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Cox Proportional Hazards Model Integrated with External Individual-level Information

cox_indi.Rd

Fits a series of composite-likelihood (weighted) stratified Cox models that integrate an external individual-level dataset via an external likelihood weight eta.

Usage

cox_indi(
  z_int,
  delta_int,
  time_int,
  stratum_int = NULL,
  z_ext,
  delta_ext,
  time_ext,
  stratum_ext = NULL,
  etas,
  max_iter = 100,
  tol = 1e-07,
  message = FALSE
)

Arguments

z_int

Matrix of covariates for the internal dataset (n_int x p).

delta_int

Event indicators for the internal dataset (0/1).

time_int

Survival times for the internal dataset.

stratum_int

Optional stratum identifiers for the internal dataset (default NULL -> single stratum).

z_ext

Matrix of covariates for the external dataset (n_ext x p).

delta_ext

Event indicators for the external dataset (0/1).

time_ext

Survival times for the external dataset.

stratum_ext

Optional stratum identifiers for the external dataset (default NULL -> single stratum).

etas

Numeric vector of nonnegative external weights. eta = 0 gives internal-only fit.

max_iter

Maximum Newton-Raphson iterations (default 100).

tol

Convergence tolerance (default 1e-7).

message

Logical; if TRUE, show a progress bar. Default FALSE.

Value

An object of class "cox_indi" containing:

eta

Sorted sequence of \(\eta\) values used.

beta

Matrix of estimated coefficients (\(p \times n_{etas}\)). Columns correspond to etas.

linear.predictors_int

Matrix of internal linear predictors for each eta (\(n_{int} \times n_{etas}\)).

linear.predictors_ext

Matrix of external linear predictors for each eta (\(n_{ext} \times n_{etas}\)).

data

List of inputs used.

Details

The fitted objective is $$\ell_\eta(\beta) = \ell_{\text{int}}(\beta) + \eta \, \ell_{\text{ext}}(\beta),$$ which is equivalent to fitting a stratified Cox model on the stacked data with observation weights 1 (internal) and eta (external), while keeping internal and external strata separated (no mixing of risk sets across cohorts).

The function fits one model per eta value. It uses a warm-start strategy: the solution at the current eta is used as the initial value for the next eta in the sorted sequence.

Examples

if (FALSE) { # \dontrun{
## Load example individual-level data
data(ExampleData_indi)

z_int       <- ExampleData_indi$internal$z
delta_int   <- ExampleData_indi$internal$status
time_int    <- ExampleData_indi$internal$time
stratum_int <- ExampleData_indi$internal$stratum

z_ext       <- ExampleData_indi$external$z
delta_ext   <- ExampleData_indi$external$status
time_ext    <- ExampleData_indi$external$time
stratum_ext <- ExampleData_indi$external$stratum

## Generate a sequence of eta values
eta_list <- generate_eta(method = "exponential", n = 50, max_eta = 100)

## Fit the composite-likelihood Cox model path
fit_path <- cox_indi(
  z_int = z_int,
  delta_int = delta_int,
  time_int = time_int,
  stratum_int = stratum_int,
  z_ext = z_ext,
  delta_ext = delta_ext,
  time_ext = time_ext,
  stratum_ext = stratum_ext,
  etas = eta_list
)

## Estimated coefficients along the eta path
fit_path$beta
} # }