prediction: Prediction probabilities for Cox proportional hazard, Shared,...
In frailtypack: Shared, Joint (Generalized) Frailty Models; Surrogate Endpoints
prediction R Documentation
Prediction probabilities for Cox proportional hazard, Shared, Joint frailty
models, Joint models for longitudinal data and a terminal event and
Trivariate joint model for longitudinal data, recurrent events and a
terminal event (linear and non-linear).
Description
For Cox proportional hazard model
A predictive probability of event between t and horizon time t+w, with w the
window of prediction.
For Gamma Shared Frailty model for clustered (not recurrent) events
Two kinds of predictive probabilities can be calculated:
- a conditional predictive probability of event between t and horizon time
t+w, i.e. given a specific group
- a marginal predictive probability of event between t and horizon time t+w,
i.e. averaged over the population
For Gaussian Shared Frailty model for clustered (not recurrent)
events
Two kinds of predictive probabilities can be calculated:
- a conditional predictive probability of event between t and horizon time
t+w, i.e. given a specific group and given a specific Gaussian random effect
\eta
- a marginal predictive probability of event between t and horizon time t+w,
i.e. averaged over the population
For Gamma Shared Frailty model for recurrent events
Two kinds of predictive probabilities can be calculated:
- A marginal predictive probability of event between t and horizon time t+w,
i.e. averaged over the population.
- a conditional predictive probability of event between t and horizon time
t+w, i.e. given a specific individual.
This prediction method is the same as the conditional gamma prediction
method applied for clustered events (see formula Pcond before).
For Gaussian Shared Frailty model for recurrent events
Two kinds of predictive probabilities can be calculated:
- A marginal predictive probability of event between t and horizon time t+w,
i.e. averaged over the population.
- a conditional predictive probability of event between t and horizon time
t+w, i.e. given a specific individual.
This prediction method is the same as the conditional Gaussian prediction
method applied for clustered events (see formula Pcond before).
It is possible to compute all these predictions in two ways on a scale of
times : - either you want a cumulative probability of developing the event
between t and t+w (with t fixed, but with a varying window of prediction w);
- either you want at a specific time the probability to develop the event in
the next w (ie, for a varying prediction time t, but for a fixed window of
prediction). See Details.
For Joint Frailty model
Prediction for two types of event can be calculated : for a terminal event
or for a new recurrent event, knowing patient's characteristics.
- Prediction of death knowing patients' characteristics :
It is to predict the probability of death in a specific time window given
the history of patient i before the time of prediction t. The history
HiJ,l, (l=1,2) is the information on covariates before time
t, but also the number of recurrences and the time of occurences. Three
types of marginal probabilities are computed:
- a prediction of death between t and t+w given that the patient had exactly
J recurrences (HiJ,1) before t
- a prediction of death between t and t+w given that the patient had at
least J recurrences (HiJ,2) before t
- a prediction of death between t and t+w considering the recurrence history
only in the parameters estimation. It corresponds to the average probability
of death between t and t+w for a patient with these given characteristics.
- Prediction of risk of a new recurrent event knowing patients'
characteristics :
It is to predict the probability of a new recurrent event in a specific time
window given the history of patient i before the time of prediction t. The
history HiJ is the information on covariates before time t, but also
the number of recurrences and the time of occurences. The marginal
probability computed is a prediction of a new recurrent event between t and
t+w given that the patient had exactly J recurrences (HiJ) before t:
It is possible to compute all these predictions in two ways : - either you
want a cumulative probability of developing the event between t and t+w
(with t fixed, but with a varying window of prediction w); - either you want
at a specific time the probability to develop the event in the next w (ie,
for a varying prediction time t, but for a fixed window of prediction). See
Details.
With Gaussian frailties (\eta), the same expressions are used but with
uiJ replaced by exp(J\etai) and g(\eta)
corresponds to the Gaussian distribution.
For Joint Nested Frailty models
Prediction of the probability of developing a terminal event between t and
t+w for subject i who survived by time t based on the visiting and disease
histories of their own and other family members observed by time t.
Let (YfiR(t)) be the history of subject i in family f,
before time t, which includes all the recurrent events and covariate
information. For disease history, let TfiD(t) = min(Tfi,t) be
the observed time to an event before t ; \deltafiD(t) the disease
indicator by time t and XfiD(t) the covariate information
observed up to time t. We define the family history of subject i in
family f by 
which includes the visiting and disease history of all subjects except for
subject i in family f as well as their covariate information by
time t.
The prediction probability can be written as :
For Joint models for longitudinal data and a terminal event
The predicted probabilities are calculated in a specific time window given
the history of biomarker measurements before the time of prediction t
(ƴi(t)). The probabilities are conditional also on
covariates before time t and that the subject was at risk at t. The
marginal predicted probability of the terminal event is
These probabilities can be calculated in several time points with fixed time
of prediction t and varying window w or with fixed window w and varying time
of prediction t. See Details for an example of how to construct time
windows.
For Trivariate joint models for longitudinal data, recurrent events
and a terminal event
The predicted probabilities are calculated in a specific time window given
the history of biomarker measurements ƴi(t) and recurrences
HiJ,1 (complete history of recurrences with known J number
of observed events) before the time of prediction t. The probabilities are
conditional also on covariates before time t and that the subject was at
risk at t. The marginal predicted probability of the terminal event is
The biomarker history can be represented using a linear (trivPenal)
or non-linear mixed-effects model (trivPenalNL).
These probabilities can be calculated in several time points with fixed time
of prediction t and varying window w or with fixed window w and varying time
of prediction t. See Details for an example of how to construct time
windows.
Usage
prediction(fit, data, data.Longi, t, window, event="Both", conditional =
FALSE, MC.sample=0, individual)
Arguments
fit
A frailtyPenal, jointPenal, longiPenal, trivPenal or trivPenalNL
object.
data
Data frame for the prediction. See Details.
data.Longi
Data frame for the prediction used for joint models with
longitudinal data. See Details.
t
Time or vector of times for prediction.
window
Window or vector of windows for prediction.
event
Only for joint and shared models. The type of event you want to
predict : "Terminal" for a terminal event, "Recurrent" for a recurrent event
or "Both". Default value is "Both". For joint nested model, only 'Terminal'
is allowed. In a shared model, if you want to predict a new recurrent event
then the argument "Recurrent" should be use. If you want to predict a new
event from clustered data, do not use this option.
conditional
Only for prediction method applied on shared models.
Provides distinction between the conditional and marginal prediction
methods. Default is FALSE.
MC.sample
Number of samples used to calculate confidence bands with a
Monte-Carlo method (with a maximum of 1000 samples). If MC.sample=0 (default
value), no confidence intervals are calculated.
individual
Only for joint nested model. Vector of individuals (of the
same family) you want to make prediction.
Details
To compute predictions with a prediction time t fixed and a variable window:
prediction(fit, datapred, t=10, window=seq(1,10,by=1))
Otherwise, you can have a variable prediction time and a fixed window.
prediction(fit, datapred, t=seq(10,20,by=1), window=5)
Or fix
both prediction time t and window.
prediction(fit, datapred,
t=10, window=5)
The data frame building is an important step. It will contain profiles of
patient on which you want to do predictions. To make predictions on a Cox
proportional hazard or a shared frailty model, only covariates need to be
included. You have to distinguish between numerical and categorical
variables (factors). If we fit a shared frailty model with two covariates
sex (factor) and age (numeric), here is the associated data frame for three
profiles of prediction.
datapred <- data.frame(sex=0,age=0) datapred$sex <-
as.factor(datapred$sex) levels(datapred$sex)<- c(1,2) datapred[1,] <-
c(1,40) # man, 40 years old datapred[2,] <- c(2,45) # woman, 45 years old
datapred[3,] <- c(1,60) # man, 60 years old
Time-dependent covariates: In the context of time-dependent
covariate, the last previous value of the covariate is used before the time
t of prediction.
