fit_P2_gated_L1: Smoothed integrated-gate penalty (P2)

In fdb: Frequentist Dynamic Borrowing for Hybrid-Control Survival Trials

Smoothed integrated-gate penalty (P2)

Description

Implements

p_{\lambda,\varepsilon}(\delta) = \lambda\int_\varepsilon^{\sqrt{\delta^2+\varepsilon^2}} [1+\exp\{(u/\widehat{SE}(\hat\delta_0)-c)/\tau\}]^{-1}du,

which provides a continuous relaxation of test-then-pool procedures driven by standardized evidence against commensurability.

Usage

fit_P2_gated_L1(
  dat,
  xnames = NULL,
  lambda,
  c = 1.64,
  tau = 0.25,
  delta_bounds = DEFAULT_DELTA_BOUNDS,
  full_fit = NULL,
  robust = FALSE,
  eps = SMOOTH_EPS,
  n_grid_opt = DEFAULT_N_GRID_OPT
)

Arguments

dat	A data frame from simulate_hybrid_cox or conforming to its column conventions.
xnames	Character vector of covariate names. If NULL, automatically detected.
lambda	Penalty strength (\lambda \ge 0).
c	Evidence threshold (default 1.64, one-sided 5% gate).
tau	Gate smoothness parameter (positive).
delta_bounds	Numeric vector of length 2 giving the optimization interval for \delta.
full_fit	Optional pre-computed full Cox fit (output of an internal helper). If NULL, the fit is computed.
robust	Use robust (Lin-Wei) Cox standard errors.
eps	Smoothing parameter for |\delta|_\varepsilon.
n_grid_opt	Number of grid points for the coarse search in the non-convex objective.

Value

A list of estimates and inference quantities, including the evidence-gate value g_hat and the raw (unstabilized) penalty curvature pen_curv_raw.

fdb documentation built on Oct. 4, 2026, 5:07 p.m.