This function computes the conditional probability of surviving later times than the last observed time for which a longitudinal measurement was available.
survfitJM(object, newdata, ...)# S3 method for jointModel
survfitJM(object, newdata, idVar = "id", simulate = TRUE, survTimes = NULL,
last.time = NULL, M = 200, CI.levels = c(0.025, 0.975), scale = 1.6, ...)
A list of class survfitJM with components:
a list with elements numeric matrices with numeric summaries of the predicted probabilities for each subject.
a copy of the survTimes argument.
a numeric vector with the time of the last available longitudinal measurement of each subject.
a list with elements numeric vectors denoting the timings of the longitudinal measurements for each subject.
a list with elements numeric vectors denoting the longitudinal responses for each subject.
a list with elements numeric matrices with predicted probabilities for each subject in each replication of the Monte Carlo scheme described above.
a numeric vector with the success rates of the Metropolis-Hastings algorithm described above for each subject.
a copy of the scale argument.
an object inheriting from class jointModel.
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 lme()) and the survival model (using coxph() or survreg())
that were supplied as the two first argument of jointModel. In addition, this data frame should contain a variable
that identifies the different subjects (see also argument idVar).
the name of the variable in newdata that identifies the different subjects.
logical; if TRUE, a Monte Carlo approach is used to estimate survival probabilities. If FALSE,
a first order estimator is used instead. (see Details)
a numeric vector of times for which prediction survival probabilities are to be computed.
a numeric vector or character string. This specifies the known time at which each of the subjects in newdat
was known to be alive. If NULL, then this is automatically taken as the last time each subject provided a longitudinal
measurement. If a numeric vector, then it is assumed to contain this last time point for each subject. If a character string, then
it should be a variable in the data frame newdata.
integer denoting how many Monte Carlo samples to use -- see Details.
a numeric vector of length two that specifies which quantiles to use for the calculation of confidence interval for the predicted probabilities -- see Details.
a numeric scalar that controls the acceptance rate of the Metropolis-Hastings algorithm -- see Details.
additional arguments; currently none is used.
Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl
Based on a fitted joint model (represented by object), and a history of longitudinal responses
\(\tilde{y}_i(t) = \{y_i(s), 0 \leq s \leq t\}\) and a covariates vector \(x_i\) (stored in
newdata), this function provides estimates of \(Pr(T_i > u | T_i > t, \tilde{y}_i(t), x_i)\), i.e., the conditional probability of surviving time \(u\) given that subject \(i\), with covariate information
\(x_i\), has survived up to time \(t\) and has provided longitudinal the measurements \(\tilde{y}_i(t)\).
To estimate \(Pr(T_i > u | T_i > t, \tilde{y}_i(t), x_i)\) and if simulate = TRUE, a
Monte Carlo procedure is followed with the following steps:
Simulate new parameter values, say \(\theta^*\), from \(N(\hat{\theta}, C(\hat{\theta}))\),
where \(\hat{\theta}\) are the MLEs and \(C(\hat{\theta})\) their large sample covariance matrix, which are extracted from
object.
Simulate random effects values, say \(b_i^*\), from their posterior distribution given survival up to time \(t\),
the vector of longitudinal responses \(\tilde{y}_i(t)\) and \(\theta^*\). This is achieved using a Metropolis-Hastings algorithm with
independent proposals from a properly centered and scaled multivariate \(t\) distribution. The scale argument controls the
acceptance rate for this algorithm.
Using \(\theta^*\) and \(b_i^*\), compute \(Pr(T_i > u | T_i > t, b_i^*, x_i; \theta^*)\).
Repeat Steps 1-3 M times.
Based on the M estimates of the conditional probabilities, we compute useful summary statistics, such as their mean, median, and
quantiles (to produce a confidence interval).
If simulate = FALSE, then survival probabilities are estimated using the formula $$Pr(T_i > u | T_i > t, \hat{b}_i, x_i;
\hat{\theta}),$$ where \(\hat{\theta}\) denotes the MLEs as above, and \(\hat{b}_i\)
denotes the empirical Bayes estimates.
Rizopoulos, D. (2012) Joint Models for Longitudinal and Time-to-Event 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 time-to-event data. Biometrics 67, 819--829.
Rizopoulos, D. (2010) JM: An R Package for the Joint Modelling of Longitudinal and Time-to-Event Data. Journal of Statistical Software 35 (9), 1--33. tools:::Rd_expr_doi("10.18637/jss.v035.i09")
jointModel, plot.survfitJM
# linear mixed model fit
fitLME <- lme(sqrt(CD4) ~ obstime + obstime:drug,
random = ~ 1 | patient, data = aids)
# cox model fit
fitCOX <- coxph(Surv(Time, death) ~ drug, data = aids.id, x = TRUE)
# joint model fit
fitJOINT <- jointModel(fitLME, fitCOX,
timeVar = "obstime", method = "weibull-PH-aGH")
# sample of the patients who are still alive
ND <- aids[aids$patient == "141", ]
ss <- survfitJM(fitJOINT, newdata = ND, idVar = "patient", M = 50)
ss
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