It should be noted, that in a data frame for both marginal and conditional
prediction on a shared frailty model for clustered data, the group must be
specified. In the case of marginal predictions this can be any number as it
does not influence predictions. However, for conditional predictions, the
group must be also included in the data set used for the model fitting. The
conditional predictions apply the empirical Bayes estimate of the frailty
from the specified cluster. Here, three individuals belong to group 5.
datapred <- data.frame(group=0, sex=0,age=0) datapred$sex <-
as.factor(datapred$sex) levels(datapred$sex)<- c(1,2) datapred[1,] <-
c(5,1,40) # man, 40 years old (cluster 5) datapred[2,] <- c(5,2,45) # woman,
45 years old (cluster 5) datapred[3,] <- c(5,1,60) # man, 60 years old
(cluster 5)
To use the prediction function on joint frailty models and trivariate joint
models, the construction will be a little bit different. In these cases, the
prediction for the terminal event takes into account covariates but also
history of recurrent event times for a patient. You have to create a data
frame with the relapse times, the indicator of event, the cluster variable
and the covariates. Relapses occurring after the prediction time may be
included but will be ignored for the prediction. A joint model with
calendar-timescale need to be fitted with Surv(start,stop,event), relapse
times correspond to the "stop" variable and indicators of event correspond
to the "event" variable (if event=0, the relapse will not be taken into
account). For patients without relapses, all the values of "event" variable
should be set to 0. Finally, the same cluster variable name needs to be in
the joint model and in the data frame for predictions ("id" in the following
example). For instance, we observe relapses of a disease and fit a joint
model adjusted for two covariates sex (1:male 2:female) and chemo (treatment
by chemotherapy 1:no 2:yes). We describe 3 different profiles of prediction
all treated by chemotherapy: 1) a man with four relapses at 100, 200, 300
and 400 days, 2) a man with only one relapse at 1000 days, 3) a woman
without relapse.
datapred <- data.frame(time=0,event=0,id=0,sex=0,chemo=0)
datapred$sex <- as.factor(datapred$sex) levels(datapred$sex) <- c(1,2)
datapred$chemo <- as.factor(datapred$chemo) levels(datapred$chemo) <- c(1,2)
datapred[1,] <- c(100,1,1,1,2) # first relapse of the patient 1 datapred[2,]
<- c(200,1,1,1,2) # second relapse of the patient 1 datapred[3,] <-
c(300,1,1,1,2) # third relapse of the patient 1 datapred[4,] <-
c(400,1,1,1,2) # fourth relapse of the patient 1 datapred[5,] <-
c(1000,1,2,1,2) # one relapse at 1000 days for patient 2 datapred[6,] <-
c(100,0,3,2,2) # patient 3 did not relapse
The data can also be the dataset used to fit the joint model. In this case,
you will obtain as many prediction rows as patients.
Finally, for the predictions using joint models for longitudinal data and a
terminal event and trivariate joint models, a data frame with the history of
the biomarker measurements must be provided. It must include data on
measurements (values and time points), cluster variable and covariates.
Measurements taken after the prediction time may be included but will be
ignored for the prediction. The same cluster variable name must be in the
data frame, in the data frame used for the joint model and in the data frame
with the recurrent event and terminal event times. For instance, we observe
two patients and each one had 5 tumor size measurements (patient 1 had an
increasing tumor size and patient 2, decreasing). The joint model used for
the predictions was adjusted on sex (1: male, 2: female), treatment (1:
sequential arm, 2: combined arm), WHO baseline performance status (1: 0
status, 2: 1 status, 3: 2 status) and previous resection of the primate
tumor (0: no, 1: yes). The data frame for the biomarker measurements can be:
datapredj_longi <- data.frame(id = 0, year = 0, tumor.size =
0, treatment = 0, age = 0, who.PS = 0, prev.resection = 0)
datapredj_longi$treatment <- as.factor(datapredj_longi$treatment)
levels(datapredj_longi$treatment) <- 1:2 datapredj_longi$age <-
as.factor(datapredj_longi$age) levels(datapredj_longi$age) <- 1:3
datapredj_longi$who.PS <- as.factor(datapredj_longi$who.PS)
levels(datapredj_longi$who.PS) <- 1:3 datapredj_longi$prev.resection <-
as.factor (datapredj_longi$prev.resection)
levels(datapredj_longi$prev.resection) <- 1:2 # patient 1: increasing tumor
size datapredj_longi[1,] <- c(1, 0,1.2 ,2,1,1,1) datapredj_longi[2,] <-
c(1,0.3,1.4,2,1,1,1) datapredj_longi[3,] <- c(1,0.6,1.9,2,1,1,1)
datapredj_longi[4,] <- c(1,0.9,2.5,2,1,1,1) datapredj_longi[5,] <-
c(1,1.5,3.9,2,1,1,1)
# patient 2: decreasing tumor size datapredj_longi[6,] <- c(2, 0,1.2
,2,1,1,1) datapredj_longi[7,] <- c(2,0.3,0.7,2,1,1,1) datapredj_longi[8,] <-
c(2,0.5,0.3,2,1,1,1) datapredj_longi[9,] <- c(2,0.7,0.1,2,1,1,1)
datapredj_longi[10,] <- c(2,0.9,0.1,2,1,1,1)
Value
The following components are included in a 'predFrailty' object obtained by
using prediction function for Cox proportional hazard and shared frailty
model.
npred
Number of individual predictions
x.time
A vector of
prediction times of interest (used for plotting predictions): vector of
prediction times t if fixed window. Otherwise vector of prediction times
t+w
window
Prediction window or vector of prediction windows
pred
Predictions estimated for each profile
icproba
Logical
value. Were confidence intervals estimated ?
predLow
Lower limit of
Monte-Carlo confidence interval for each prediction
predHigh
Upper
limit of Monte-Carlo confidence interval for each prediction
type
Type of prediction probability (marginal or conditional)
group
For conditional probability, the list of group on which you
make predictions
The following components are included in a 'predJoint' object obtained by
using prediction function for joint frailty model.
npred
Number of individual predictions
x.time
A vector of
prediction times of interest (used for plotting predictions): vector of
prediction times t if fixed window. Otherwise vector of prediction times
t+w
window
Prediction window or vector of prediction windows
group
Id of each patient
pred1
Estimation of probability of
type 1: exactly j recurrences
pred2
Estimation of probability of
type 2: at least j recurrences
pred3
Estimation of probability of
type 3
pred1_rec
Estimation of prediction of relapse
icproba
Logical value. Were confidence intervals estimated ?
predlow1
Lower limit of Monte-Carlo confidence interval for
probability of type 1
predhigh1
Upper limit of Monte-Carlo
confidence interval for probability of type 1
predlow2
Lower limit
of Monte-Carlo confidence interval for probability of type 2
predhigh2
Upper limit of Monte-Carlo confidence interval for
probability of type 2
predlow3
Lower limit of Monte-Carlo confidence
interval for probability of type 3
predhigh3
Upper limit of
Monte-Carlo confidence interval for probability of type 3
predhigh1_rec
Upper limit of Monte-Carlo confidence interval for
prediction of relapse
predlow1_rec
Lower limit of Monte-Carlo
confidence interval for prediction of relapse
The following components are included in a 'predLongi' object obtained by
using prediction function for joint models with longitudinal data.
npred
Number of individual predictions
x.time
A vector of
prediction times of interest (used for plotting predictions): vector of
prediction times t if fixed window. Otherwise vector of prediction times
t+w
window
Prediction window or vector of prediction windows
group
Id of each patient
pred
Estimation of probability
icproba
Logical value. Were confidence intervals estimated?
predLow
Lower limit of Monte-Carlo confidence intervals
predHigh
Upper limit of Monte-Carlo confidence intervals
trivariate
Logical value. Are the prediction calculated from the
trivariate model?
