multivPenal: Fit a multivariate frailty model for two types of recurrent...
In frailtypack: Shared, Joint (Generalized) Frailty Models; Surrogate Endpoints
multivPenal R Documentation
Fit a multivariate frailty model for two types of recurrent events and a
terminal event.
Description
Fit a multivariate frailty model for two types of recurrent events with a
terminal event using a penalized likelihood estimation on the hazard
function or a parametric estimation. Right-censored data are allowed.
Left-truncated data and stratified analysis are not possible. Multivariate
frailty models allow studying, with a joint model, three survival dependent
processes for two types of recurrent events and a terminal event.
Multivariate joint frailty models are applicable in mainly two settings.
First, when focus is on the terminal event and we wish to account for the
effect of previous endogenous recurrent event. Second, when focus is on a
recurrent event and we wish to correct for informative censoring.
The multivariate frailty model for two types of recurrent events with a
terminal event is (in the calendar or time-to-event timescale):
where r0l(t), (l∈{1,3}) and r0(t) are
respectively the recurrent and terminal event baseline hazard functions, and
\beta1,\beta2,\beta3 the regression coefficient vectors associated
with Zi(t) the covariate vector. The covariates could be different
for the different event hazard functions and may be time-dependent. We
consider that death stops new occurrences of recurrent events of any type,
hence given t>D, dNR(l)*(t), (l∈{1,2}) takes the value 0.
Thus, the terminal and the two recurrent event processes are not independent
or even conditional upon frailties and covariates. We consider the hazard
functions of recurrent events among individuals still alive.
components in the above multivariate frailty model are linked together by
two Gaussian and correlated random effects ui,vi:
(ui,vi)T ~ N(0,\Sigmauv), with
Dependencies between these three types of event are taken into account by
two correlated random effects and parameters \theta1,\theta2 the
variance of the random effects and \alpha1,\alpha2 the coefficients
for these random effects into the terminal event part. If \alpha1 and
\theta1 are both significantly different from 0, then the recurrent
events of type 1 and death are significantly associated (the sign of the
association is the sign of \alpha1). If \alpha2 and
\theta2 are both significantly different from 0, then the recurrent
events of type 2 and death are significantly associated (the sign of the
association is the sign of \alpha2). If \rho, the correlation
between the two random effects, is significantly different from 0, then the
recurrent events of type 1 and the recurrent events of type 2 are
significantly associated (the sign of the association is the sign of
\rho).
Usage
multivPenal(formula, formula.Event2, formula.terminalEvent, data, initialize
= TRUE, recurrentAG = FALSE, n.knots, kappa, maxit = 350, hazard =
"Splines", nb.int, print.times = TRUE)
Arguments
formula
a formula object, with the response for the first recurrent
event on the left of a \sim operator, and the terms on the right. The
response must be a survival object as returned by the 'Surv' function like
in survival package. Interactions are possible using * or :.
formula.Event2
a formula object, with the response for the second
recurrent event on the left of a \sim operator, and the terms on the
right. The response must be a survival object as returned by the 'Surv'
function like in survival package. Interactions are possible using * or :.
formula.terminalEvent
a formula object, with the response for the
terminal event on the left of a \sim operator, and the terms on the
right. The response must be a survival object as returned by the 'Surv'
function like in survival package.
data
a 'data.frame' with the variables used in 'formula',
'formula.Event2' and 'formula.terminalEvent'.
initialize
Logical value to initialize regression coefficients and
baseline hazard functions parameters. When the estimation is semi-parametric
with splines, this initialization produces also values for smoothing
parameters (by cross validation). When initialization is requested, the
program first fit two shared frailty models (for the two types of recurrent
events) and a Cox proportional hazards model (for the terminal event).
Default is TRUE.
recurrentAG
Logical value. Is Andersen-Gill model fitted? If so
indicates that recurrent event times with the counting process approach of
Andersen and Gill is used. This formulation can be used for dealing with
time-dependent covariates. The default is FALSE.
n.knots
integer vector of length 3 (for the three outcomes) giving
the number of knots to use. First is for the recurrent of type 1, second is
for the recurrent of type 2 and third is for the terminal event hazard
function. Value required in the penalized likelihood estimation. It
corresponds to the (n.knots+2) splines functions for the approximation of
the hazard or the survival functions. Number of knots must be between 4 and
20. (See Note)
kappa
vector of length 3 (for the three outcomes) for positive
smoothing parameters in the penalized likelihood estimation. First is for
the recurrent of type 1, second is for the recurrent of type 2 and third is
for the terminal event hazard function. The coefficient kappa of the
integral of the squared second derivative of hazard function in the fit
(penalized log likelihood). Initial values for the kappas can be obtained
with the option "initialize=TRUE". We advise the user to identify several
possible tuning parameters, note their defaults and look at the sensitivity
of the results to varying them. Value required.(See Note)
maxit
maximum number of iterations for the Marquardt algorithm.
