| Type: | Package |
| Title: | Estimation and Additional Tools for Alternative Shared Frailty Models |
| Version: | 1.13 |
| Date: | 2025-04-05 |
| Author: | Diego Gallardo [aut, cre], Marcelo Bourguignon [aut], John Santibanez [ctb] |
| Maintainer: | Diego Gallardo <dgallardo@ubiobio.cl> |
| Description: | Provide estimation and data generation tools for some new multivariate frailty models. This version includes the gamma, inverse Gaussian, weighted Lindley, Birnbaum-Saunders, truncated normal, mixture of inverse Gaussian, mixture of Birnbaum-Saunders and generalized exponential as the distribution for the frailty terms. For the basal model, it is considered a parametric approach based on the exponential, Weibull and the piecewise exponential distributions as well as a semiparametric approach. For details, see Gallardo and Bourguignon (2025) <doi:10.1002/bimj.70044> and Gallardo et al. (2024) <doi:10.1007/s11222-024-10458-w>. |
| Depends: | R (≥ 4.0.0), stats |
| Imports: | survival, pracma, expint, msm |
| Suggests: | frailtyHL |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | no |
| Packaged: | 2025-04-05 00:39:26 UTC; Diego |
| Repository: | CRAN |
| Date/Publication: | 2025-04-05 15:10:06 UTC |
Computes the baseline cumulative hazard function.
Description
Provides the baseline cumulative hazard function (\Lambda_0) for an object with extrafrail class.
Usage
baseCH(t, fit)
Arguments
t |
the vector of times for which the baseline cumulative hazard function should be computed. |
fit |
an object with extrafrail class. |
Details
Provides the baseline cumulative hazard function. When the baseline distribution is assumed as
the Weibull model, this function is \Lambda_0(t)=\lambda t^{\rho}. For the piecewise
exponential model, this function is \Lambda_0(t)=\sum_{j=1}^L \lambda_j \nabla_j(t),
where \nabla_j(t)=0, if t<a_{j-1}, \nabla_j(t)=t-a_{j-1}, if a_{j-1}\leq t < a_{j}
and \nabla_j(t)=a_j-a_{j-1}, if t\geq a_{j}, with a=(a_0=0, a_1, \ldots, a_{j-1}), the
corresponding partition time.
Value
a vector with the same length that t, including the baseline cumulative hazard function related to t.
Author(s)
Diego Gallardo and Marcelo Bourguignon.
References
Gallardo, D.I., Bourguignon, M. (2022) The multivariate weighted Lindley frailty model for cluster failure time data. Submitted.
Examples
#require(frailtypack)
require(survival)
data(rats, package="frailtyHL")
#Example for WL frailty model
fit.WL <- frailty.fit(survival::Surv(time, status) ~ rx + survival::cluster(litter),
dist.frail="WL", data = rats)
baseCH(c(80,90,100),fit.WL)
Fitted different shared frailty models
Description
frailty.fit computes the maximum likelihood estimates based on the EM algorithm for the shared gamma, inverse gaussian, weighted Lindley, Birnbaum-Saunders, truncated normal, mixture of inverse gaussian and mixture of Birbaum-Saunders frailty models.
Usage
frailty.fit(formula, data, dist.frail="gamma", dist = "np", prec = 1e-04,
max.iter = 1000, part=NULL)
Arguments
formula |
A formula that contains on the left hand side an object of the type Surv and on the right hand side a +cluster(id) statement, possibly with the covariates definition. |
data |
A data.frame in which the formula argument can be evaluated |
dist.frail |
the distribution assumed for the frailty. Supported values: gamma (GA also is valid), IG (inverse gaussian), WL (weighted Lindley), BS (Birnbaum-Saunders), TN (truncated normal), MIG (mixture of IG), MBS (mixture of BS) and GE (generalized exponential). |
dist |
the distribution assumed for the basal model. Supported values: weibull, pe (piecewise exponential), exponential and np (non-parametric). |
prec |
The convergence tolerance for parameters. |
max.iter |
The maximum number of iterations. |
part |
partition time (only for piecewise exponential distribution). |
Details
For the weibull, exponential and piecewise exponential distributions as the basal model, the M1-step is performed using the optim function. For the non-parametric case, the M1-step is based on the coxph function from the survival package.
