weibull.frailty: Weibull Model with Gamma Frailties

In JM: Joint Modeling of Longitudinal and Survival Data

Weibull Model with Gamma Frailties

Description

Fits a Weibull model with Gamma frailties for multivariate survival data under maximum likelihood

Usage

weibull.frailty(formula = formula(data), data = parent.frame(), 
    id = "id", subset, na.action, init, control = list())

Arguments

formula	an object of class formula: a symbolic description of the model to be fitted. The response must be a survival object as returned by function Surv().
data	an optional data frame containing the variables specified in the model.
id	either a character string denoting a variable name in data or a numeric vector specifying which event times belong to the same cluster (e.g., hospital, patient, etc.).
subset	an optional vector specifying a subset of observations to be used in the fitting process.
na.action	what to do with missing values.
init	a numeric vector of length p + 3 of initial values. The first p elements should correspond to the regression coefficients for the covariates, and the last 3 to log-scale, log-shape, and log-frailty-variance, respectively. See Details.
control	a list of control values with components: optimizer a character string indicating which optimizer to use; options are "optim" (default) and "nlminb". parscale the parscale control argument for optim(), or the scale argument for nlminb(). It should be a numeric vector of length equal to the number of parameters. Default is 0.01 for all parameters. maxit the maximum number of iterations. Default is 500. numeriDeriv a character string indicating which type of numerical derivative to use to compute the Hessian matrix; options are "fd" denoting the forward difference approximation, and "cd" (default) denoting the central difference approximation. eps.Hes tolerance value used in the numerical derivative method. Default is 1e-03.

Details

The fitted model is defined as follows:

λ(t_i | ω_i) = λ_0(t_i) ω_i \exp(x_i^T β),

where i denotes the subject, λ(.) denotes the hazard function, conditionally on the frailty ω_i, x_i is a vector of covariates with corresponding regression coefficients β, and λ_0(.) is the Weibull baseline hazard defined as λ_0(t) = shape * scale * t^{shape -1}. Finally, for the frailties we assume ω_i ~ Gamma(η, η), with η^{-1} denoting the unknown variance of ω_i's.

Value

an object of class weibull.frailty with components:

coefficients	a list with the estimated coefficients values. The components of this list are: betas, scale, shape, and var.frailty, and correspond to the coefficients with the same name.
hessian	the hessian matrix at convergence. For the shape, scale, and var-frailty parameters the Hessian is computed on the log scale.
logLik	the log-likelihood value.
control	a copy of the control argument.
y	an object of class Surv containing the observed event times and the censoring indicator.
x	the design matrix of the model.
id	a numeric vector specifying which event times belong to the same cluster.
nam.id	the value of argument id, if that was a character string.
terms	the term component of the fitted model.
data	a copy of data or the created model.frame.
call	the matched call.

Note

weibull.frailty() currently supports only right-censored data.

Author(s)

Dimitris Rizopoulos [e-mail]

Examples

weibull.frailty(Surv(time, status) ~ age + sex, kidney)

JM documentation built on Aug. 8, 2022, 5:09 p.m.