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Fit Cox Model with Multi-Domain Transfer Learning and Elastic Net Penalty

cox_MDTL_enet.Rd

Fits a Cox Proportional Hazards model that integrates external information (Transfer Learning) using an Elastic Net regularization path. The method incorporates prior knowledge from external coefficients (beta) and an optional weight matrix (vcov), controlled by the transfer learning parameter eta.

The objective function minimizes the negative partial likelihood plus a transfer learning penalty term \(\eta (\beta - \beta_{ext})^T Q (\beta - \beta_{ext})\) and the Elastic Net penalty.

Usage

cox_MDTL_enet(
  z,
  delta,
  time,
  stratum = NULL,
  beta,
  vcov = NULL,
  eta = NULL,
  alpha = NULL,
  lambda = NULL,
  nlambda = 100,
  lambda.min.ratio = ifelse(n < p, 0.05, 0.001),
  lambda.early.stop = FALSE,
  tol = 1e-04,
  Mstop = 1000,
  max.total.iter = (Mstop * nlambda),
  group = 1:ncol(z),
  group.multiplier = NULL,
  standardize = T,
  nvar.max = ncol(z),
  group.max = length(unique(group)),
  stop.loss.ratio = 0.01,
  actSet = TRUE,
  actIter = Mstop,
  actGroupNum = sum(unique(group) != 0),
  actSetRemove = F,
  returnX = FALSE,
  trace.lambda = FALSE,
  message = FALSE,
  data_sorted = FALSE,
  ...
)

Arguments

z

Matrix of predictors (n x p).

delta

Vector of event indicators (1 for event, 0 for censored).

time

Vector of observed survival times.

stratum

Vector indicating the stratum membership. If NULL, all observations are assumed to be in the same stratum.

beta

Vector of external coefficients (length p). This represents the prior knowledge or "source" model coefficients.

vcov

Optional weighting matrix (p x p) for the external information. Typically the inverse covariance matrix (precision matrix) of the external estimator. If NULL, defaults to the identity matrix.

eta

Scalar. The transfer learning parameter (>= 0). Controls the strength of the external information. eta = 0 ignores external info.

alpha

The Elastic Net mixing parameter, with \(0 \le \alpha \le 1\). alpha=1 is the lasso penalty, and alpha=0 the ridge penalty.

lambda

Optional user-supplied lambda sequence. If NULL, the algorithm generates its own sequence.

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 sample size relative to features.

lambda.early.stop

Logical. Whether to stop early if the deviance changes minimally.

tol

Convergence threshold for coordinate descent.

Mstop

Maximum number of iterations per lambda step.

max.total.iter

Maximum total iterations across all lambda values.

group

Vector describing the grouping of the coefficients. Default is 1:ncol(z) (no grouping).

group.multiplier

Vector of multipliers for each group size.

standardize

Logical. Should the predictors be standardized before fitting? Default is TRUE.

nvar.max

Maximum number of variables allowed in the model.

group.max

Maximum number of groups allowed in the model.

stop.loss.ratio

Ratio of loss change to stop the path early.

actSet

Logical. Whether to use active set convergence strategy.

actIter

Number of iterations for active set.

actGroupNum

Number of active groups.

actSetRemove

Logical. Whether to remove inactive groups from the active set.

returnX

Logical. If TRUE, returns the standardized design matrix and other data details.

trace.lambda

Logical. If TRUE, prints the current lambda during fitting.

message

Logical. If TRUE, prints warnings and progress messages.

data_sorted

Logical. Internal flag indicating if data is already sorted by time/stratum.

...

Additional arguments.

Value

An object of class "cox_MDTL_enet" containing:

  • beta: Matrix of estimated coefficients (p x nlambda).

  • lambda: The sequence of lambda values used.

  • likelihood: Vector of negative partial log-likelihood values.

  • df: Degrees of freedom for each lambda.

  • W: Matrix of exponential linear predictors.

  • iter: Number of iterations for each lambda.

  • data: List of input data.

Examples

# \donttest{
data(ExampleData_highdim)
train_dat_highdim <- ExampleData_highdim$train
beta_external_highdim <- ExampleData_highdim$beta_external

cox_MDTL_enet_est <- cox_MDTL_enet(
  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,
  alpha = 1
)
# }