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 |
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 |
control |
a list of control values with components:
|
Details
The fitted model is defined as follows:
\lambda(t_i | \omega_i) = \lambda_0(t_i) \omega_i \exp(x_i^T \beta),
where i
denotes the subject, \lambda(\cdot)
denotes the hazard function, conditionally on the frailty \omega_i
, x_i
is a vector of covariates with corresponding regression
coefficients \beta
, and \lambda_0(\cdot)
is the Weibull baseline hazard defined as \lambda_0(t) = shape *
scale * t^{shape -1}
. Finally, for the frailties we assume \omega_i \sim 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: |
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 |
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 right-censored data.
Author(s)
Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl
Examples
weibull.frailty(Surv(time, status) ~ age + sex, kidney)