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Cox MDTL with Ridge Regularization

cox_MDTL_ridge.Rd

Fits a Cox Proportional Hazards model that simultaneously incorporates:

  1. Transfer Learning: A Mahalanobis distance penalty that shrinks coefficients towards external reference coefficients (beta), controlled by the parameter eta.

  2. Ridge Regularization: An L2-norm penalty on the coefficients to handle high-dimensional data or multicollinearity, controlled by the sequence of lambda values.

The function computes the solution path over a sequence of lambda values for a fixed eta.

Usage

cox_MDTL_ridge(
  z,
  delta,
  time,
  stratum = NULL,
  beta = NULL,
  vcov = NULL,
  eta = NULL,
  lambda = NULL,
  nlambda = 100,
  penalty.factor = 0.999,
  tol = 1e-04,
  Mstop = 50,
  backtrack = FALSE,
  message = FALSE,
  data_sorted = FALSE,
  beta_initial = 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.

eta

A single non-negative numeric value controlling the weight of the external information (Mahalanobis distance penalty). If NULL, defaults to 0 (no transfer learning).

lambda

Optional numeric vector of regularization parameters. If NULL, a sequence is generated automatically.

nlambda

Integer. The number of lambda values to generate if lambda is NULL. Default is 100.

penalty.factor

Numeric value used to determine the elastic net mixing parameter alpha. The function sets alpha = 1 - penalty.factor. A value close to 1 (default 0.999) results in alpha close to 0, enforcing a Ridge-like penalty.

tol

Convergence tolerance for the optimization algorithm. Default is 1e-4.

Mstop

Maximum number of iterations. Default is 50.

backtrack

Logical. If TRUE, uses backtracking line search. Default is FALSE.

message

Logical. If TRUE, progress messages are printed.

data_sorted

Logical. If TRUE, assumes input data is already sorted by stratum and time.

beta_initial

Optional initial coefficient vector for warm start.

...

Additional arguments passed to internal functions.

Value

An object of class "cox_MDTL_ridge" containing:

lambda

The sequence of lambda values used.

beta

A matrix of estimated coefficients (p x nlambda).

linear.predictors

A matrix of linear predictors (n x nlambda).

likelihood

A vector of log-partial likelihoods for each lambda.

data

A list containing the input data (z, time, delta, stratum).

Examples

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

cox_MDTL_ridge_est <- 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,
  eta = 0.5
)
} # }