References
A. Krol, L. Ferrer, JP. Pignon, C. Proust-Lima, M. Ducreux, O.
Bouche, S. Michiels, V. Rondeau (2016). Joint Model for Left-Censored
Longitudinal Data, Recurrent Events and Terminal Event: Predictive Abilities
of Tumor Burden for Cancer Evolution with Application to the FFCD 2000-05
Trial. Biometrics 72(3) 907-16.
A. Mauguen, B. Rachet, S. Mathoulin-Pelissier, G. MacGrogan, A. Laurent, V.
Rondeau (2013). Dynamic prediction of risk of death using history of cancer
recurrences in joint frailty models. Statistics in Medicine,
32(30), 5366-80.
V. Rondeau, A. Laurent, A. Mauguen, P. Joly, C. Helmer (2015). Dynamic
prediction models for clustered and interval-censored outcomes:
investigating the intra-couple correlation in the risk of dementia.
Statistical Methods in Medical Research
Examples
## Not run:
#####################################################
#### prediction on a COX or SHARED frailty model ####
#####################################################
data(readmission)
#-- here is a generated cluster (31 clusters of 13 subjects)
readmission <- transform(readmission,group=id%%31+1)
#-- we compute predictions of death
#-- we extract last row of each subject for the time of death
readmission <- aggregate(readmission,by=list(readmission$id),
FUN=function(x){x[length(x)]})[,-1]
##-- predictions on a Cox proportional hazard model --##
cox <- frailtyPenal(Surv(t.stop,death)~sex+dukes,
n.knots=10,kappa=10000,data=readmission)
#-- construction of the data frame for predictions
datapred <- data.frame(sex=0,dukes=0)
datapred$sex <- as.factor(datapred$sex)
levels(datapred$sex)<- c(1,2)
datapred$dukes <- as.factor(datapred$dukes)
levels(datapred$dukes)<- c(1,2,3)
datapred[1,] <- c(1,2) # man, dukes 2
datapred[2,] <- c(2,3) # woman, dukes 3
#-- prediction of death for two patients between 100 and 100+w,
#-- with w in (50,100,...,1900)
pred.cox <- prediction(cox,datapred,t=100,window=seq(50,1900,50))
plot(pred.cox)
#-- prediction of death for two patients between t and t+400,
#-- with t in (100,150,...,1500)
pred.cox2 <- prediction(cox,datapred,t=seq(100,1500,50),window=400)
plot(pred.cox2)
##-- predictions on a shared frailty model for clustered data --##
sha <- frailtyPenal(Surv(t.stop,death)~cluster(group)+sex+dukes,
n.knots=10,kappa=10000,data=readmission)
#-- marginal prediction
# a group must be specified but it does not influence the results
# in the marginal predictions setting
datapred$group[1:2] <- 1
pred.sha.marg <- prediction(sha,datapred,t=100,window=seq(50,1900,50))
plot(pred.sha.marg)
#-- conditional prediction, given a specific cluster (group=5)
datapred$group[1:2] <- 5
pred.sha.cond <- prediction(sha,datapred,t=100,window=seq(50,1900,50),
conditional = TRUE)
plot(pred.sha.cond)
##-- marginal prediction of a recurrent event, on a shared frailty model
data(readmission)
datapred <- data.frame(t.stop=0,event=0,id=0,sex=0,dukes=0)
datapred$sex <- as.factor(datapred$sex)
levels(datapred$sex)<- c(1,2)
datapred$dukes <- as.factor(datapred$dukes)
levels(datapred$dukes)<- c(1,2,3)
datapred[1,] <- c(100,1,1,1,2) #man, dukes 2, 3 recurrent events
datapred[2,] <- c(200,1,1,1,2)
datapred[3,] <- c(300,1,1,1,2)
datapred[4,] <- c(350,0,2,1,2) #man, dukes 2 0 recurrent event
#-- Shared frailty model with gamma distribution
sha <- frailtyPenal(Surv(t.stop,event)~cluster(id)+sex+dukes,n.knots=10,
kappa=10000,data=readmission)
pred.sha.rec.marg <- prediction(sha,datapred,t=200,window=seq(50,1900,50),
event='Recurrent',MC.sample=100)
plot(pred.sha.rec.marg,conf.bands=TRUE)
##-- conditional prediction of a recurrent event, on a shared frailty model
pred.sha.rec.cond <- prediction(sha,datapred,t=200,window=seq(50,1900,50),
event='Recurrent',conditional = TRUE,MC.sample=100)
plot(pred.sha.rec.cond,conf.bands=TRUE)
#####################################################
######## prediction on a JOINT frailty model ########
#####################################################
data(readmission)
##-- predictions of death on a joint model --##
joi <- frailtyPenal(Surv(t.start,t.stop,event)~cluster(id)
+sex+dukes+terminal(death),formula.terminalEvent=~sex
+dukes,data=readmission,n.knots=10,kappa=c(100,100),recurrentAG=TRUE)
#-- construction of the data frame for predictions
datapredj <- data.frame(t.stop=0,event=0,id=0,sex=0,dukes=0)
datapredj$sex <- as.factor(datapredj$sex)
levels(datapredj$sex) <- c(1,2)
datapredj$dukes <- as.factor(datapredj$dukes)
levels(datapredj$dukes) <- c(1,2,3)
datapredj[1,] <- c(100,1,1,1,2)
datapredj[2,] <- c(200,1,1,1,2)
datapredj[3,] <- c(300,1,1,1,2)
datapredj[4,] <- c(400,1,1,1,2)
datapredj[5,] <- c(380,1,2,1,2)
#-- prediction of death between 100 and 100+500 given relapses
pred.joint0 <- prediction(joi,datapredj,t=100,window=500,event = "Terminal")
print(pred.joint0)
#-- prediction of death between 100 and 100+w given relapses
# (with confidence intervals)
pred.joint <- prediction(joi,datapredj,t=100,window=seq(50,1500,50),
event = "Terminal",MC.sample=100)
plot(pred.joint,conf.bands=TRUE)
# each y-value of the plot corresponds to the prediction between [100,x]
#-- prediction of death between t and t+500 given relapses
pred.joint2 <- prediction(joi,datapredj,t=seq(100,1000,50),
window=500,event = "Terminal")
plot(pred.joint2)
# each y-value of the plot corresponds to the prediction between [x,x+500],
#or in the next 500
#-- prediction of relapse between 100 and 100+w given relapses
# (with confidence intervals)
pred.joint <- prediction(joi,datapredj,t=100,window=seq(50,1500,50),
event = "Recurrent",MC.sample=100)
plot(pred.joint,conf.bands=TRUE)
# each y-value of the plot corresponds to the prediction between [100,x]
#-- prediction of relapse and death between 100 and 100+w given relapses
# (with confidence intervals)
pred.joint <- prediction(joi,datapredj,t=100,window=seq(50,1500,50),
event = "Both",MC.sample=100)
plot(pred.joint,conf.bands=TRUE)
# each y-value of the plot corresponds to the prediction between [100,x]
#############################################################################
### prediction on a JOINT model for longitudinal data and a terminal event ####
#############################################################################
data(colorectal)
data(colorectalLongi)
# Survival data preparation - only terminal events
colorectalSurv <- subset(colorectal, new.lesions == 0)
#-- construction of the data-frame for predictions
#-- biomarker observations
datapredj_longi <- data.frame(id = 0, year = 0, tumor.size = 0, treatment = 0,
age = 0, who.PS = 0, prev.resection = 0)
datapredj_longi$treatment <- as.factor(datapredj_longi$treatment)
