weibull_dispersion_function: Estimate Weibull Dispersion for Accelerated Failure Time...

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Estimate Weibull Dispersion for Accelerated Failure Time Model

Description

Computes the dispersion parameter (sigma^2 = scale^2) for a Weibull accelerated failure time (AFT) model, supporting right-censored survival data. The returned value is sigma^2, where sigma is the Weibull scale parameter matching survreg$scale.

This both provides a tool for actually fitting Weibull AFT Models, and boilerplate code for users who wish to incorporate Lagrangian multiplier smoothing splines into their own custom models.

Usage

weibull_dispersion_function(
  mu,
  y,
  order_indices,
  family,
  observation_weights,
  VhalfInv,
  status
)

Arguments

mu	Predicted survival times
y	Observed response/survival times
order_indices	Indices to align status with response
family	Weibull AFT model family specification; unused here and retained for interface compatibility.
observation_weights	Optional observation weights
VhalfInv	Inverse square root of the correlation matrix; unused here and retained for interface compatibility.
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.

Value

Dispersion estimate (sigma^2) for the Weibull AFT model, i.e., the squared scale parameter. The Weibull scale (sigma) matching survreg$scale is sqrt() of this value.

See Also

weibull_scale for the underlying scale estimation function

Examples

## Simulate survival data with covariates
set.seed(1234)
n <- 1000
t1 <- rnorm(n)
t2 <- rbinom(n, 1, 0.5)

## Generate survival times with Weibull-like structure
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))

## Example of using dispersion function
mu <- mean(y)
order_indices <- seq_along(y)
weights <- rep(1, n)

## Estimate dispersion (= scale^2 = sigma^2)
dispersion_est <- weibull_dispersion_function(
  mu = mu,
  y = y,
  order_indices = order_indices,
  family = weibull_family(),
  observation_weights = weights,
  VhalfInv = NULL,
  status = status
)

print(dispersion_est)          # sigma^2
print(sqrt(dispersion_est))    # sigma (comparable to survreg$scale)

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