Fit an Accelerated Failure Time Model with Non-Proportional Hazards

Fits the Anderson (1991) AFT regression model where both location (mu) and scale (sigma) are functions of covariates, and sigma can depend on mu through a theta polynomial.

Usage

vldaft(
  formula,
  data,
  dist = c("weibull", "logistic", "normal", "cauchy", "gamma"),
  theta = 0L,
  theta_vars = NULL,
  nu = 1,
  init = NULL,
  control = list(),
  adjust = TRUE,
  backend = c("c", "rust")
)

Arguments

formula: A formula of the form Surv(time, status) ~ loc_vars | scale_vars. Left of | specifies location (mu) covariates, right specifies scale (gamma) covariates. If no | is present, all covariates enter the location model and scale has intercept only.
data: A data frame.
dist: Character string specifying the error distribution: "weibull" (default), "logistic", "normal", "cauchy", or "gamma".
theta: Integer, order of the theta polynomial linking log(sigma) to mu. 0 = no coupling (default), 1 = linear in mu, 2 = quadratic, etc.
theta_vars: A one-sided formula specifying which location covariates form mu* (the mu that feeds into the theta polynomial for sigma). Default NULL means all location covariates.
nu: Numeric, shape parameter for the gamma distribution (only used when dist = "gamma").
init: Numeric vector of initial parameter values, or NULL for zeros.
control: A list of control parameters. See Details.
adjust: Logical, whether to center covariates (default TRUE).
backend: Character, which computation backend to use: "c" (default) or "rust".

Value

An object of class "vldaft".

Details

The model assumes $$\log(T) = \mu + \sigma \cdot \varepsilon$$ where the location is a linear function of covariates, $$\mu = \beta_0 + \beta_1 x_1 + \cdots + \beta_p x_p$$ and the log-dispersion can depend on covariates and on the location: $$\log(\sigma) = \gamma_0 + \gamma_1 z_1 + \cdots + \gamma_q z_q + \theta_1 \mu^{*} + \theta_2 \mu^{*2} + \cdots$$ Here $\mu^{*} = \mu - \bar{\mu}$ is the centered location. When $\theta_1 = 0$, this reduces to the standard linear location AFT model with proportional hazards under a Weibull distribution. The error distribution $F$ can be Weibull (extreme value), logistic, normal, Cauchy, or gamma.

Control parameters:

acc: Convergence accuracy (default 0.0001)
maxiter: Maximum Newton-Raphson iterations (default 50)
maxhalv: Maximum step halvings (default 20)

References

Anderson, K.M. (1991). A nonproportional hazards Weibull accelerated failure time regression model. Biometrics, 47, 281-288.