levels(datapredj_longi$treatment) <- 1:2
datapredj_longi$age <- as.factor(datapredj_longi$age)
levels(datapredj_longi$age) <- 1:3
datapredj_longi$who.PS <- as.factor(datapredj_longi$who.PS)
levels(datapredj_longi$who.PS) <- 1:3
datapredj_longi$prev.resection <- as.factor(datapredj_longi$prev.resection)
levels(datapredj_longi$prev.resection) <- 1:2
# patient 1: increasing tumor size
datapredj_longi[1,] <- c(1, 0,1.2 ,2,1,1,1)
datapredj_longi[2,] <- c(1,0.3,1.4,2,1,1,1)
datapredj_longi[3,] <- c(1,0.6,1.9,2,1,1,1)
datapredj_longi[4,] <- c(1,0.9,2.5,2,1,1,1)
datapredj_longi[5,] <- c(1,1.5,3.9,2,1,1,1)
# patient 2: decreasing tumor size
datapredj_longi[6,] <- c(2, 0,1.2 ,2,1,1,1)
datapredj_longi[7,] <- c(2,0.3,0.7,2,1,1,1)
datapredj_longi[8,] <- c(2,0.5,0.3,2,1,1,1)
datapredj_longi[9,] <- c(2,0.7,0.1,2,1,1,1)
datapredj_longi[10,] <- c(2,0.9,0.1,2,1,1,1)
#-- terminal event
datapredj <- data.frame(id = 0, treatment = 0, age = 0, who.PS = 0,
prev.resection = 0)
datapredj$treatment <- as.factor(datapredj$treatment)
levels(datapredj$treatment) <- 1:2
datapredj$age <- as.factor(datapredj$age)
levels(datapredj$age) <- 1:3
datapredj$who.PS <- as.factor(datapredj$who.PS)
datapredj$prev.resection <- as.factor(datapredj$prev.resection)
levels(datapredj$prev.resection) <- 1:2
levels(datapredj$who.PS) <- 1:3
datapredj[1,] <- c(1,2,1,1,1)
datapredj[2,] <- c(2,2,1,1,1)
model.spli.CL <- longiPenal(Surv(time1, state) ~ age + treatment + who.PS
+ prev.resection, tumor.size ~ year * treatment + age + who.PS ,
colorectalSurv, data.Longi = colorectalLongi, random = c("1", "year"),
id = "id", link = "Current-level", left.censoring = -3.33, n.knots = 6,
kappa = 1)
#-- prediction of death between 1 year and 1+2 given history of the biomarker
pred.jointLongi0 <- prediction(model.spli.CL, datapredj, datapredj_longi,
t = 1, window = 2)
print(pred.jointLongi0)
#-- prediction of death between 1 year and 1+w given history of the biomarker
pred.jointLongi <- prediction(model.spli.CL, datapredj, datapredj_longi,
t = 1, window = seq(0.5, 2.5, 0.2), MC.sample = 100)
plot(pred.jointLongi, conf.bands = TRUE)
# each y-value of the plot corresponds to the prediction between [1,x]
#-- prediction of death between t and t+0.5 given history of the biomarker
pred.jointLongi2 <- prediction(model.spli.CL, datapredj, datapredj_longi,
t = seq(1, 2.5, 0.5), window = 0.5, MC.sample = 100)
plot(pred.jointLongi2, conf.bands = TRUE)
# each y-value of the plot corresponds to the prediction between [x,x+0.5],
#or in the next 0.5
#############################################################################
##### marginal prediction on a JOINT NESTED model for a terminal event ######
#############################################################################
#*--Warning! You can compute this prediction method with ONLY ONE family
#*--by dataset of prediction.
#*--Please make sure your data frame contains a column for individuals AND a
#*--column for the reference number of the family chosen.
data(readmission)
readmissionNested <- transform(readmission,group=id%%30+1)
#-- construction of the data frame for predictions :
#-- family 5 was selected for the prediction
DataPred <- readmissionNested[which(readmissionNested$group==5),]
#-- Fitting the model
modJointNested_Splines <-
frailtyPenal(formula = Surv(t.start, t.stop, event)~subcluster(id)+
cluster(group) + dukes + terminal(death),formula.terminalEvent
=~dukes, data = readmissionNested, recurrentAG = TRUE,n.knots = 8,
kappa = c(9.55e+9, 1.41e+12), initialize = TRUE)
#-- Compute prediction over the individuals 274 and 4 of the family 5
predRead <- prediction(modJointNested_Splines, data=DataPred,t=500,
window=seq(100,1500,200), conditional=FALSE, individual = c(274, 4))
#########################################################################
##### prediction on TRIVARIATE JOINT model (linear and non-linear) ######
#########################################################################
data(colorectal)
data(colorectalLongi)
#-- construction of the data frame for predictions
#-- history of recurrences and terminal event
datapredj <- data.frame(time0 = 0, time1 = 0, new.lesions = 0, id = 0,
treatment = 0, age = 0, who.PS = 0, prev.resection =0)
datapredj$treatment <- as.factor(datapredj$treatment)
levels(datapredj$treatment) <- 1:2
datapredj$age <- as.factor(datapredj$age)
levels(datapredj$age) <- 1:3
datapredj$who.PS <- as.factor(datapredj$who.PS)
levels(datapredj$who.PS) <- 1:3
datapredj$prev.resection <- as.factor(datapredj$prev.resection)
levels(datapredj$prev.resection) <- 1:2
datapredj[1,] <- c(0,0.4,1,1,2,1,1,1)
datapredj[2,] <- c(0.4,1.2,1,1,2,1,1,1)
datapredj[3,] <- c(0,0.5,1,2,2,1,1,1)
# Linear trivariate joint model
# (computation takes around 40 minutes)
model.trivPenal <-trivPenal(Surv(time0, time1, new.lesions) ~ cluster(id)
+ age + treatment + who.PS + 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 = TRUE,
n.knots = 6, kappa=c(0.01, 2), method.GH="Pseudo-adaptive",
n.nodes=7, init.B = c(-0.07, -0.13, -0.16, -0.17, 0.42, #recurrent events covarates
-0.23, -0.1, -0.09, -0.12, 0.8, -0.23, #terminal event covariates
3.02, -0.30, 0.05, -0.63, -0.02, -0.29, 0.11, 0.74)) #biomarker covariates
#-- prediction of death between 1 year and 1+2
pred.jointTri0 <- prediction(model.trivPenal, datapredj,
datapredj_longi, t = 1, window = 2)
print(pred.jointTri0)
#-- prediction of death between 1 year and 1+w
pred.jointTri <- prediction(model.trivPenal, datapredj,
datapredj_longi, t = 1, window = seq(0.5, 2.5, 0.2), MC.sample = 100)
plot(pred.jointTri, conf.bands = TRUE)
#-- prediction of death between t and t+0.5
pred.jointTri2 <- prediction(model.trivPenal, datapredj,
datapredj_longi, t = seq(1, 2.5, 0.5), window = 0.5, MC.sample = 100)
plot(pred.jointTri2, conf.bands = TRUE)
###############################
# 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")
#-- prediction of death between 1 year and 1+2
pred.jointTriNL0 <- prediction(model.trivPenalNL, datapredj,
datapredj_longi, t = 1, window = 2)
print(pred.jointTriNL0)
#-- prediction of death between 1 year and 1+w
pred.jointTriNL <- prediction(model.trivPenalNL, datapredj,
datapredj_longi, t = 1, window = seq(0.5, 2.5, 0.2), MC.sample = 100)
plot(pred.jointTriNL, conf.bands = TRUE)
#-- prediction of death between t and t+0.5
pred.jointTriNL2 <- prediction(model.trivPenalNL, datapredj,
datapredj_longi, t = seq(2, 3, 0.2), window = 0.5, MC.sample = 100)
plot(pred.jointTriNL2, conf.bands = TRUE)
## End(Not run)
frailtypack documentation built on Oct. 20, 2024, 1:08 a.m.
