Dynamic predictions for the longitudinal data sub-model
Calculates the conditional expected longitudinal values for a
new subject from the last observation time given their longitudinal
history data and a fitted mjoint object.
dynLong( object, newdata, newSurvData = NULL, u = NULL, type = "first-order", M = 200, scale = 1.6, ci, progress = TRUE, ntimes = 100, level = 1 )
object |
an object inheriting from class |
newdata |
a list of |
newSurvData |
a |
u |
an optional time that must be greater than the last observed
measurement time. If omitted (default is |
type |
a character string for whether a first-order
( |
M |
for |
scale |
a numeric scalar that scales the variance parameter of the proposal distribution for the Metropolis-Hastings algorithm, which therefore controls the acceptance rate of the sampling algorithm. |
ci |
a numeric value with value in the interval (0, 1) specifying
the confidence interval level for predictions of |
progress |
logical: should a progress bar be shown on the console to
indicate the percentage of simulations completed? Default is
|
ntimes |
an integer controlling the number of points to discretize the
extrapolated time region into. Default is |
level |
an optional integer giving the level of grouping to be used in
extracting the residuals from object. Level values increase from outermost
to innermost grouping, with level 0 corresponding to the population model
fit and level 1 corresponding to subject-specific model fit. Defaults to
|
Dynamic predictions for the longitudinal data sub-model based on an observed measurement history for the longitudinal outcomes of a new subject are based on either a first-order approximation or Monte Carlo simulation approach, both of which are described in Rizopoulos (2011). Namely, given that the subject was last observed at time t, we calculate the conditional expectation of each longitudinal outcome at time u as
E[y_k(u) | T ≥ t, y, θ] \approx x^T(u)β_k + z^T(u)\hat{b}_k,
where T is the failure time for the new subject, and y is the stacked-vector of longitudinal measurements up to time t.
First order predictions
For type="first-order", \hat{b} is the mode of the posterior
distribution of the random effects given by
\hat{b} = {\arg \max}_b f(b | y, T ≥ t; θ).
The predictions are based on plugging in θ = \hat{θ}, which
is extracted from the mjoint object.
Monte Carlo simulation predictions
For type="simulated", θ is drawn from a multivariate
normal distribution with means \hat{θ} and variance-covariance
matrix both extracted from the fitted mjoint object via the
coef() and vcov() functions. \hat{b} is drawn from the
the posterior distribution of the random effects
f(b | y, T ≥ t; θ)
by means of a Metropolis-Hasting algorithm with independent multivariate
non-central t-distribution proposal distributions with
non-centrality parameter \hat{b} from the first-order prediction and
variance-covariance matrix equal to scale \times the inverse
of the negative Hessian of the posterior distribution. The choice os
scale can be used to tune the acceptance rate of the
Metropolis-Hastings sampler. This simulation algorithm is iterated M
times, at each time calculating the conditional survival probability.
A list object inheriting from class dynLong. The list returns
the arguments of the function and a list containing K
data.frames of 2 columns, with first column (named
timeVar[k]; see mjoint) denoting times and the second
column (named y.pred) denoting the expected outcome at each time
point.
Graeme L. Hickey (graemeleehickey@gmail.com)
Rizopoulos D. Dynamic predictions and prospective accuracy in joint models for longitudinal and time-to-event data. Biometrics. 2011; 67: 819–829.
## Not run:
# Fit a joint model with bivariate longitudinal outcomes
data(heart.valve)
hvd <- heart.valve[!is.na(heart.valve$log.grad) & !is.na(heart.valve$log.lvmi), ]
fit2 <- mjoint(
formLongFixed = list("grad" = log.grad ~ time + sex + hs,
"lvmi" = log.lvmi ~ time + sex),
formLongRandom = list("grad" = ~ 1 | num,
"lvmi" = ~ time | num),
formSurv = Surv(fuyrs, status) ~ age,
data = list(hvd, hvd),
inits = list("gamma" = c(0.11, 1.51, 0.80)),
timeVar = "time",
verbose = TRUE)
hvd2 <- droplevels(hvd[hvd$num == 1, ])
dynLong(fit2, hvd2)
dynLong(fit2, hvd2, u = 7) # outcomes at 7-years only
out <- dynLong(fit2, hvd2, type = "simulated")
out
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