gcmrec: General Class of Models for recurrent event data

In isglobal-brge/gcmrec: General class of models for recurrent event data

General Class of Models for recurrent event data

Description

Fits the parameters for the general semiparametric model for recurrent events proposed by Peña and Hollander (2004). This class of models incorporates an effective age function which encodes the changes that occur after each event occurrence such as the impact of an intervention, it allows for the modeling of the impact of accumulating event occurrences on the unit, it admits a link function in which the effect of possibly time-dependent covariates are incorporated, and it allows the incorporation of unobservable frailty components which induce dependencies among the inter-event times for each unit.

Usage

gcmrec(formula, data, effageData = NULL, s, Frailty = FALSE, 
    alphaSeed, betaSeed, xiSeed, tol = 10^(-6), maxit = 100, 
    rhoFunc = "alpha to k", typeEffage = "perfect", 
    maxXi = "Newton-Raphson", se = "Information matrix", 
    cancer = NULL)

Arguments

formula	A formula object. If a formula object is supplied it must have a Survr object as the response on the left of the '~' operator and a term on the right. Covariates are needed.
data	A data frame in which to interpret the variables named in the formula. This data frame must contain the variables called "id","time" and "event" for subject identification, time of interocurrence, and censored status (coded 1: event, 0:censored), respectively. Furthermore, we can have some covariates. Alternatively, it can also be a list containing the elements "n" and "subjects". Number of subjects must be recorded in "n". The element "subject" must have the following elements: subj, k, tau, caltimes, gaptimes, intercepts, slopes, lastperrep, perrepind, effage, effagebegin, and covariate including this information: subj: Subject number or identificator. k: Number of recurrences (time 0 must be included). tau: Administrative time, time of study termination. caltimes: Calendar times at each recurrence (time 0 must be included). gaptimes: Gap times at each recurrence (time 0 must be included). intercepts: Intercept value for the effect after each recurrence. slopes: Slope value for the effect after each each recurrence. lastperrep: Element from Brown and Proschan minimal repair model. perrepind: Element from Brown and Proschan minimal repair model. effagebegin: Initial value for effective age. effage: Effective age after each recurrence. covariate: covariate value at each recurrence. See either GeneratedData or hydraulic data sets as an example.
effageData	List containing the information about effective age. The list must have the elements described in the option 2 of data argument. If NULL we generate these elements under perfect repair model or minimal repair one depending on the 'typeEffage' argument (see below).
s	A selected calendar time.
Frailty	Logical value. Is model with frailties fitted? If so parameters for General Class of Models with frailty component are estimated.
alphaSeed	Seed value for \alpha.
betaSeed	Seed value for \beta.
xiSeed	Seed value for \xi.
tol	Tolerance for maximization procedures.
maxit	Maximum number of iterations in maximization procedures.
rhoFunc	A character string specifying the effects attributable to the accumulating event occurrences, \rho(k;\alpha). Possible values are "Identity" for \rho(k;\alpha)=1 or "alpha to k" for \rho(k;\alpha)=\alpha^k. The default is "alpha to k". Only the first words are required, e.g "Id","a". Future versions will include other functions such as Markovian model for tumor occurrences, \rho(k;\alpha)=\alpha-k+1 proposed by Gail et al. (1980).
typeEffage	Effective age function. Possible value are "perfect" or "minimal" for perfect repair model or minimal repair model, respectively. The default is "perfect". Only the first words are required, e.g "p","m"
maxXi	Maximization method for marginal likelihood with respect to \xi. Possible values are "Newton-Raphson" for Newton-Raphson maximization procedure or "Brent" for Brent's method maximization in one dimension. The default value is "Newton-Raphson". Only the first words are required, e.g. "N","B"
se	Standard errors of parameters. Possible values are 'Information matrix' or 'Jacknife' for inverse of the partial likelihood information matrix or jacnife estimates, respectively.
cancer	Effective age for fitting a cancer model proposed by Gonzalez et al (2005). This variable contains the information of the effect of treatments administred after cancer relapses coded as "CR", "PR" or "SD" depending on if complete, partial, or null response (stable disease) is achieved. See lymphoma data set as an example.

