Dynamic predictions for the time-to-event data sub-model
Calculates the conditional time-to-event distribution for a
new subject from the last observation time given their longitudinal
history data and a fitted mjoint object.
dynSurv( object, newdata, newSurvData = NULL, u = NULL, horizon = NULL, type = "first-order", M = 200, scale = 2, ci, progress = TRUE )
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 |
horizon |
an optional horizon time. Instead of specifying a specific
time |
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
|
Dynamic predictions for the time-to-event 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 survival probability at time u > t as
P[T ≥ u | T ≥ t; y, θ] \approx \frac{S(u | \hat{b}; θ)}{S(t | \hat{b}; θ)},
where T is the failure time for the new subject, y is the stacked-vector of longitudinal measurements up to time t and S(u | \hat{b}; θ) is the survival function.
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 dynSurv. The list returns
the arguments of the function and a data.frame with first column
(named u) denoting times and the subsequent columns returning
summary statistics for the conditional failure probabilities For
type="first-order", a single column named surv is appended.
For type="simulated", four columns named mean, median,
lower and upper are appended, denoting the mean, median and
lower and upper confidence intervals from the Monte Carlo draws. Additional
objects are returned that are used in the intermediate calculations.
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.
Taylor JMG, Park Y, Ankerst DP, Proust-Lima C, Williams S, Kestin L, et al. Real-time individual predictions of prostate cancer recurrence using joint models. Biometrics. 2013; 69: 206–13.
mjoint, dynLong, and
plot.dynSurv.
## 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, ])
dynSurv(fit2, hvd2)
dynSurv(fit2, hvd2, u = 7) # survival at 7-years only
out <- dynSurv(fit2, hvd2, type = "simulated")
out
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.