weibull_qp_score_function: Compute Gradient of Log-Likelihood of Weibull Accelerated...

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Compute Gradient of Log-Likelihood of Weibull Accelerated Failure Model

Description

Calculates the gradient of log-likelihood for a Weibull accelerated failure time (AFT) survival model, supporting right-censored survival data.

Usage

weibull_qp_score_function(
  X,
  y,
  mu,
  order_list,
  dispersion,
  VhalfInv,
  observation_weights,
  status
)

Arguments

X	Design matrix
y	Response vector
mu	Predicted mean vector
order_list	List of observation indices per partition
dispersion	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).
VhalfInv	Inverse square root of correlation matrix; unused here and retained for interface compatibility.
observation_weights	Observation weights
status	Censoring indicator (1 = event, 0 = censored)

Details

Needed if using "blockfit", correlation structures, or quadratic programming with Weibull AFT models.

The gradient is computed on a scale that omits the 1/sigma prefactor. Specifically, the true score is (1/sigma) * X^T diag(w) (exp(z) - status), but both this function and the corresponding information matrix used internally omit 1/sigma and 1/sigma^2 respectively, so the Newton-Raphson step G*u remains correct. This matches the convention in unconstrained_fit_weibull.

Value

Numeric column vector representing the gradient with respect to coefficients.

Examples

set.seed(1234)
t1 <- rnorm(1000)
t2 <- rbinom(1000, 1, 0.5)
yraw <- rexp(exp(0.01*t1 + 0.01*t2))
status <- rbinom(1000, 1, 0.25)
yobs <- ifelse(status, runif(length(yraw), 0, yraw), yraw)
df <- data.frame(
  y = yobs,
  t1 = t1,
  t2 = t2
)

## Example using blockfit for t2 as a linear term - output does not look
# different, but internal methods used for fitting change
model_fit <- lgspline(y ~ spl(t1) + t2,
                      df,
                      unconstrained_fit_fxn = unconstrained_fit_weibull,
                      family = weibull_family(),
                      need_dispersion_for_estimation = TRUE,
                      qp_score_function = weibull_qp_score_function,
                      dispersion_function = weibull_dispersion_function,
                      glm_weight_function = weibull_glm_weight_function,
                      schur_correction_function = weibull_schur_correction,
                      K = 1,
                      blockfit = TRUE,
                      opt = FALSE,
                      status = status,
                      verbose = TRUE)

print(summary(model_fit))

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