.5,
  B            = 5,
  cv.criteria  = "CIndex_pooled",
  message      = TRUE,
  seed         = 123
)
} # }