epoce {frailtypack}

Estimators of the Expected Prognostic Observed Cross-Entropy (EPOCE) for evaluating predictive accuracy of joint models.

Description

This function computes estimators of the Expected Prognostic Observed Cross-Entropy (EPOCE) for evaluating the predictive accuracy of joint models using frailtyPenal, longiPenal, trivPenal or trivPenalNL. On the same data as used for estimation of the joint model, this function computes both the Mean Prognosis Observed Loss (MPOL) and the Cross-Validated Prognosis Observed Loss (CVPOL), two estimators of EPOCE. The latter corrects the MPOL estimate for over-optimism by approximated cross-validation. On external, this function only computes MPOL.

Usage

epoce(fit, pred.times, newdata = NULL, newdata.Longi = NULL)

Arguments

fit

A jointPenal, longiPenal, trivPenal or trivPenalNL object.

pred.times

Time or vector of times to compute epoce.

newdata

Optional. In case of joint models obtained with frailtyPenal, trivPenal or trivPenalNL. For models inheriting from trivPenal or trivPenalNL class, if newdata is given, newdata.Longi must be given as well. When missing, the data used for estimating the fit are used, and CVPOL and MPOL are computed (internal validation). When newdata is specified, only MPOL is computed on this new dataset (external validation). The new dataset and the dataset used in the estimation must have the same covariates with the same coding without missing data.

newdata.Longi

Optional. In case of joint models obtained with longiPenal, trivPenal or trivPenalNL. For models inheriting from longiPenal, if the newdata.Longi is given, newdata must be NULL, but for models from trivPenal or trivPenalNL class, if newdata.Longi is given, newdata must be provided as well. The two datasets newdata and newdata.Longi must include the information concerning the same patients with the same characteristics and the appropriate data on follow up (recurrences for newdata and longitudinal measurements for newdata.Longi).

Value

data

name of the data used to compute epoce

new.data

a boolean which is FALSE if computation is done on the same data as for estimation, and TRUE otherwise

pred.times

time or vector of times used in the function

mpol

values of MPOL for each pred.times

cvpol

values of CVPOL for each pred.times

IndivContrib

all the contributions to the log-likelihood for each pred.times

AtRisk

number of subject still at risk for each pred.times

References

D. Commenges, B. Liquet, C. Proust-Lima (2012). Choice of prognostic estimators in joint models by estimating differences of expected conditional Kullback-Leibler risks. Biometrics, 68(2), 380-387.

Examples

## Not run: 

########################################
#### EPOCE on a joint frailty model ####
########################################

data(readmission)

modJoint.gap <- frailtyPenal(Surv(t.start,t.stop,event)~ cluster(id) +
  dukes + charlson + sex + chemo + terminal(death),
  formula.terminalEvent = ~ dukes + charlson + sex + chemo ,
  data = readmission, n.knots = 8, kappa =c(2.11e+08,9.53e+11),
  recurrentAG=TRUE)

# computation on the same dataset
temps <- c(200,500,800,1100)
epoce <- epoce(modJoint.gap,temps)

print(epoce)
plot(epoce,type = "cvpol")

# computation on a new dataset
# here a sample of readmission with the first 50 subjects
s <- readmission[1:100,]
epoce <- epoce(modJoint.gap,temps,newdata=s)

print(epoce)
plot(epoce,type = "mpol")

#################################################
#### EPOCE on a joint  model for a biomarker ####
#########   and a terminal event  ###############
#################################################

data(colorectal)
data(colorectalLongi)

# Survival data preparation - only terminal events 
colorectalSurv <- subset(colorectal, new.lesions == 0)

modLongi <- longiPenal(Surv(time0, time1, state) ~ age +
treatment + who.PS, tumor.size ~  year*treatment + age +
who.PS, colorectalSurv, data.Longi =colorectalLongi,
random = c("1", "year"),  id = "id", link = "Random-effects", 
left.censoring = -3.33, hazard = "Weibull", 
method.GH = "Pseudo-adaptive")

# computation on the same dataset
time <- c(1, 1.5, 2, 2.5)
epoce <- epoce(modLongi,time)

print(epoce)
plot(epoce, type = "cvpol")

# computation on a new dataset
# here a sample of colorectal data with the first 50 subjects
s <-  subset(colorectal, new.lesions == 0 & id%in%1:50)
s.Longi <- subset(colorectalLongi, id%in%1:50)
epoce <- epoce(modLongi, time, newdata = s, newdata.Longi = s.Longi)

print(epoce)
plot(epoce, type = "mpol")


###################################################
#### EPOCE on a joint model for a biomarker, ######
#### recurrent events and a terminal event   ######
###################################################

data(colorectal)
data(colorectalLongi)

# Linear model for the biomarker
# (computation takes around 30 minutes)
model.trivPenalNL <-trivPenal(Surv(gap.time, new.lesions) ~ cluster(id)
+ age + treatment + who.PS + prev.resection + terminal(state),
formula.terminalEvent =~ age + treatment + who.PS + prev.resection, 
tumor.size ~ year * treatment + age + who.PS, data = colorectal,
data.Longi = colorectalLongi, random = c("1", "year"), id = "id", 
link = "Random-effects", left.censoring = -3.33, recurrentAG = FALSE,
hazard = "Weibull", method.GH="Pseudo-adaptive", n.nodes=7)

# computation on the same dataset
time <- c(1, 1.5, 2, 2.5)

# (computation takes around 10 minutes)
epoce <- epoce(model.trivPenalNL,time)
print(epoce)
plot(epoce, type = "cvpol")

# computation on a new dataset
# here a sample of colorectal data with the first 100 subjects
s <-  subset(colorectal,  id%in%1:100)
s.Longi <- subset(colorectalLongi, id%in%1:100)
# (computation takes around 10 minutes)
epoce <- epoce(model.trivPenalNL, time, newdata = s, newdata.Longi = s.Longi)

print(epoce)
plot(epoce, type = "mpol")



# Non-linear model for the biomarker

# No information on dose - creation of a dummy variable 
colorectalLongi$dose <- 1

# (computation can take around 40 minutes)
model.trivPenalNL <- trivPenalNL(Surv(time0, time1, new.lesions) ~ cluster(id) + age + treatment
 + terminal(state), formula.terminalEvent =~ age + treatment, biomarker = "tumor.size",
 formula.KG ~ 1, formula.KD ~ treatment, dose = "dose", time.biomarker = "year", 
 data = colorectal, data.Longi =colorectalLongi, random = c("y0", "KG"), id = "id", 
 init.B = c(-0.22, -0.16, -0.35, -0.19, 0.04, -0.41, 0.23), init.Alpha = 1.86,
 init.Eta = c(0.5, 0.57, 0.5, 2.34), init.Biomarker = c(1.24, 0.81, 1.07, -1.53),
 recurrentAG = TRUE, n.knots = 5, kappa = c(0.01, 2), method.GH = "Pseudo-adaptive")

# computation on the same dataset
time <- c(1, 1.5, 2, 2.5)

epoce <- epoce(model.trivPenalNL, time)



## End(Not run)