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| prediction | R Documentation |
Prediction probabilities for Cox proportional hazard, Shared, Joint frailty models, Joint models for longitudinal data and a terminal event and Trivariate joint model for longitudinal data, recurrent events and a terminal event (linear and non-linear).
Description
For Cox proportional hazard model
A predictive probability of event between t and horizon time t+w, with w the window of prediction.
For Gamma Shared Frailty model for clustered (not recurrent) events
Two kinds of predictive probabilities can be calculated:
- a conditional predictive probability of event between t and horizon time t+w, i.e. given a specific group
- a marginal predictive probability of event between t and horizon time t+w, i.e. averaged over the population
For Gaussian Shared Frailty model for clustered (not recurrent) events
Two kinds of predictive probabilities can be calculated:
- a conditional predictive probability of event between t and horizon time
t+w, i.e. given a specific group and given a specific Gaussian random effect
\eta
- a marginal predictive probability of event between t and horizon time t+w, i.e. averaged over the population
For Gamma Shared Frailty model for recurrent events
Two kinds of predictive probabilities can be calculated:
- A marginal predictive probability of event between t and horizon time t+w, i.e. averaged over the population.
- a conditional predictive probability of event between t and horizon time t+w, i.e. given a specific individual.
This prediction method is the same as the conditional gamma prediction
method applied for clustered events (see formula Pcond before).
For Gaussian Shared Frailty model for recurrent events
Two kinds of predictive probabilities can be calculated:
- A marginal predictive probability of event between t and horizon time t+w, i.e. averaged over the population.
- a conditional predictive probability of event between t and horizon time t+w, i.e. given a specific individual.
This prediction method is the same as the conditional Gaussian prediction
method applied for clustered events (see formula Pcond before).
It is possible to compute all these predictions in two ways on a scale of times : - either you want a cumulative probability of developing the event between t and t+w (with t fixed, but with a varying window of prediction w); - either you want at a specific time the probability to develop the event in the next w (ie, for a varying prediction time t, but for a fixed window of prediction). See Details.
For Joint Frailty model
Prediction for two types of event can be calculated : for a terminal event or for a new recurrent event, knowing patient's characteristics.
- Prediction of death knowing patients' characteristics :
It is to predict the probability of death in a specific time window given the history of patient i before the time of prediction t. The history HiJ,l, (l=1,2) is the information on covariates before time t, but also the number of recurrences and the time of occurences. Three types of marginal probabilities are computed:
- a prediction of death between t and t+w given that the patient had exactly J recurrences (HiJ,1) before t
- a prediction of death between t and t+w given that the patient had at least J recurrences (HiJ,2) before t
- a prediction of death between t and t+w considering the recurrence history only in the parameters estimation. It corresponds to the average probability of death between t and t+w for a patient with these given characteristics.
- Prediction of risk of a new recurrent event knowing patients' characteristics :
It is to predict the probability of a new recurrent event in a specific time
window given the history of patient i before the time of prediction t. The
history HiJ is the information on covariates before time t, but also
the number of recurrences and the time of occurences. The marginal
probability computed is a prediction of a new recurrent event between t and
t+w given that the patient had exactly J recurrences (HiJ) before t:
It is possible to compute all these predictions in two ways : - either you want a cumulative probability of developing the event between t and t+w (with t fixed, but with a varying window of prediction w); - either you want at a specific time the probability to develop the event in the next w (ie, for a varying prediction time t, but for a fixed window of prediction). See Details.
With Gaussian frailties (\eta), the same expressions are used but with
uiJ replaced by exp(J\etai) and g(\eta)
corresponds to the Gaussian distribution.
For Joint Nested Frailty models
Prediction of the probability of developing a terminal event between t and t+w for subject i who survived by time t based on the visiting and disease histories of their own and other family members observed by time t.
Let (YfiR(t)) be the history of subject i in family f,
before time t, which includes all the recurrent events and covariate
information. For disease history, let TfiD(t) = min(Tfi,t) be
the observed time to an event before t ; \deltafiD(t) the disease
indicator by time t and XfiD(t) the covariate information
observed up to time t. We define the family history of subject i in
family f by
which includes the visiting and disease history of all subjects except for subject i in family f as well as their covariate information by time t.
The prediction probability can be written as :
For Joint models for longitudinal data and a terminal event
The predicted probabilities are calculated in a specific time window given the history of biomarker measurements before the time of prediction t (ƴi(t)). The probabilities are conditional also on covariates before time t and that the subject was at risk at t. The marginal predicted probability of the terminal event is
These probabilities can be calculated in several time points with fixed time of prediction t and varying window w or with fixed window w and varying time of prediction t. See Details for an example of how to construct time windows.
For Trivariate joint models for longitudinal data, recurrent events and a terminal event
The predicted probabilities are calculated in a specific time window given the history of biomarker measurements ƴi(t) and recurrences HiJ,1 (complete history of recurrences with known J number of observed events) before the time of prediction t. The probabilities are conditional also on covariates before time t and that the subject was at risk at t. The marginal predicted probability of the terminal event is
The biomarker history can be represented using a linear (trivPenal)
or non-linear mixed-effects model (trivPenalNL).
These probabilities can be calculated in several time points with fixed time of prediction t and varying window w or with fixed window w and varying time of prediction t. See Details for an example of how to construct time windows.
Usage
prediction(fit, data, data.Longi, t, window, event="Both", conditional =
FALSE, MC.sample=0, individual)
Arguments
fit |
A frailtyPenal, jointPenal, longiPenal, trivPenal or trivPenalNL object. |
data |
Data frame for the prediction. See Details. |
data.Longi |
Data frame for the prediction used for joint models with longitudinal data. See Details. |
t |
Time or vector of times for prediction. |
window |
Window or vector of windows for prediction. |
event |
Only for joint and shared models. The type of event you want to predict : "Terminal" for a terminal event, "Recurrent" for a recurrent event or "Both". Default value is "Both". For joint nested model, only 'Terminal' is allowed. In a shared model, if you want to predict a new recurrent event then the argument "Recurrent" should be use. If you want to predict a new event from clustered data, do not use this option. |
conditional |
Only for prediction method applied on shared models. Provides distinction between the conditional and marginal prediction methods. Default is FALSE. |
MC.sample |
Number of samples used to calculate confidence bands with a Monte-Carlo method (with a maximum of 1000 samples). If MC.sample=0 (default value), no confidence intervals are calculated. |
individual |
Only for joint nested model. Vector of individuals (of the same family) you want to make prediction. |
Details
To compute predictions with a prediction time t fixed and a variable window:
prediction(fit, datapred, t=10, window=seq(1,10,by=1))
Otherwise, you can have a variable prediction time and a fixed window.
prediction(fit, datapred, t=seq(10,20,by=1), window=5)
Or fix both prediction time t and window.
prediction(fit, datapred, t=10, window=5)
The data frame building is an important step. It will contain profiles of patient on which you want to do predictions. To make predictions on a Cox proportional hazard or a shared frailty model, only covariates need to be included. You have to distinguish between numerical and categorical variables (factors). If we fit a shared frailty model with two covariates sex (factor) and age (numeric), here is the associated data frame for three profiles of prediction.
datapred <- data.frame(sex=0,age=0) datapred$sex <- as.factor(datapred$sex) levels(datapred$sex)<- c(1,2) datapred[1,] <- c(1,40) # man, 40 years old datapred[2,] <- c(2,45) # woman, 45 years old datapred[3,] <- c(1,60) # man, 60 years old
Time-dependent covariates: In the context of time-dependent covariate, the last previous value of the covariate is used before the time t of prediction.
