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Cross-Validation for Cox MDTL with Ridge Regularization

cv.cox_MDTL_ridge.Rd

Performs k-fold cross-validation to simultaneously tune the hyperparameter eta (transfer learning weight) and the regularization parameter lambda for the Cox MDTL model with a Ridge penalty (L2-norm).

This function evaluates the model performance across a grid of eta and lambda values. It is efficient for high-dimensional data where an Elastic Net penalty is not required, focusing purely on Ridge regression to handle multicollinearity and overfitting.

Usage

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

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.

lambda

Optional user-supplied lambda sequence. If NULL, the function computes its own sequence based on nlambda.

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.

...

Additional arguments passed to the underlying fitting function.

Value

An object of class "cv.cox_MDTL_ridge" containing:

best

A list containing the optimal results:

  • best_eta: The selected eta value.

  • best_lambda: The selected lambda value.

  • best_beta: The coefficient vector corresponding to the optimal parameters.

  • criteria: The selection criterion used.

integrated_stat.full_results

A data frame of performance metrics for all combinations of eta and lambda.

integrated_stat.best_per_eta

A data frame summarizing the best lambda and performance metric for each eta.

integrated_stat.betahat_best

A matrix of coefficients for the best lambda at each eta.

criteria

The selection criterion used.

nfolds

The number of folds used.

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 = 50, max_eta = 10)

cv.cox_MDTL_ridge_est <- cv.cox_MDTL_ridge(
  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"
)
} # }