Default is 350.
hazard
Type of hazard functions: "Splines" for semi-parametric hazard
functions with the penalized likelihood estimation, "Piecewise-per" for
piecewise constant hazard function using percentile, "Piecewise-equi" for
piecewise constant hazard function using equidistant intervals, "Weibull"
for parametric Weibull function. Default is "Splines".
nb.int
An integer vector of length 3 (for the three outcomes). First
is the Number of intervals (between 1 and 20) for the recurrent of type 1
parametric hazard functions ("Piecewise-per", "Piecewise-equi"). Second is
the Number of intervals (between 1 and 20) for the recurrent of type 2
parametric hazard functions ("Piecewise-per", "Piecewise-equi"). Third is
Number of intervals (between 1 and 20) for the death parametric hazard
functions ("Piecewise-per", "Piecewise-equi")
print.times
a logical parameter to print iteration process. Default
is TRUE.
Value
Parameters estimates of a multivariate joint frailty model, more
generally a 'multivPenal' object. Methods defined for 'multivPenal' objects
are provided for print, plot and summary. The following components are
included in a 'multivPenal' object for multivariate Joint frailty models.
b
sequence of the corresponding estimation of the splines
coefficients, the random effects variances, the coefficients of the
frailties and the regression coefficients.
call
The code used for
fitting the model.
n
the number of observations used in the fit.
groups
the number of subjects used in the fit.
n.events
the
number of recurrent events of type 1 observed in the fit.
n.events2
the number of the recurrent events of type 2 observed in
the fit.
n.deaths
the number of deaths observed in the fit.
loglikPenal
the complete marginal penalized log-likelihood in the
semi-parametric case.
loglik
the marginal log-likelihood in the
parametric case.
LCV
the approximated likelihood cross-validation
criterion in the semi parametric case (with H minus the converged Hessian
matrix, and l(.) the full
log-likelihood.
LCV=\frac{1}{n}(trace(H^{-1}_{pl}H) - l(.))
)
AIC
the Akaike information Criterion for the parametric
case.
AIC=\frac{1}{n}(np - l(.))
theta1
variance of the
frailty parameter for recurrences of type 1 (\bold{Var}(u_i))
theta2
variance of the frailty parameter for recurrences of type 2
(\bold{Var}(v_i))
alpha1
the coefficient associated with the
frailty parameter u_i in the terminal hazard function.
alpha2
the coefficient associated with the frailty parameter
v_i in the terminal hazard function.
rho
the correlation
coefficient between u_i and v_i
npar
number of
parameters.
coef
the regression coefficients.
nvar
A vector
with the number of covariates of each type of hazard function as
components.
varH
the variance matrix of all parameters before
positivity constraint transformation (theta, the regression coefficients and
the spline coefficients). Then, the delta method is needed to obtain the
estimated variance parameters.
varHIH
the robust estimation of the
variance matrix of all parameters (theta, the regression coefficients and
the spline coefficients).
formula
the formula part of the code used
for the model for the recurrent event.
formula.Event2
the formula
part of the code used for the model for the second recurrent event.
formula.terminalEvent
the formula part of the code used for the model
for the terminal event.
x1
vector of times for hazard functions of
the recurrent events of type 1 are estimated. By default
seq(0,max(time),length=99), where time is the vector of survival times.
lam1
matrix of hazard estimates and confidence bands for recurrent
events of type 1.
xSu1
vector of times for the survival function of
the recurrent event of type 1.
surv1
matrix of baseline survival
estimates and confidence bands for recurrent events of type 1.
x2
vector of times for the recurrent event of type 2 (see x1 value).
lam2
the same value as lam1 for the recurrent event of type 2.