It should be noted, that in a data frame for both marginal and conditional prediction on a shared frailty model for clustered data, the group must be specified. In the case of marginal predictions this can be any number as it does not influence predictions. However, for conditional predictions, the group must be also included in the data set used for the model fitting. The conditional predictions apply the empirical Bayes estimate of the frailty from the specified cluster. Here, three individuals belong to group 5.
datapred <- data.frame(group=0, sex=0,age=0) datapred$sex <- as.factor(datapred$sex) levels(datapred$sex)<- c(1,2) datapred[1,] <- c(5,1,40) # man, 40 years old (cluster 5) datapred[2,] <- c(5,2,45) # woman, 45 years old (cluster 5) datapred[3,] <- c(5,1,60) # man, 60 years old (cluster 5)
To use the prediction function on joint frailty models and trivariate joint models, the construction will be a little bit different. In these cases, the prediction for the terminal event takes into account covariates but also history of recurrent event times for a patient. You have to create a data frame with the relapse times, the indicator of event, the cluster variable and the covariates. Relapses occurring after the prediction time may be included but will be ignored for the prediction. A joint model with calendar-timescale need to be fitted with Surv(start,stop,event), relapse times correspond to the "stop" variable and indicators of event correspond to the "event" variable (if event=0, the relapse will not be taken into account). For patients without relapses, all the values of "event" variable should be set to 0. Finally, the same cluster variable name needs to be in the joint model and in the data frame for predictions ("id" in the following example). For instance, we observe relapses of a disease and fit a joint model adjusted for two covariates sex (1:male 2:female) and chemo (treatment by chemotherapy 1:no 2:yes). We describe 3 different profiles of prediction all treated by chemotherapy: 1) a man with four relapses at 100, 200, 300 and 400 days, 2) a man with only one relapse at 1000 days, 3) a woman without relapse.
datapred <- data.frame(time=0,event=0,id=0,sex=0,chemo=0) datapred$sex <- as.factor(datapred$sex) levels(datapred$sex) <- c(1,2) datapred$chemo <- as.factor(datapred$chemo) levels(datapred$chemo) <- c(1,2) datapred[1,] <- c(100,1,1,1,2) # first relapse of the patient 1 datapred[2,] <- c(200,1,1,1,2) # second relapse of the patient 1 datapred[3,] <- c(300,1,1,1,2) # third relapse of the patient 1 datapred[4,] <- c(400,1,1,1,2) # fourth relapse of the patient 1 datapred[5,] <- c(1000,1,2,1,2) # one relapse at 1000 days for patient 2 datapred[6,] <- c(100,0,3,2,2) # patient 3 did not relapse
The data can also be the dataset used to fit the joint model. In this case, you will obtain as many prediction rows as patients.
Finally, for the predictions using joint models for longitudinal data and a terminal event and trivariate joint models, a data frame with the history of the biomarker measurements must be provided. It must include data on measurements (values and time points), cluster variable and covariates. Measurements taken after the prediction time may be included but will be ignored for the prediction. The same cluster variable name must be in the data frame, in the data frame used for the joint model and in the data frame with the recurrent event and terminal event times. For instance, we observe two patients and each one had 5 tumor size measurements (patient 1 had an increasing tumor size and patient 2, decreasing). The joint model used for the predictions was adjusted on sex (1: male, 2: female), treatment (1: sequential arm, 2: combined arm), WHO baseline performance status (1: 0 status, 2: 1 status, 3: 2 status) and previous resection of the primate tumor (0: no, 1: yes). The data frame for the biomarker measurements can be:
datapredj_longi <- data.frame(id = 0, year = 0, tumor.size = 0, treatment = 0, age = 0, who.PS = 0, prev.resection = 0) datapredj_longi$treatment <- as.factor(datapredj_longi$treatment) levels(datapredj_longi$treatment) <- 1:2 datapredj_longi$age <- as.factor(datapredj_longi$age) levels(datapredj_longi$age) <- 1:3 datapredj_longi$who.PS <- as.factor(datapredj_longi$who.PS) levels(datapredj_longi$who.PS) <- 1:3 datapredj_longi$prev.resection <- as.factor (datapredj_longi$prev.resection) levels(datapredj_longi$prev.resection) <- 1:2 # patient 1: increasing tumor size datapredj_longi[1,] <- c(1, 0,1.2 ,2,1,1,1) datapredj_longi[2,] <- c(1,0.3,1.4,2,1,1,1) datapredj_longi[3,] <- c(1,0.6,1.9,2,1,1,1) datapredj_longi[4,] <- c(1,0.9,2.5,2,1,1,1) datapredj_longi[5,] <- c(1,1.5,3.9,2,1,1,1) # patient 2: decreasing tumor size datapredj_longi[6,] <- c(2, 0,1.2 ,2,1,1,1) datapredj_longi[7,] <- c(2,0.3,0.7,2,1,1,1) datapredj_longi[8,] <- c(2,0.5,0.3,2,1,1,1) datapredj_longi[9,] <- c(2,0.7,0.1,2,1,1,1) datapredj_longi[10,] <- c(2,0.9,0.1,2,1,1,1)
Value
The following components are included in a 'predFrailty' object obtained by using prediction function for Cox proportional hazard and shared frailty model.
npred |
Number of individual predictions |
x.time |
A vector of prediction times of interest (used for plotting predictions): vector of prediction times t if fixed window. Otherwise vector of prediction times t+w |
window |
Prediction window or vector of prediction windows |
pred |
Predictions estimated for each profile |
icproba |
Logical value. Were confidence intervals estimated ? |
predLow |
Lower limit of Monte-Carlo confidence interval for each prediction |
predHigh |
Upper limit of Monte-Carlo confidence interval for each prediction |
type |
Type of prediction probability (marginal or conditional) |
group |
For conditional probability, the list of group on which you make predictions |
The following components are included in a 'predJoint' object obtained by using prediction function for joint frailty model.
npred |
Number of individual predictions |
x.time |
A vector of prediction times of interest (used for plotting predictions): vector of prediction times t if fixed window. Otherwise vector of prediction times t+w |
window |
Prediction window or vector of prediction windows |
group |
Id of each patient |
pred1 |
Estimation of probability of type 1: exactly j recurrences |
pred2 |
Estimation of probability of type 2: at least j recurrences |
pred3 |
Estimation of probability of type 3 |
pred1_rec |
Estimation of prediction of relapse |
icproba |
Logical value. Were confidence intervals estimated ? |
predlow1 |
Lower limit of Monte-Carlo confidence interval for probability of type 1 |
predhigh1 |
Upper limit of Monte-Carlo confidence interval for probability of type 1 |
predlow2 |
Lower limit of Monte-Carlo confidence interval for probability of type 2 |
predhigh2 |
Upper limit of Monte-Carlo confidence interval for probability of type 2 |
predlow3 |
Lower limit of Monte-Carlo confidence interval for probability of type 3 |
predhigh3 |
Upper limit of Monte-Carlo confidence interval for probability of type 3 |
predhigh1_rec |
Upper limit of Monte-Carlo confidence interval for prediction of relapse |
predlow1_rec |
Lower limit of Monte-Carlo confidence interval for prediction of relapse |
The following components are included in a 'predLongi' object obtained by using prediction function for joint models with longitudinal data.
npred |
Number of individual predictions |
x.time |
A vector of prediction times of interest (used for plotting predictions): vector of prediction times t if fixed window. Otherwise vector of prediction times t+w |
window |
Prediction window or vector of prediction windows |
group |
Id of each patient |
pred |
Estimation of probability |
icproba |
Logical value. Were confidence intervals estimated? |
predLow |
Lower limit of Monte-Carlo confidence intervals |
predHigh |
Upper limit of Monte-Carlo confidence intervals |
trivariate |
Logical value. Are the prediction calculated from the trivariate model? |
References
A. Krol, L. Ferrer, JP. Pignon, C. Proust-Lima, M. Ducreux, O. Bouche, S. Michiels, V. Rondeau (2016). Joint Model for Left-Censored Longitudinal Data, Recurrent Events and Terminal Event: Predictive Abilities of Tumor Burden for Cancer Evolution with Application to the FFCD 2000-05 Trial. Biometrics 72(3) 907-16.
