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Cox Proportional Hazards Model with Mahalanobis Distance Transfer Learning

cox_MDTL.Rd

Fits a Cox proportional hazards model incorporating external information via a Mahalanobis distance penalty. This approach penalizes the deviation of the estimated coefficients from external reference coefficients (beta), weighted by a specified matrix (typically the inverse covariance matrix).

Usage

cox_MDTL(
  z,
  delta,
  time,
  stratum = NULL,
  beta,
  vcov = NULL,
  etas,
  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) acting as the weighting matrix \(Q\) in the Mahalanobis penalty. Note: In standard Mahalanobis distance formulations, this should be the inverse of the covariance matrix (precision matrix). If not provided, an identity matrix is used.

etas

A numeric vector of tuning parameters (scalars) to evaluate.

tol

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

Mstop

Maximum number of iterations for Newton-Raphson. 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.

Value

An object of class "Cox_MDTL" containing:

eta

The vector of eta values evaluated.

beta

A matrix of estimated coefficients (p x n_eta).

linear.predictors

A matrix of linear predictors (n x n_eta).

likelihood

A vector of log-partial likelihoods for each eta.

data

A list containing the input data used.

Details

The objective function minimizes the negative log-partial likelihood plus a penalty term: $$P(\beta) = \frac{\eta}{2} (\beta - \beta_{ext})^T Q (\beta - \beta_{ext})$$ where:

  • \(\beta_{ext}\) is the vector of external coefficients.

  • \(Q\) is the weighting matrix (derived from vcov).

  • \(\eta\) is the tuning parameter controlling the strength of the external information.

If vcov is NULL, \(Q\) defaults to the identity matrix, reducing the penalty to a standard Euclidean distance (Ridge-type shrinkage towards beta).

Examples

if (FALSE) { # \dontrun{
data(ExampleData_lowdim)
train_dat_lowdim <- ExampleData_lowdim$train
beta_external_lowdim <- ExampleData_lowdim$beta_external_fair

eta_list <- generate_eta(method = "exponential", n = 50, max_eta = 5)

cox_MDTL_est <- cox_MDTL(
  z = train_dat_lowdim$z,
  delta = train_dat_lowdim$status,
  time = train_dat_lowdim$time,
  beta = beta_external_lowdim,
  vcov = NULL,
  etas = eta_list
)
} # }