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Stability Selection for MDTL-Integrated Cox Elastic-Net Models

cox_MDTL_enet.StabSelect.Rd

Performs stability selection for the Mahalanobis-distance–based transfer-learning Cox elastic-net model (cox_MDTL_enet) by repeatedly refitting the model on bootstrap or subsampled datasets and aggregating variable selection frequencies across replicates. This procedure yields a more robust measure of variable importance that is less sensitive to a single data split.

Usage

cox_MDTL_enet.StabSelect(
  z,
  delta,
  time,
  stratum = NULL,
  beta,
  vcov = NULL,
  etas = NULL,
  alpha = 1,
  lambda = NULL,
  nlambda = 100,
  lambda.min.ratio = 0.1,
  nfolds = 5,
  cv.criteria = c("V&VH", "LinPred", "CIndex_pooled", "CIndex_foldaverage"),
  c_index_stratum = NULL,
  message = FALSE,
  seed = NULL,
  B = 50,
  fraction_sample = 0.5,
  ncores = 1,
  ...
)

Arguments

z

A numeric matrix or data frame of covariates (n x p).

delta

A numeric vector of event indicators (1 = event, 0 = censored).

time

A numeric vector of observed times.

stratum

Optional numeric or factor vector indicating strata. If NULL, all subjects are assumed to be in the same stratum.

beta

A numeric vector of external coefficients (length p).

vcov

Optional numeric matrix (p x p) representing the weighting matrix \(Q\) for the Mahalanobis penalty. Typically the inverse covariance matrix. If NULL, defaults to the identity matrix.

etas

A numeric vector of candidate eta values to be evaluated.

alpha

The Elastic Net mixing parameter, with \(0 \le \alpha \le 1\). alpha = 1 is the Lasso penalty, and alpha = 0 is the Ridge penalty. If NULL, defaults to 1 (Lasso).

lambda

Optional user-supplied lambda sequence. If NULL, typical usage is to have the program compute its own lambda sequence based on nlambda and lambda.min.ratio.

nlambda

The number of lambda values. Default is 100.

lambda.min.ratio

Smallest value for lambda, as a fraction of lambda.max. Default depends on the sample size relative to the number of predictors.

nfolds

Integer. Number of cross-validation folds. Default is 5.

cv.criteria

Character string specifying the cross-validation criterion. Choices are:

  • "V&VH" (default): Verweij & Van Houwelingen partial likelihood loss.

  • "LinPred": Loss based on the prognostic performance of the linear predictor.

  • "CIndex_pooled": Harrell's C-index computed by pooling predictions across folds.

  • "CIndex_foldaverage": Harrell's C-index computed within each fold and averaged.

c_index_stratum

Optional stratum vector. Required only when cv.criteria involves stratified C-index calculation but the model itself is unstratified.

message

Logical. If TRUE, progress messages are printed.

seed

Optional integer. Random seed for reproducible fold assignment.

B

Integer. Number of bootstrap/subsampling replicates used for stability selection. Default is 50.

fraction_sample

Numeric in (0, 1]. Fraction of the original sample size used in each replicate. Default is 0.5.

ncores

Integer. Number of parallel cores. Default 1 (sequential execution).

...

Additional arguments passed to the underlying fitting function.

Value

An object of class "StabSelect" containing:

  • stability_path — a numeric matrix storing selection probabilities for each variable–lambda pair across the B replicates.

  • lambda — the global lambda sequence used for the underlying elastic-net fits.

Examples

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

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

mdtl.StabSelect <- cox_MDTL_enet.StabSelect(
  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         = eta_list,
  cv.criteria  = "CIndex_pooled",
  B            = 20,
  message      = TRUE
)

# Visualize selection with a chosen threshold
plot(mdtl.StabSelect, threshold = 0.75)
} # }