A. Mauguen, B. Rachet, S. Mathoulin-Pelissier, G. MacGrogan, A. Laurent, V. Rondeau (2013). Dynamic prediction of risk of death using history of cancer recurrences in joint frailty models. Statistics in Medicine, 32(30), 5366-80.
V. Rondeau, A. Laurent, A. Mauguen, P. Joly, C. Helmer (2015). Dynamic prediction models for clustered and interval-censored outcomes: investigating the intra-couple correlation in the risk of dementia. Statistical Methods in Medical Research
Examples
## Not run:
#####################################################
#### prediction on a COX or SHARED frailty model ####
#####################################################
data(readmission)
#-- here is a generated cluster (31 clusters of 13 subjects)
readmission <- transform(readmission,group=id%%31+1)
#-- we compute predictions of death
#-- we extract last row of each subject for the time of death
readmission <- aggregate(readmission,by=list(readmission$id),
FUN=function(x){x[length(x)]})[,-1]
##-- predictions on a Cox proportional hazard model --##
cox <- frailtyPenal(Surv(t.stop,death)~sex+dukes,
n.knots=10,kappa=10000,data=readmission)
#-- construction of the data frame for predictions
datapred <- data.frame(sex=0,dukes=0)
datapred$sex <- as.factor(datapred$sex)
levels(datapred$sex)<- c(1,2)
datapred$dukes <- as.factor(datapred$dukes)
levels(datapred$dukes)<- c(1,2,3)
datapred[1,] <- c(1,2) # man, dukes 2
datapred[2,] <- c(2,3) # woman, dukes 3
#-- prediction of death for two patients between 100 and 100+w,
#-- with w in (50,100,...,1900)
pred.cox <- prediction(cox,datapred,t=100,window=seq(50,1900,50))
plot(pred.cox)
#-- prediction of death for two patients between t and t+400,
#-- with t in (100,150,...,1500)
pred.cox2 <- prediction(cox,datapred,t=seq(100,1500,50),window=400)
plot(pred.cox2)
##-- predictions on a shared frailty model for clustered data --##
sha <- frailtyPenal(Surv(t.stop,death)~cluster(group)+sex+dukes,
n.knots=10,kappa=10000,data=readmission)
#-- marginal prediction
# a group must be specified but it does not influence the results
# in the marginal predictions setting
datapred$group[1:2] <- 1
pred.sha.marg <- prediction(sha,datapred,t=100,window=seq(50,1900,50))
plot(pred.sha.marg)
#-- conditional prediction, given a specific cluster (group=5)
datapred$group[1:2] <- 5
pred.sha.cond <- prediction(sha,datapred,t=100,window=seq(50,1900,50),
conditional = TRUE)
plot(pred.sha.cond)
##-- marginal prediction of a recurrent event, on a shared frailty model
data(readmission)
datapred <- data.frame(t.stop=0,event=0,id=0,sex=0,dukes=0)
datapred$sex <- as.factor(datapred$sex)
levels(datapred$sex)<- c(1,2)
datapred$dukes <- as.factor(datapred$dukes)
levels(datapred$dukes)<- c(1,2,3)
datapred[1,] <- c(100,1,1,1,2) #man, dukes 2, 3 recurrent events
datapred[2,] <- c(200,1,1,1,2)
datapred[3,] <- c(300,1,1,1,2)
datapred[4,] <- c(350,0,2,1,2) #man, dukes 2 0 recurrent event
#-- Shared frailty model with gamma distribution
sha <- frailtyPenal(Surv(t.stop,event)~cluster(id)+sex+dukes,n.knots=10,
kappa=10000,data=readmission)
pred.sha.rec.marg <- prediction(sha,datapred,t=200,window=seq(50,1900,50),
event='Recurrent',MC.sample=100)
plot(pred.sha.rec.marg,conf.bands=TRUE)
##-- conditional prediction of a recurrent event, on a shared frailty model
pred.sha.rec.cond <- prediction(sha,datapred,t=200,window=seq(50,1900,50),
event='Recurrent',conditional = TRUE,MC.sample=100)
plot(pred.sha.rec.cond,conf.bands=TRUE)
#####################################################
######## prediction on a JOINT frailty model ########
#####################################################
data(readmission)
##-- predictions of death on a joint model --##
joi <- frailtyPenal(Surv(t.start,t.stop,event)~cluster(id)
+sex+dukes+terminal(death),formula.terminalEvent=~sex
+dukes,data=readmission,n.knots=10,kappa=c(100,100),recurrentAG=TRUE)
#-- construction of the data frame for predictions
datapredj <- data.frame(t.stop=0,event=0,id=0,sex=0,dukes=0)
datapredj$sex <- as.factor(datapredj$sex)
levels(datapredj$sex) <- c(1,2)
datapredj$dukes <- as.factor(datapredj$dukes)
levels(datapredj$dukes) <- c(1,2,3)
datapredj[1,] <- c(100,1,1,1,2)
datapredj[2,] <- c(200,1,1,1,2)
datapredj[3,] <- c(300,1,1,1,2)
datapredj[4,] <- c(400,1,1,1,2)
datapredj[5,] <- c(380,1,2,1,2)
#-- prediction of death between 100 and 100+500 given relapses
pred.joint0 <- prediction(joi,datapredj,t=100,window=500,event = "Terminal")
print(pred.joint0)
#-- prediction of death between 100 and 100+w given relapses
# (with confidence intervals)
pred.joint <- prediction(joi,datapredj,t=100,window=seq(50,1500,50),
event = "Terminal",MC.sample=100)
plot(pred.joint,conf.bands=TRUE)
# each y-value of the plot corresponds to the prediction between [100,x]
#-- prediction of death between t and t+500 given relapses
pred.joint2 <- prediction(joi,datapredj,t=seq(100,1000,50),
window=500,event = "Terminal")
plot(pred.joint2)
# each y-value of the plot corresponds to the prediction between [x,x+500],
#or in the next 500
#-- prediction of relapse between 100 and 100+w given relapses
# (with confidence intervals)
pred.joint <- prediction(joi,datapredj,t=100,window=seq(50,1500,50),
event = "Recurrent",MC.sample=100)
plot(pred.joint,conf.bands=TRUE)
# each y-value of the plot corresponds to the prediction between [100,x]
#-- prediction of relapse and death between 100 and 100+w given relapses
# (with confidence intervals)
pred.joint <- prediction(joi,datapredj,t=100,window=seq(50,1500,50),
event = "Both",MC.sample=100)
plot(pred.joint,conf.bands=TRUE)
# each y-value of the plot corresponds to the prediction between [100,x]
#############################################################################
### prediction on a JOINT model for longitudinal data and a terminal event ####
#############################################################################
data(colorectal)
data(colorectalLongi)
# Survival data preparation - only terminal events
colorectalSurv <- subset(colorectal, new.lesions == 0)
#-- construction of the data-frame for predictions
#-- biomarker observations
datapredj_longi <- data.frame(id = 0, year = 0, tumor.size = 0, treatment = 0,
age = 0, who.PS = 0, prev.resection = 0)
datapredj_longi$treatment <- as.factor(datapredj_longi$treatment)
levels(datapredj_longi$treatment) <- 1:2
datapredj_longi$age <- as.factor(datapredj_longi$age)
levels(datapredj_longi$age) <- 1:3
datapredj_longi$who.PS <- as.factor(datapredj_longi$who.PS)
levels(datapredj_longi$who.PS) <- 1:3
datapredj_longi$prev.resection <- as.factor(datapredj_longi$prev.resection)
