Weibull Model with Gamma Frailties
Description
Fits a Weibull model with Gamma frailties for multivariate survival data under maximum likelihood
Usage
1 2  weibull.frailty(formula = formula(data), data = parent.frame(),
id = "id", subset, na.action, init, control = list())

Arguments
formula 
an object of class 
data 
an optional data frame containing the variables specified in the model. 
id 
either a character string denoting a variable name in 
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 logscale, logshape, and logfrailtyvariance, respectively. See Details. 
control 
a list of control values with components:

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: 
hessian 
the hessian matrix at convergence. For the shape, scale, and varfrailty parameters the Hessian is computed on the log scale. 
logLik 
the loglikelihood value. 
control 
a copy of the 
y 
an object of class 
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 
terms 
the term component of the fitted model. 
data 
a copy of 
call 
the matched call. 
Note
weibull.frailty()
currently supports only rightcensored data.
Author(s)
Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl
Examples
1  weibull.frailty(Surv(time, status) ~ age + sex, kidney)
