weibull.frailty {JM} | R Documentation |
Fits a Weibull model with Gamma frailties for multivariate survival data under maximum likelihood
weibull.frailty(formula = formula(data), data = parent.frame(), id = "id", subset, na.action, init, control = list())
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:
|
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.
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. |
weibull.frailty()
currently supports only right-censored data.
Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl
weibull.frailty(Surv(time, status) ~ age + sex, kidney)