Value
an object of class "extrafrail" is returned. The object returned for this functions is a list containing the following components:
coefficients |
A named vector of coefficients |
se |
A named vector of the standard errors for the estimated coefficients. |
t |
The vector of times. |
delta |
The failure indicators. |
id |
A variable indicating the cluster which belongs each observation. |
x |
The regressor matrix based on cov.formula (without intercept term). |
dist |
The distribution assumed for the basal model. |
dist.frail |
The distribution assumed for the frailty variable. |
tau |
The Kendall's tau coefficient. |
logLik |
The log-likelihood function (only when the Weibull model is specified for the basal distribution). |
Lambda0 |
The observed times and the associated cumulative hazard function (only when the non-parametric option is specified for the basal distribution) |
part |
the partition time (only for piecewise exponential model). |
Author(s)
Diego Gallardo, Marcelo Bourguignon and John Santibanez.
References
Gallardo, D.I., Bourguignon, M. (2022) The shared weighted Lindley frailty model for cluster failure time data. Biometrical journal, 67, e70044.
Gallardo, D.I., Bourguignon, M., Romeo, J. (2024) Birnbaum-Saunders frailty regression models for clustered survival data. Statistics and Computing, 34, 141.
Examples
require(survival)
#require(frailtyHL)
data(rats, package="frailtyHL")
#Fit for WL frailty model
fit.WL <- frailty.fit(survival::Surv(time, status)~ rx+ survival::cluster(litter),
dist.frail="WL", data = rats)
summary(fit.WL)
#Fit for gamma frailty model
fit.GA <- frailty.fit(survival::Surv(time, status) ~ rx + survival::cluster(litter),
dist.frail="gamma", data = rats)
summary(fit.GA)
Generated random variables from the weighted Lindley distribution.
Description
Generated random variables from the weighted Lindley distribution with mean 1.
Usage
rWL(n, theta = 1)
Arguments
n |
number of observations. If length(n) > 1, the length is taken to be the number required. |
theta |
variance of the variable. |
Details
The weighted Lindley distribution has probability density function
f(z;\theta)=\frac{\theta}{2\Gamma(\theta)}a_{\theta}^{-b_{\theta}-1}z^{b_{\theta}-1}(1+z)\exp\left(-\frac{z}{a_{\theta}}\right), \quad z, \theta>0,
where a_{\theta}=\frac{\theta(\theta+4)}{2(\theta+2)} and b_{\theta}=\frac{4}{\theta(\theta+4)}. Under
this parametrization, E(Z)=1 and Var(Z)=\theta.
Value
a vector of length n with the generated values.
Author(s)
Diego Gallardo and Marcelo Bourguignon.
References
Gallardo, D.I., Bourguignon, M. (2022) The multivariate weighted Lindley frailty model for cluster failure time data. Submitted.
Examples
rWL(10, theta=0.5)
Print a summary for a object of the "extrafrail" class.
Description
Summarizes the results for a object of the "extrafrail" class.
Usage
## S3 method for class 'extrafrail'
summary(object, ...)
Arguments
object |
an object of the "extrafrail" class. |
... |
for extra arguments. |
Details
Supported frailty models are: - gamma frailty model - inverse gaussian frailty model - weighted frailty model - Birnbaum-Saunders frailty model - Truncated normal frailty model - Mixture of inverse gaussian frailty model - Mixture of Birnbaum-Saunders frailty model
Value
A complete summary for the coefficients extracted from a "extrafrail" object.
Author(s)
Diego Gallardo and Marcelo Bourguignon.
References
Gallardo and Bourguignon (2022).
Examples
#require(frailtyHL)
require(survival)
data(rats, package="frailtyHL")
fit <- frailty.fit(survival::Surv(time, status) ~ rx + survival::cluster(litter),
dist.frail="WL", data = rats)
summary(fit)