weibull_glm_weight_function: Weibull GLM Weight Function for Constructing Information...

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Weibull GLM Weight Function for Constructing Information Matrix

Description

Computes the working weights used in the Weibull AFT information matrix, including the observation-weight contribution returned on the vector scale.

Usage

weibull_glm_weight_function(
  mu,
  y,
  order_indices,
  family,
  dispersion,
  observation_weights,
  status
)

Arguments

mu	Predicted survival times
y	Observed response/survival times
order_indices	Order of observations when partitioned to match "status" to "response"
family	Weibull AFT family; unused here and retained for interface compatibility.
dispersion	Estimated dispersion parameter (sigma^2 = scale^2). The lgspline framework stores and passes dispersion (sigma^2); the Weibull scale (sigma) matching survreg$scale is sqrt(dispersion).
observation_weights	Weights of observations submitted to function
status	Censoring indicator (1 = event, 0 = censored) Indicates whether an event of interest occurred (1) or the observation was right-censored (0). In survival analysis, right-censoring occurs when the full survival time is unknown, typically because the study ended or the subject was lost to follow-up before the event of interest occurred.

Details

This function generates weights used in constructing the information matrix after unconstrained estimates have been found. Specifically, it is used in the construction of the \textbf{U} and \textbf{G} matrices following initial unconstrained parameter estimation.

These weights are analogous to the variance terms in generalized linear models (GLMs). Like logistic regression uses \mu(1-\mu), Poisson regression uses e^{\mu}, and Linear regression uses constant weights, Weibull AFT models use \exp((\log y - \log \mu)/\sigma) where \sigma = \sqrt{\text{dispersion}} is the scale parameter.

Value

Numeric vector of working weights for the information matrix, including observation weights when finite and a fallback of 1s when the natural Weibull weights are non-finite.

Examples

## Demonstration of glm weight function in constrained model estimation
set.seed(1234)
n <- 1000
t1 <- rnorm(n)
t2 <- rbinom(n, 1, 0.5)

## Generate survival times
lambda <- exp(0.5 * t1 + 0.3 * t2)
yraw <- rexp(n, rate = 1/lambda)

## Introduce right-censoring
status <- rbinom(n, 1, 0.75)
y <- ifelse(status, yraw, runif(length(yraw), 0, yraw))

## Fit model demonstrating use of custom glm weight function
model_fit <- lgspline(y ~ spl(t1) + t2,
                      data.frame(y = y, t1 = t1, t2 = t2),
                      unconstrained_fit_fxn = unconstrained_fit_weibull,
                      family = weibull_family(),
                      need_dispersion_for_estimation = TRUE,
                      dispersion_function = weibull_dispersion_function,
                      glm_weight_function = weibull_glm_weight_function,
                      schur_correction_function = weibull_schur_correction,
                      status = status,
                      opt = FALSE,
                      K = 1)

print(summary(model_fit))

lgspline documentation built on May 8, 2026, 5:07 p.m.