Description Usage Arguments Details Value Initial Values References Examples
Model for Survival Analysis of Unbalanced Clusters using Archimedes Copula's.
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data 
Input dataframe containing all variables. 
time 
Which variable name is the time covariate? 
status 
The status indicator, 0=alive, 1=dead. 
clusters 
The variable name describing the clusters. 
covariates 
A vector of one or more covariates to be included in the model. Categorical covariates should be a factor in this data frame. 
stage 
Denotes whether the onestage ( 
copula 
Denotes which copula to use. Can be 
marginal 
Denotes which marginal survival function to use. Can be 
n.piecewise 
For 
init.values 
A List object which contains the initial values for the parameters. This depends on the choice of the parameters 
baselevels 
Denotes the level of a categorical covariate in the 
verbose 
Print some inbetween results as well as computation progress. 
summary.print 
Logical value to print a short summary at the end of the computation. 
optim.method 
Method used for optimization in onestage estimation or in second stage of twostage estimation. Can either be 
optim.bounds 
Lower and upper bounds on the variables for the 
All copula models, regardless the choice of the marginal survival function, can be fitted with the twostage approach.
The onestage approach, however, is only available for the "Weibull"
and "PiecewiseExp"
marginal survival functions choice.
The onestage approach is preferred as it leads to less biased estimates in the case of small sample sizes.
When no initial values for the parameters are given, initial values for the optimisation procedure will be derived in the following way.
Initial values for the marginal survival functions are obtained by estimating the parameters marginally, i.e., without taking into consideration the copula function.
In the twostage approach, these estimates are fixed, whereas in the onestage approach, they are parameters in the optimisation.
The association parameter is set arbitrarily to 0.5 for "Clayton"
0.55 for "GH"
.
An initial value for the association parameter can be supplied as c(theta=value)
Initial values for the marginal survival function parameters can only be supplied for the "Weibull"
choice as c(lambda=value,rho=value)
Initial values for the beta parameters from continuous covariates can be supplied as c(beta_variablename=value)
Initial values for the beta parameters from categorical covariates can be supplied as c(beta_variablename_level=value)
S3 List object
Parameters
: Data frame containing estimates and standard errors of parameters.
Kendall_Tau
: Vector containing estimate and standard error of Kendall's Tau.
ParametersCov
: If available, covariance matrix of the parameters. For 2stage approaches this is only available for the Weibull marginal.
logllh
: The loglikelihood value.
parameter.call
: A list containing all arguments given to the function, as well as the initial parameter values and the elapsed time.
Initial values are provided in a list()
object as following:
list(lambda=c(0.5),
rho=0.5,
theta=0.5
beta=c(0.5))
Not all initial values need to be provided! If only some of the initial values are provided, all initial parameters will be estimated (see Details), but the provided initial values will overwrite the generated ones.
Depending on the stage
and marginal
parameter,
different initial values can be provided:
OneStage:
Weibull Marginal
lambda
: Single initial value for marginal survival function.
rho
: Single initial value for marginal survival function.
theta
: Single initial value for the association parameter.
beta:
Vector of multiple initial values for the continuous/categorical covariates.
Piecewise Exponential Marginal
lambda
: Vector of multiple initial value for marginal survival function. The length of this vector should be the number of n.piecewise
(see note down below).
theta
: Single initial value for the association parameter.
beta:
Vector of multiple initial values for the continuous/categorical covariates.
TwoStage:
Weibull or Cox Marginal
theta
: Single initial value for the association parameter.
Piecewise Exponential Marginal
lambda
: Vector of multiple initial value for marginal survival function. The length of this vector should be the number of n.piecewise
(see note down below).
theta
: Single initial value for the association parameter.
beta:
Vector of multiple initial values for the continuous/categorical covariates.
Initial Values Boundaries
λ>0
ρ>0
θ:
GH Copula: θ>0 & θ<1
Clayton Copula: θ>0
Note on lambda
and beta
For the Piecewise Exponential marginal, multiple λ's should be provided
in the lambda
slot as a vector. This vector can have a maximum length of the
number of pieces there were chosen (n.piecewise
). In the scenario not all λ's
are provided, only the first few λ's are overwritten.
In the beta
slot, as many β's should be provided as there are
covariates
(as well as in the same order of the covariates
parameter). If one of the covariates is a
categorical variable (factor
), multiple β's should be provided for
a single covariate (namely the number of levels minus 1). In the scenario not all β's
are provided, only the first few β's are overwritten.
Prenen L, Braekers R, Duchateau L (2017). Extending the Archimedean copula methodology to model multivariate survival data grouped in clusters of variable size. Journal of the Royal Statistical Society, 6, 124.
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## Not run:
data("insem",package="Sunclarco")
result1 < SunclarcoModel(data=insem,time="Time",status="Status",
clusters="Herd",covariates="Heifer",
stage=1,copula="Clayton",marginal="Weibull")
summary(result1)
result2 < SunclarcoModel(data=insem,time="Time",status="Status",
clusters="Herd",covariates="Heifer",
stage=1,copula="GH",marginal="PiecewiseExp")
summary(result2)
result3 < SunclarcoModel(data=kidney,time="time",status="status",
clusters="id",covariates="sex",
stage=2,copula="Clayton",marginal="Weibull")
summary(result3)
result4 < SunclarcoModel(data=kidney,time="time",status="status",
clusters="id",covariates="sex",
stage=2,copula="Clayton",marginal="Cox")
summary(result4)
## End(Not run)

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