xSu2
vector of times for the survival function of the recurrent event
of type 2
surv2
the same value as surv1 for the recurrent event of
type 2.
xEnd
vector of times for the terminal event (see x1 value).
lamEnd
the same value as lam1 for the terminal event.
xSuEnd
vector of times for the survival function of the terminal
event
survEnd
the same value as surv1 for the terminal event.
median1
The value of the median survival and its confidence bands for the recurrent event of type 1.
median2
The value of the median survival and its confidence bands for the recurrent event of type 2.
medianEnd
The value of the median survival and its confidence bands for the terminal event.
type.of.Piecewise
Type of Piecewise hazard functions (1:"percentile",
0:"equidistant").
n.iter
number of iterations needed to converge.
type.of.hazard
Type of hazard functions (0:"Splines", "1:Piecewise",
"2:Weibull").
n.knots
a vector with number of knots for estimating
the baseline functions.
kappa
a vector with the smoothing parameters
in the penalized likelihood estimation corresponding to each baseline
function as components.
n.knots.temp
initial value for the number of
knots.
zi
splines knots.
time
knots for Piecewise hazard
function for the recurrent event of type 1.
timedc
knots for
Piecewise hazard function for the terminal event.
time2
knots for
Piecewise hazard function for the recurrent event of type 2.
noVar
indicator vector for recurrent, death and recurrent 2
explanatory variables.
nvarRec
number of the recurrent of type 1
explanatory variables.
nvarEnd
number of death explanatory
variables.
nvarRec2
number of the recurrent of type 2 explanatory
variables.
nbintervR
Number of intervals (between 1 and 20) for the
the recurrent of type 1 parametric hazard functions ("Piecewise-per",
"Piecewise-equi").
nbintervDC
Number of intervals (between 1 and 20)
for the death parametric hazard functions ("Piecewise-per",
"Piecewise-equi").
nbintervR2
Number of intervals (between 1 and 20)
for the the recurrent of type 2 parametric hazard functions
("Piecewise-per", "Piecewise-equi").
istop
Vector of the convergence
criteria.
shape.weib
shape parameters for the Weibull hazard
function.
scale.weib
scale parameters for the Weibull hazard
function.
martingale.res
martingale residuals for each cluster (recurrent of
type 1).
martingale2.res
martingale residuals for each cluster
(recurrent of type 2).
martingaledeath.res
martingale residuals for
each cluster (death).
frailty.pred
empirical Bayes prediction of the
first frailty term.
frailty2.pred
empirical Bayes prediction of the
second frailty term.
frailty.var
variance of the empirical Bayes
prediction of the first frailty term.
frailty2.var
variance of the
empirical Bayes prediction of the second frailty term.
frailty.corr
Correlation between the empirical Bayes prediction of
the two frailty.
linear.pred
linear predictor: uses Beta'X + ui in
the multivariate frailty models.
linear2.pred
linear predictor: uses
Beta'X + vi in the multivariate frailty models.
lineardeath.pred
linear predictor for the terminal part form the
multivariate frailty models: Beta'X + alpha1 ui + alpha2 vi
global_chisq
Recurrent event of type 1: a vector with the values of
each multivariate Wald test.
dof_chisq
Recurrent event of type 1: a
vector with the degree of freedom for each multivariate Wald test.
global_chisq.test
Recurrent event of type 1: a binary variable equals
to 0 when no multivariate Wald is given, 1 otherwise.
p.global_chisq
Recurrent event of type 1: a vector with the p-values
for each global multivariate Wald test.
names.factor
Recurrent event
of type 1: Names of the "as.factor" variables.
global_chisq2
Recurrent event of type 2: a vector with the values of
each multivariate Wald test.
dof_chisq2
Recurrent event of type 2: a
vector with the degree of freedom for each multivariate Wald test.
global_chisq.test2
Recurrent event of type 2: a binary variable
equals to 0 when no multivariate Wald is given, 1 otherwise.
p.global_chisq2
Recurrent event of type 2: a vector with the p_values
for each global multivariate Wald test.
names.factor2
Recurrent
event of type 2: Names of the "as.factor" variables.
global_chisq_d
Terminal event: a vector with the values of each
multivariate Wald test.
dof_chisq_d
Terminal event: a vector with
the degree of freedom for each multivariate Wald test.
global_chisq.test_d
Terminal event: a binary variable equals to 0
when no multivariate Wald is given, 1 otherwise.
p.global_chisq_d
Terminal event: a vector with the p-values for each
global multivariate Wald test.
names.factordc
Terminal event: Names
of the "as.factor" variables.
