weibull.frailty {JM}R Documentation

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 | omega_i) = λ_0(t_i) omega_i exp(x_i^T β),

where i denotes the subject, λ(.) denotes the hazard function, conditionally on the frailty omega_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 omega_i ~ Gamma(eta, eta), with eta^{-1} denoting the unknown variance of omega_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 d.rizopoulos@erasmusmc.nl

Examples

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

[Package JM version 0.2-2 Index]