Conditional Logistic Regression with Mahalanobis Distance Transfer Learning (CLR-MDTL)

Fits a series of Conditional Logistic Regression models that incorporate external coefficient information via a Mahalanobis distance penalty, suitable for matched case-control studies.

Usage

ncc_MDTL(
  y,
  z,
  stratum,
  beta,
  vcov = NULL,
  etas,
  tol = 1e-04,
  Mstop = 50,
  backtrack = FALSE,
  message = FALSE,
  beta_initial = NULL
)

Arguments

y: Numeric vector of binary outcomes (0 = control, 1 = case).
z: Numeric matrix of covariates.
stratum: Numeric or factor vector defining the matched sets (strata). Required.
beta: Numeric vector of external coefficients (length ncol(z)). Required.
vcov: Optional numeric matrix (ncol(z) x ncol(z)) acting as the weighting matrix $Q$ in the Mahalanobis penalty. Typically the inverse of the external covariance (precision matrix). If NULL, defaults to the identity matrix.
etas: Numeric vector of tuning parameters to evaluate. Required.
tol: Convergence tolerance for the Newton-Raphson algorithm. Default 1e-4.
Mstop: Maximum number of Newton-Raphson iterations. Default 50.
backtrack: Logical. If TRUE, uses backtracking line search. Default FALSE.
message: Logical. If TRUE, progress messages are printed. Default FALSE.
beta_initial: Optional initial coefficient vector for warm start.

Value

An object of class "ncc_MDTL" and "cox_MDTL" containing the estimation results for each eta value. See cox_MDTL for a description of the return components.

Details

This function maps the Conditional Logistic Regression problem to a Cox PH model with fixed event time $T=1$ and event indicator $\delta=y$, then calls cox_MDTL as the core engine.

The objective function minimizes the negative conditional log-likelihood plus a Mahalanobis distance penalty: $$P(\beta) = \frac{\eta}{2} (\beta - \beta_{ext})^T Q (\beta - \beta_{ext})$$ where $Q$ is the weighting matrix (identity if vcov is NULL).

Setting etas = 0 recovers the standard CLR (no external information).
Larger eta enforces stronger agreement with beta.
If vcov = NULL, $Q = I$ (Euclidean/Ridge-type shrinkage towards beta).

Examples

if (FALSE) { # \dontrun{
data(ExampleData_cc)
train_cc <- ExampleData_cc$train

y       <- train_cc$y
z       <- train_cc$z
sets    <- train_cc$stratum
beta_ext <- ExampleData_cc$beta_external

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

fit <- ncc_MDTL(
  y      = y,
  z      = z,
  stratum = sets,
  beta   = beta_ext,
  vcov   = NULL,
  etas   = eta_list
)
} # }