Details

Estimation with frailties are implemented using expectation-maximization (EM) algorithm. In this procedure, we need to maximize the marginal likelihood with respect to \xi. This maximization is a one-dimensional maximization without derivarives. First we bracket the maximizing value, and the we obtain it using Brent's method in one dimension. When we implement this algorithm, we re-parameterize \xi using \xi^*=log(\xi) to alleviate the problem of getting negative estimates for \xi. Iteration is terminated when successive values of \xi/(1+\xi) differ by no more than the "tol" parameter. Maybe estimation under frailty model can be not too fast.

Value

a gcmrec object. Methods defined for gcmrec objects are provided for print and plot.

References

Pe\~na, E. and M. Hollander (2004). Mathematical Reliability: An Expository Perspective, Chapter 6. Models for Recurrent Events in Reliability and Survival Analysis, pp. 105-123. Kluwer Academic Publishers.

M. Gail, T Santner, and C Brown (1980). An analysis of comparative carfinogenesis experiments based on multiple times to tumor. Biometrics 36, 255-266.

JR Gonzalez, E Peña, E Slate (2005). Modelling treatment effect after cancer relapses, with application to recurrences in indolent non-Hodgkin's lymphomas. Stat Med, submitted.

R. Brent. Algorithms for Minimization Without Derivatives. Prentice-Hall, New York, 1973.

Examples

###################################
## Models using different data formats
###################################

#
#    Data input as a data frame
#

#   We use the well-known bladder cancer data set from survival package

data(bladder, package="survival")

# we compute the interocurrence time
bladder2$time<-bladder2$stop-bladder2$start


# If we execute:
#     gcmrec(Survr(id,time,event)~rx+size+number,data=bladder2,s=2060)

# We will obtain the following error message:
#   Error in Survr(id, time, event) : Data doesn't match...

# This means that we have some patients without right-censoring time. So,
# we understand that the last event coincides with the end of study. 
# Consequently,we need to add a line with time 0 and status value equal 
# to 0, too. To do so, we can use the function "addCenTime" as follows:

bladderOK<-addCenTime(bladder2) 

# Now, we can fit the model using this new data set:

gcmrec(Survr(id,time,event)~rx+size+number,data=bladderOK,s=2060)



#
#    Data as a list. See either GeneratedData or hydraulic data 
#                    sets as an example.
#

#
# We can fit the model by transforming our data in a data frame 
# using "List.to.Dataframe" function:
#

data(hydraulic)
hydraulicOK<-List.to.Dataframe(hydraulic)
gcmrec(Survr(id,time,event)~covar.1+covar.2,data=hydraulicOK,s=4753)



#
# Our model allows us to incorporate effective age information
#
# To illustrate this example, we will use a simulated data set generated 
# under the minimal repair model with probability of perfect repair equal to 0.6
#
# As we have the data in a list, first we need to obtain a data frame containing
# the time, event, and covariates information:
#

data(GeneratedData)
temp<-List.to.Dataframe(GeneratedData)

# then, we can fit the model incorporating the information about the effective 
#        age in the effageData argument:

gcmrec(Survr(id,time,event)~covar.1+covar.2, data=temp, 
                    effageData=GeneratedData, s=100)




#####################################################################
##  How to fit minimal or perfect repair models, with and without frailties
#####################################################################

# Model with frailties 

mod.Fra<-gcmrec(Survr(id,time,event)~rx+size+number,data=bladderOK,s=2060,Frailty=TRUE)
print(mod.Fra)


# effective age function: perfect repair and minimal repair models 
# (models without frailties)

data(readmission)

# perfect
mod.per<-gcmrec(Survr(id,time,event)~as.factor(dukes),data=readmission,
    s=3000,typeEffage="per")
print(mod.per)

# minimal
mod.min<-gcmrec(Survr(id,time,event)~as.factor(dukes),data=readmission,
   s=3000,typeEffage="min")
print(mod.min)


#####################################################################
##  How to fit models with \rho function equal to identity 
#####################################################################

data(lymphoma)

gcmrec(Survr(id, time, event) ~ as.factor(distrib), 
    data = lymphoma, s = 1000, Frailty = TRUE, rhoFunc = "Ident")


#####################################################################
##  How to fit cancer model
#####################################################################


mod.can<-gcmrec(Survr(id,time,event)~as.factor(distrib), data=lymphoma,
     s=1000, Frailty=TRUE,  cancer=lymphoma$effage)

#  standard errors can be obtained by adding se="Jacknife".
# This procedure can be very time consuming

 

isglobal-brge/gcmrec documentation built on April 24, 2024, 6:11 a.m.