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Conditional Logistic Regression with KL Divergence (CLR-KL)

ncckl.Rd

Fits a series of Conditional Logistic Regression models that integrate external coefficient information (beta) using Kullback–Leibler (KL) divergence, suitable for matched case-control studies.

Usage

ncckl(
  y,
  z,
  stratum,
  etas,
  beta,
  method = c("breslow", "exact"),
  Mstop = 100,
  tol = 1e-04,
  message = FALSE,
  comb_max = 1e+07
)

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). This is required for CLR.

etas

Numeric vector of tuning parameters. Controls the strength of external information integration.

beta

Numeric vector of external coefficients. Used to compute the KL divergence penalty.

method

Character string specifying the tie-handling method ("breslow" or "exact").

Mstop

Integer. Maximum number of Newton-Raphson iterations. Default 100.

tol

Numeric. Convergence tolerance. Default 1e-4.

message

Logical. If TRUE, prints progress during fitting. Default FALSE.

comb_max

Integer. Maximum number of combinations for the method = "exact" calculation. Default 1e7.

Value

An object of class "coxkl" (inherited from coxkl_ties) containing the estimation results for each eta value, including estimated coefficients, linear predictors, and log-partial likelihoods.

Details

This function maps the Conditional Logistic Regression problem to the Cox Proportional Hazards model with fixed event time \(T=1\) and event indicator \(\delta=y\). It utilizes the coxkl_ties core engine to perform the data integration via the KL divergence penalty.

  • Method: The method ("breslow" or "exact") specifies which form of the partial likelihood is used. For 1:M matched case-control studies, "breslow" and "exact" yield identical results, but "exact" is theoretically preferable. For \(n:m\) matched designs (\(n>1\)), the results will differ.

  • External Information: Larger values of the tuning parameter eta enforce stronger agreement with the external coefficients beta.

  • Standard CLR: Setting etas = 0 (or including 0 in the sequence) recovers the standard Maximum Likelihood Estimates for Conditional Logistic Regression.

See also

coxkl_ties for the core function documentation.

Examples

if (FALSE) { # \dontrun{
# Load the matched case-control example data
data(ExampleData_cc)
train_cc <- ExampleData_cc$train

y <- train_cc$y
z <- train_cc$z
sets <- train_cc$stratum

eta_list <- generate_eta(method = "exponential", n = 50, max_eta = 50)
external_beta <- ExampleData_cc$beta_external

# Fit CLR-KL using the Breslow approximation
ncckl.fit_breslow <- ncckl(y = y, z = z, stratum = sets, 
                                 eta = eta_list, beta = external_beta,
                                 method = "breslow")
} # }