Note
"kappa" (kappa[1], kappa[2] and kappa[3]) and "n.knots" (n.knots[1],
n.knots[2] and n.knots[3]) are the arguments that the user has to change if
the fitted model does not converge. "n.knots" takes integer values between
4 and 20. But with n.knots=20, the model will take a long time to converge.
So, usually, begin first with n.knots=7, and increase it step by step until
it converges. "kappa" only takes positive values. So, choose a value for
kappa (for instance 10000), and if it does not converge, multiply or divide
this value by 10 or 5 until it converges. Moreover, it may be useful to
change the value of the initialize argument.
References
Mazroui Y., Mathoulin-Pellissier S., MacGrogan G., Brouste V., Rondeau V.
(2013). Multivariate frailty models for two types of recurrent events with
an informative terminal event : Application to breast cancer data.
Biometrical journal, 55(6), 866-884.
See Also
terminal,event2,
print.multivPenal,summary.multivPenal,plot.multivPenal
Examples
###--- Multivariate Frailty model ---###
data(dataMultiv)
# (computation takes around 60 minutes)
modMultiv.spli <- multivPenal(Surv(TIMEGAP,INDICREC)~cluster(PATIENT)+v1+v2+
event2(INDICMETA)+terminal(INDICDEATH),formula.Event2=~v1+v2+v3,
formula.terminalEvent=~v1,data=dataMultiv,n.knots=c(8,8,8),
kappa=c(1,1,1),initialize=FALSE)
print(modMultiv.spli)
modMultiv.weib <- multivPenal(Surv(TIMEGAP,INDICREC)~cluster(PATIENT)+v1+v2+
event2(INDICMETA)+terminal(INDICDEATH),formula.Event2=~v1+v2+v3,
formula.terminalEvent=~v1,data=dataMultiv,hazard="Weibull")
print(modMultiv.weib)
modMultiv.cpm <- multivPenal(Surv(TIMEGAP,INDICREC)~cluster(PATIENT)+v1+v2+
event2(INDICMETA)+terminal(INDICDEATH),formula.Event2=~v1+v2+v3,
formula.terminalEvent=~v1,data=dataMultiv,hazard="Piecewise-per",
nb.int=c(6,6,6))
print(modMultiv.cpm)
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| multivPenal | R Documentation |
Fit a multivariate frailty model for two types of recurrent events and a terminal event.
Description
Fit a multivariate frailty model for two types of recurrent events with a terminal event using a penalized likelihood estimation on the hazard function or a parametric estimation. Right-censored data are allowed. Left-truncated data and stratified analysis are not possible. Multivariate frailty models allow studying, with a joint model, three survival dependent processes for two types of recurrent events and a terminal event. Multivariate joint frailty models are applicable in mainly two settings. First, when focus is on the terminal event and we wish to account for the effect of previous endogenous recurrent event. Second, when focus is on a recurrent event and we wish to correct for informative censoring.
The multivariate frailty model for two types of recurrent events with a terminal event is (in the calendar or time-to-event timescale):
where r0l(t), (l∈{1,3}) and r0(t) are
respectively the recurrent and terminal event baseline hazard functions, and
\beta1,\beta2,\beta3 the regression coefficient vectors associated
with Zi(t) the covariate vector. The covariates could be different
for the different event hazard functions and may be time-dependent. We
consider that death stops new occurrences of recurrent events of any type,
hence given t>D, dNR(l)*(t), (l∈{1,2}) takes the value 0.
Thus, the terminal and the two recurrent event processes are not independent
or even conditional upon frailties and covariates. We consider the hazard
functions of recurrent events among individuals still alive.
components in the above multivariate frailty model are linked together by
two Gaussian and correlated random effects ui,vi:
(ui,vi)T ~ N(0,\Sigmauv), with
Dependencies between these three types of event are taken into account by
two correlated random effects and parameters \theta1,\theta2 the
variance of the random effects and \alpha1,\alpha2 the coefficients
for these random effects into the terminal event part. If \alpha1 and
\theta1 are both significantly different from 0, then the recurrent
events of type 1 and death are significantly associated (the sign of the
association is the sign of \alpha1). If \alpha2 and
\theta2 are both significantly different from 0, then the recurrent
events of type 2 and death are significantly associated (the sign of the
association is the sign of \alpha2). If \rho, the correlation
between the two random effects, is significantly different from 0, then the
recurrent events of type 1 and the recurrent events of type 2 are
significantly associated (the sign of the association is the sign of
\rho).
