Description Usage Arguments Details Value Author(s) References See Also Examples
Using the available longitudinal information up to a starting time point, this function computes an estimate of the ROC and the AUC at a horizon time point based on joint models.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  aucJM(object, newdata, Tstart, ...)
## S3 method for class 'JMbayes'
aucJM(object, newdata, Tstart, Thoriz = NULL,
Dt = NULL, idVar = "id", simulate = FALSE, M = 100, ...)
## S3 method for class 'mvJMbayes'
aucJM(object, newdata, Tstart, Thoriz = NULL,
Dt = NULL, idVar = "id", M = 100, ...)
rocJM(object, newdata, Tstart, ...)
## S3 method for class 'JMbayes'
rocJM(object, newdata, Tstart, Thoriz = NULL,
Dt = NULL, idVar = "id", simulate = FALSE, M = 100, ...)
## S3 method for class 'mvJMbayes'
rocJM(object, newdata, Tstart, Thoriz = NULL,
Dt = NULL, idVar = "id", M = 100, ...)

object 
an object inheriting from class 
newdata 
a data frame that contains the longitudinal and covariate information for the subjects for which prediction
of survival probabilities is required. The names of the variables in this data frame must be the same as in the data frames that
were used to fit the linear mixed effects model (using 
Tstart 
numeric scalar denoting the time point up to which longitudinal information is to be used to derive predictions. 
Thoriz 
numeric scalar denoting the time point for which a prediction of the survival status is of interest;

Dt 
numeric scalar denoting the length of the time interval of prediction; either 
idVar 
the name of the variable in 
simulate 
logical; if 
M 
a numeric scalar denoting the number of Monte Carlo samples; see 
... 
additional arguments; currently none is used. 
Based on a fitted joint model (represented by object
) and using the data supplied in argument newdata
, this function
computes the following estimate of the AUC:
\mbox{AUC}(t, Δ t) = \mbox{Pr} \bigl [ π_i(t + Δ t \mid t) < π_j(t + Δ t \mid t) \mid \{ T_i^* \in (t, t + Δ t] \} \cap \{ T_j^* > t + Δ t \} \bigr ],
with i and j denote a randomly selected pair of subjects, and
π_i(t + Δ t \mid t) and π_j(t + Δ t \mid t) denote the conditional survival probabilities calculated by
survfitJM
for these two subjects, for different time windows Δ t specified by argument Dt
using
the longitudinal information recorded up to time t =
Tstart
.
The estimate of \mbox{AUC}(t, Δ t) provided by aucJM()
is in the spirit of Harrell's
cindex, that is for the comparable subjects (i.e., the ones whose observed event times can be ordered), we
compare their dynamic survival probabilities calculated by survfitJM
. For the subjects who due to
censoring we do not know if they are comparable, they contribute in the AUC with the probability that they would
have been comparable.
A list of class aucJM
with components:
auc 
a numeric scalar denoting the estimated prediction error. 
Tstart 
a copy of the 
Thoriz 
a copy of the 
nr 
a numeric scalar denoting the number of subjects at risk at time 
classObject 
the class of 
nameObject 
the name of 
Dimitris Rizopoulos [email protected]
Antolini, L., Boracchi, P., and Biganzoli, E. (2005). A timedependent discrimination index for survival data. Statistics in Medicine 24, 3927–3944.
Harrell, F., Kerry, L. and Mark, D. (1996). Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Statistics in Medicine 15, 361–387.
Heagerty, P. and Zheng, Y. (2005). Survival model predictive accuracy and ROC curves. Biometrics 61, 92–105.
Rizopoulos, D. (2016). The R package JMbayes for fitting joint models for longitudinal and timetoevent data using MCMC. Journal of Statistical Software 72(7), 1–45. doi:10.18637/jss.v072.i07.
Rizopoulos, D. (2012) Joint Models for Longitudinal and TimetoEvent Data: with Applications in R. Boca Raton: Chapman and Hall/CRC.
Rizopoulos, D. (2011). Dynamic predictions and prospective accuracy in joint models for longitudinal and timetoevent data. Biometrics 67, 819–829.
survfitJM
, dynCJM
, jointModelBayes
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  ## Not run:
# we construct the composite event indicator (transplantation or death)
pbc2$status2 < as.numeric(pbc2$status != "alive")
pbc2.id$status2 < as.numeric(pbc2.id$status != "alive")
# we fit the joint model using splines for the subjectspecific
# longitudinal trajectories and a splineapproximated baseline
# risk function
lmeFit < lme(log(serBilir) ~ ns(year, 3),
random = list(id = pdDiag(form = ~ ns(year, 3))), data = pbc2)
survFit < coxph(Surv(years, status2) ~ drug, data = pbc2.id, x = TRUE)
jointFit < jointModelBayes(lmeFit, survFit, timeVar = "year")
# AUC using data up to year 5 with horizon at year 8
aucJM(jointFit, pbc2, Tstart = 5, Thoriz = 8)
plot(rocJM(jointFit, pbc2, Tstart = 5, Thoriz = 8))
## End(Not run)

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