levels(datapredj_longi$prev.resection) <- 1:2
# patient 1: increasing tumor size
datapredj_longi[1,] <- c(1, 0,1.2 ,2,1,1,1)
datapredj_longi[2,] <- c(1,0.3,1.4,2,1,1,1)
datapredj_longi[3,] <- c(1,0.6,1.9,2,1,1,1)
datapredj_longi[4,] <- c(1,0.9,2.5,2,1,1,1)
datapredj_longi[5,] <- c(1,1.5,3.9,2,1,1,1)
# patient 2: decreasing tumor size
datapredj_longi[6,] <- c(2, 0,1.2 ,2,1,1,1)
datapredj_longi[7,] <- c(2,0.3,0.7,2,1,1,1)
datapredj_longi[8,] <- c(2,0.5,0.3,2,1,1,1)
datapredj_longi[9,] <- c(2,0.7,0.1,2,1,1,1)
datapredj_longi[10,] <- c(2,0.9,0.1,2,1,1,1)
#-- terminal event
datapredj <- data.frame(id = 0, treatment = 0, age = 0, who.PS = 0,
prev.resection = 0)
datapredj$treatment <- as.factor(datapredj$treatment)
levels(datapredj$treatment) <- 1:2
datapredj$age <- as.factor(datapredj$age)
levels(datapredj$age) <- 1:3
datapredj$who.PS <- as.factor(datapredj$who.PS)
datapredj$prev.resection <- as.factor(datapredj$prev.resection)
levels(datapredj$prev.resection) <- 1:2
levels(datapredj$who.PS) <- 1:3
datapredj[1,] <- c(1,2,1,1,1)
datapredj[2,] <- c(2,2,1,1,1)
model.spli.CL <- longiPenal(Surv(time1, state) ~ age + treatment + who.PS
+ prev.resection, tumor.size ~ year * treatment + age + who.PS ,
colorectalSurv, data.Longi = colorectalLongi, random = c("1", "year"),
id = "id", link = "Current-level", left.censoring = -3.33, n.knots = 6,
kappa = 1)
#-- prediction of death between 1 year and 1+2 given history of the biomarker
pred.jointLongi0 <- prediction(model.spli.CL, datapredj, datapredj_longi,
t = 1, window = 2)
print(pred.jointLongi0)
#-- prediction of death between 1 year and 1+w given history of the biomarker
pred.jointLongi <- prediction(model.spli.CL, datapredj, datapredj_longi,
t = 1, window = seq(0.5, 2.5, 0.2), MC.sample = 100)
plot(pred.jointLongi, conf.bands = TRUE)
# each y-value of the plot corresponds to the prediction between [1,x]
#-- prediction of death between t and t+0.5 given history of the biomarker
pred.jointLongi2 <- prediction(model.spli.CL, datapredj, datapredj_longi,
t = seq(1, 2.5, 0.5), window = 0.5, MC.sample = 100)
plot(pred.jointLongi2, conf.bands = TRUE)
# each y-value of the plot corresponds to the prediction between [x,x+0.5],
#or in the next 0.5
#############################################################################
##### marginal prediction on a JOINT NESTED model for a terminal event ######
#############################################################################
#*--Warning! You can compute this prediction method with ONLY ONE family
#*--by dataset of prediction.
#*--Please make sure your data frame contains a column for individuals AND a
#*--column for the reference number of the family chosen.
data(readmission)
readmissionNested <- transform(readmission,group=id%%30+1)
#-- construction of the data frame for predictions :
#-- family 5 was selected for the prediction
DataPred <- readmissionNested[which(readmissionNested$group==5),]
#-- Fitting the model
modJointNested_Splines <-
frailtyPenal(formula = Surv(t.start, t.stop, event)~subcluster(id)+
cluster(group) + dukes + terminal(death),formula.terminalEvent
=~dukes, data = readmissionNested, recurrentAG = TRUE,n.knots = 8,
kappa = c(9.55e+9, 1.41e+12), initialize = TRUE)
#-- Compute prediction over the individuals 274 and 4 of the family 5
predRead <- prediction(modJointNested_Splines, data=DataPred,t=500,
window=seq(100,1500,200), conditional=FALSE, individual = c(274, 4))
#########################################################################
##### prediction on TRIVARIATE JOINT model (linear and non-linear) ######
#########################################################################
data(colorectal)
data(colorectalLongi)
#-- construction of the data frame for predictions
#-- history of recurrences and terminal event
datapredj <- data.frame(time0 = 0, time1 = 0, new.lesions = 0, id = 0,
treatment = 0, age = 0, who.PS = 0, prev.resection =0)
datapredj$treatment <- as.factor(datapredj$treatment)
levels(datapredj$treatment) <- 1:2
datapredj$age <- as.factor(datapredj$age)
levels(datapredj$age) <- 1:3
datapredj$who.PS <- as.factor(datapredj$who.PS)
levels(datapredj$who.PS) <- 1:3
datapredj$prev.resection <- as.factor(datapredj$prev.resection)
levels(datapredj$prev.resection) <- 1:2
datapredj[1,] <- c(0,0.4,1,1,2,1,1,1)
datapredj[2,] <- c(0.4,1.2,1,1,2,1,1,1)
datapredj[3,] <- c(0,0.5,1,2,2,1,1,1)
# Linear trivariate joint model
# (computation takes around 40 minutes)
model.trivPenal <-trivPenal(Surv(time0, time1, new.lesions) ~ cluster(id)
+ age + treatment + who.PS + terminal(state),
formula.terminalEvent =~ age + treatment + who.PS + prev.resection,
tumor.size ~ year * treatment + age + who.PS, data = colorectal,
data.Longi = colorectalLongi, random = c("1", "year"), id = "id",
link = "Random-effects", left.censoring = -3.33, recurrentAG = TRUE,
n.knots = 6, kappa=c(0.01, 2), method.GH="Pseudo-adaptive",
n.nodes=7, init.B = c(-0.07, -0.13, -0.16, -0.17, 0.42, #recurrent events covarates
-0.23, -0.1, -0.09, -0.12, 0.8, -0.23, #terminal event covariates
3.02, -0.30, 0.05, -0.63, -0.02, -0.29, 0.11, 0.74)) #biomarker covariates
#-- prediction of death between 1 year and 1+2
pred.jointTri0 <- prediction(model.trivPenal, datapredj,
datapredj_longi, t = 1, window = 2)
print(pred.jointTri0)
#-- prediction of death between 1 year and 1+w
pred.jointTri <- prediction(model.trivPenal, datapredj,
datapredj_longi, t = 1, window = seq(0.5, 2.5, 0.2), MC.sample = 100)
plot(pred.jointTri, conf.bands = TRUE)
#-- prediction of death between t and t+0.5
pred.jointTri2 <- prediction(model.trivPenal, datapredj,
datapredj_longi, t = seq(1, 2.5, 0.5), window = 0.5, MC.sample = 100)
plot(pred.jointTri2, conf.bands = TRUE)
###############################
# No information on dose - creation of a dummy variable
colorectalLongi$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")
#-- prediction of death between 1 year and 1+2
pred.jointTriNL0 <- prediction(model.trivPenalNL, datapredj,
datapredj_longi, t = 1, window = 2)
print(pred.jointTriNL0)
#-- prediction of death between 1 year and 1+w
pred.jointTriNL <- prediction(model.trivPenalNL, datapredj,
datapredj_longi, t = 1, window = seq(0.5, 2.5, 0.2), MC.sample = 100)
plot(pred.jointTriNL, conf.bands = TRUE)
#-- prediction of death between t and t+0.5
pred.jointTriNL2 <- prediction(model.trivPenalNL, datapredj,
datapredj_longi, t = seq(2, 3, 0.2), window = 0.5, MC.sample = 100)
plot(pred.jointTriNL2, conf.bands = TRUE)
## End(Not run)
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