Usage
multivPenal(formula, formula.Event2, formula.terminalEvent, data, initialize
= TRUE, recurrentAG = FALSE, n.knots, kappa, maxit = 350, hazard =
"Splines", nb.int, print.times = TRUE)
Arguments
formula |
a formula object, with the response for the first recurrent
event on the left of a |
formula.Event2 |
a formula object, with the response for the second
recurrent event on the left of a |
formula.terminalEvent |
a formula object, with the response for the
terminal event on the left of a |
data |
a 'data.frame' with the variables used in 'formula', 'formula.Event2' and 'formula.terminalEvent'. |
initialize |
Logical value to initialize regression coefficients and baseline hazard functions parameters. When the estimation is semi-parametric with splines, this initialization produces also values for smoothing parameters (by cross validation). When initialization is requested, the program first fit two shared frailty models (for the two types of recurrent events) and a Cox proportional hazards model (for the terminal event). Default is TRUE. |
recurrentAG |
Logical value. Is Andersen-Gill model fitted? If so indicates that recurrent event times with the counting process approach of Andersen and Gill is used. This formulation can be used for dealing with time-dependent covariates. The default is FALSE. |
n.knots |
integer vector of length 3 (for the three outcomes) giving the number of knots to use. First is for the recurrent of type 1, second is for the recurrent of type 2 and third is for the terminal event hazard function. Value required in the penalized likelihood estimation. It corresponds to the (n.knots+2) splines functions for the approximation of the hazard or the survival functions. Number of knots must be between 4 and 20. (See Note) |
kappa |
vector of length 3 (for the three outcomes) for positive smoothing parameters in the penalized likelihood estimation. First is for the recurrent of type 1, second is for the recurrent of type 2 and third is for the terminal event hazard function. The coefficient kappa of the integral of the squared second derivative of hazard function in the fit (penalized log likelihood). Initial values for the kappas can be obtained with the option "initialize=TRUE". We advise the user to identify several possible tuning parameters, note their defaults and look at the sensitivity of the results to varying them. Value required.(See Note) |
maxit |
maximum number of iterations for the Marquardt algorithm. Default is 350. |
hazard |
Type of hazard functions: "Splines" for semi-parametric hazard functions with the penalized likelihood estimation, "Piecewise-per" for piecewise constant hazard function using percentile, "Piecewise-equi" for piecewise constant hazard function using equidistant intervals, "Weibull" for parametric Weibull function. Default is "Splines". |
nb.int |
An integer vector of length 3 (for the three outcomes). First is the Number of intervals (between 1 and 20) for the recurrent of type 1 parametric hazard functions ("Piecewise-per", "Piecewise-equi"). Second is the Number of intervals (between 1 and 20) for the recurrent of type 2 parametric hazard functions ("Piecewise-per", "Piecewise-equi"). Third is Number of intervals (between 1 and 20) for the death parametric hazard functions ("Piecewise-per", "Piecewise-equi") |
print.times |
a logical parameter to print iteration process. Default is TRUE. |
Value
Parameters estimates of a multivariate joint frailty model, more generally a 'multivPenal' object. Methods defined for 'multivPenal' objects are provided for print, plot and summary. The following components are included in a 'multivPenal' object for multivariate Joint frailty models.
b |
sequence of the corresponding estimation of the splines coefficients, the random effects variances, the coefficients of the frailties and the regression coefficients. |
call |
The code used for fitting the model. |
n |
the number of observations used in the fit. |
groups |
the number of subjects used in the fit. |
n.events |
the number of recurrent events of type 1 observed in the fit. |
n.events2 |
the number of the recurrent events of type 2 observed in the fit. |
n.deaths |
the number of deaths observed in the fit. |
loglikPenal |
the complete marginal penalized log-likelihood in the semi-parametric case. |
loglik |
the marginal log-likelihood in the parametric case. |
LCV |
the approximated likelihood cross-validation criterion in the semi parametric case (with H minus the converged Hessian matrix, and l(.) the full log-likelihood.
) |
AIC |
the Akaike information Criterion for the parametric case.
|
theta1 |
variance of the
frailty parameter for recurrences of type 1 |
theta2 |
variance of the frailty parameter for recurrences of type 2
|
alpha1 |
the coefficient associated with the
frailty parameter |
alpha2 |
the coefficient associated with the frailty parameter
|
rho |
the correlation
coefficient between |
npar |
number of parameters. |
coef |
the regression coefficients. |
nvar |
A vector with the number of covariates of each type of hazard function as components. |
varH |
the variance matrix of all parameters before positivity constraint transformation (theta, the regression coefficients and the spline coefficients). Then, the delta method is needed to obtain the estimated variance parameters. |
varHIH |
the robust estimation of the variance matrix of all parameters (theta, the regression coefficients and the spline coefficients). |
formula |
the formula part of the code used for the model for the recurrent event. |
formula.Event2 |
the formula part of the code used for the model for the second recurrent event. |
formula.terminalEvent |
the formula part of the code used for the model for the terminal event. |
x1 |
vector of times for hazard functions of the recurrent events of type 1 are estimated. By default seq(0,max(time),length=99), where time is the vector of survival times. |
lam1 |
matrix of hazard estimates and confidence bands for recurrent events of type 1. |
xSu1 |
vector of times for the survival function of the recurrent event of type 1. |
surv1 |
matrix of baseline survival estimates and confidence bands for recurrent events of type 1. |
x2 |
vector of times for the recurrent event of type 2 (see x1 value). |
lam2 |
the same value as lam1 for the recurrent event of type 2. |
xSu2 |
vector of times for the survival function of the recurrent event of type 2 |
surv2 |
the same value as surv1 for the recurrent event of type 2. |
xEnd |
vector of times for the terminal event (see x1 value). |
lamEnd |
the same value as lam1 for the terminal event. |
xSuEnd |
vector of times for the survival function of the terminal event |
survEnd |
the same value as surv1 for the terminal event. |
median1 |
The value of the median survival and its confidence bands for the recurrent event of type 1. |
median2 |
The value of the median survival and its confidence bands for the recurrent event of type 2. |
medianEnd |
The value of the median survival and its confidence bands for the terminal event. |
type.of.Piecewise |
Type of Piecewise hazard functions (1:"percentile", 0:"equidistant"). |
n.iter |
number of iterations needed to converge. |
type.of.hazard |
Type of hazard functions (0:"Splines", "1:Piecewise", "2:Weibull"). |
n.knots |
a vector with number of knots for estimating the baseline functions. |
kappa |
a vector with the smoothing parameters in the penalized likelihood estimation corresponding to each baseline function as components. |
n.knots.temp |
initial value for the number of knots. |
zi |
splines knots. |
time |
knots for Piecewise hazard function for the recurrent event of type 1. |
timedc |
knots for Piecewise hazard function for the terminal event. |
time2 |
knots for Piecewise hazard function for the recurrent event of type 2. |
noVar |
indicator vector for recurrent, death and recurrent 2 explanatory variables. |
nvarRec |
number of the recurrent of type 1 explanatory variables. |
nvarEnd |
number of death explanatory variables. |
nvarRec2 |
number of the recurrent of type 2 explanatory variables. |
nbintervR |
Number of intervals (between 1 and 20) for the the recurrent of type 1 parametric hazard functions ("Piecewise-per", "Piecewise-equi"). |
nbintervDC |
Number of intervals (between 1 and 20) for the death parametric hazard functions ("Piecewise-per", "Piecewise-equi"). |
nbintervR2 |
Number of intervals (between 1 and 20) for the the recurrent of type 2 parametric hazard functions ("Piecewise-per", "Piecewise-equi"). |
istop |
Vector of the convergence criteria. |
shape.weib |
shape parameters for the Weibull hazard function. |
scale.weib |
scale parameters for the Weibull hazard function. |
martingale.res |
martingale residuals for each cluster (recurrent of type 1). |
martingale2.res |
martingale residuals for each cluster (recurrent of type 2). |
martingaledeath.res |
martingale residuals for each cluster (death). |
frailty.pred |
empirical Bayes prediction of the first frailty term. |
frailty2.pred |
empirical Bayes prediction of the second frailty term. |
frailty.var |
variance of the empirical Bayes prediction of the first frailty term. |
frailty2.var |
variance of the empirical Bayes prediction of the second frailty term. |
frailty.corr |
Correlation between the empirical Bayes prediction of the two frailty. |
linear.pred |
linear predictor: uses Beta'X + ui in the multivariate frailty models. |
linear2.pred |
linear predictor: uses Beta'X + vi in the multivariate frailty models. |
lineardeath.pred |
linear predictor for the terminal part form the multivariate frailty models: Beta'X + alpha1 ui + alpha2 vi |
global_chisq |
Recurrent event of type 1: a vector with the values of each multivariate Wald test. |
dof_chisq |
Recurrent event of type 1: a vector with the degree of freedom for each multivariate Wald test. |
global_chisq.test |
Recurrent event of type 1: a binary variable equals to 0 when no multivariate Wald is given, 1 otherwise. |
p.global_chisq |
Recurrent event of type 1: a vector with the p-values for each global multivariate Wald test. |
names.factor |
Recurrent event of type 1: Names of the "as.factor" variables. |
global_chisq2 |
Recurrent event of type 2: a vector with the values of each multivariate Wald test. |
dof_chisq2 |
Recurrent event of type 2: a vector with the degree of freedom for each multivariate Wald test. |
global_chisq.test2 |
Recurrent event of type 2: a binary variable equals to 0 when no multivariate Wald is given, 1 otherwise. |
p.global_chisq2 |
Recurrent event of type 2: a vector with the p_values for each global multivariate Wald test. |
names.factor2 |
Recurrent event of type 2: Names of the "as.factor" variables. |
global_chisq_d |
Terminal event: a vector with the values of each multivariate Wald test. |
dof_chisq_d |
Terminal event: a vector with the degree of freedom for each multivariate Wald test. |
global_chisq.test_d |
Terminal event: a binary variable equals to 0 when no multivariate Wald is given, 1 otherwise. |
p.global_chisq_d |
Terminal event: a vector with the p-values for each global multivariate Wald test. |
names.factordc |
Terminal event: Names of the "as.factor" variables. |
Note
"kappa" (kappa[1], kappa[2] and kappa[3]) and "n.knots" (n.knots[1], n.knots[2] and n.knots[3]) are the arguments that the user has to change if the fitted model does not converge. "n.knots" takes integer values between 4 and 20. But with n.knots=20, the model will take a long time to converge. So, usually, begin first with n.knots=7, and increase it step by step until it converges. "kappa" only takes positive values. So, choose a value for kappa (for instance 10000), and if it does not converge, multiply or divide this value by 10 or 5 until it converges. Moreover, it may be useful to change the value of the initialize argument.
References
Mazroui Y., Mathoulin-Pellissier S., MacGrogan G., Brouste V., Rondeau V. (2013). Multivariate frailty models for two types of recurrent events with an informative terminal event : Application to breast cancer data. Biometrical journal, 55(6), 866-884.
See Also
terminal,event2,
print.multivPenal,summary.multivPenal,plot.multivPenal
Examples
###--- Multivariate Frailty model ---###
data(dataMultiv)
# (computation takes around 60 minutes)
modMultiv.spli <- multivPenal(Surv(TIMEGAP,INDICREC)~cluster(PATIENT)+v1+v2+
event2(INDICMETA)+terminal(INDICDEATH),formula.Event2=~v1+v2+v3,
formula.terminalEvent=~v1,data=dataMultiv,n.knots=c(8,8,8),
kappa=c(1,1,1),initialize=FALSE)
print(modMultiv.spli)
modMultiv.weib <- multivPenal(Surv(TIMEGAP,INDICREC)~cluster(PATIENT)+v1+v2+
event2(INDICMETA)+terminal(INDICDEATH),formula.Event2=~v1+v2+v3,
formula.terminalEvent=~v1,data=dataMultiv,hazard="Weibull")
print(modMultiv.weib)
modMultiv.cpm <- multivPenal(Surv(TIMEGAP,INDICREC)~cluster(PATIENT)+v1+v2+
event2(INDICMETA)+terminal(INDICDEATH),formula.Event2=~v1+v2+v3,
formula.terminalEvent=~v1,data=dataMultiv,hazard="Piecewise-per",
nb.int=c(6,6,6))
print(modMultiv.cpm)
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