mjoint objectThis function takes a model fit from an mjoint object and
calculates standard errors and confidence intervals for the main
longitudinal and survival coefficient parameters, including the latent
association parameters, using bootstrapping (Efron and Tibshirani, 2000).
bootSE(
object,
nboot = 100,
ci = 0.95,
use.mle = TRUE,
verbose = FALSE,
control = list(),
progress = TRUE,
ncores = 1,
safe.boot = FALSE,
...
)An object of class bootSE.
an object inheriting from class mjoint for a joint model
of time-to-event and multivariate longitudinal data.
the number of bootstrap samples. Default is nboot=100.
the confidence interval to be estimated using the
percentile-method. Default is ci=0.95 for a 95% confidence
interval.
logical: should the algorithm use the maximizer from the
converged model in object as initial values for coefficients in each
bootstrap iteration. Default is use.mle=TRUE.
logical: if TRUE, the parameter estimates and other
convergence statistics are value are printed at each iteration of the MCEM
algorithm. Default is FALSE.
a list of control values with components:
nMCinteger: the initial number of Monte Carlo samples to be
used for integration in the burn-in phase of the MCEM. Default is
nMC=100K.
nMCscaleinteger: the scale factor for the increase in Monte
Carlo size when Monte Carlo has not reduced from the previous iteration.
Default is nMCscale=5.
nMCmaxinteger: the maximum number of Monte Carlo samples
that the algorithm is allowed to reach. Default is nMCmax=20000.
burnininteger: the number of iterations for 'burn-in' phase
of the optimization algorithm. It is computationally inefficient to use a
large number of Monte Carlo samples early on until one is approximately
near the maximum likelihood estimate. Default is burnin=100K
for type='antithetic' or type='montecarlo' and
burnin=5 for type='sobol' or type='halton'. For
standard methods, such a large burn-in will generally be unnecessary and
can be reduced on an application-specific basis.
mcmaxIterinteger: the maximum number of MCEM algorithm
iterations allowed. Default is mcmaxIter=burnin+200.
convCritcharacter string: the convergence criterion to be used. See Details.
gammaOptcharacter string: by default (gammaOpt='NR'),
\(\gamma\) is updated using a one-step Newton-Raphson iteration, with the
Hessian matrix calculated exactly. If gammaOpt='GN', a Gauss-Newton
algorithm-type iteration is implemented, where the Hessian matrix is
approximated based on calculations similar to those used for calculating
the empirical information matrix? If it is used, then the step-length is
adjusted by a nominal scaling parameter of 0.5 in order to reduce the
chance of over-shooting the maximizer.
tol0numeric: tolerance value for convergence in the
parameters; see Details. Default is tol0=1e-03.
tol1numeric: tolerance value for convergence in the
parameters; see Details. Default is tol1=1e-03.
tol2numeric: tolerance value for convergence in the
parameters; see Details. Default is tol2=5e-03 for
type='antithetic' or type='montecarlo' and tol2=1e-03
for type='sobol' or type='halton'.
tol.emnumeric: tolerance value for convergence in the
multivariate linear mixed model (MV-LMM). When \(K > 1\), the optimal
initial parameters are those from the MV-LMM, which is estimated using a
separate EM algorithm. Since both the E- and M-steps are available in
closed-form, this algorithm convergences relatively rapidly with a high
precision. Default is min(1e-04, tol2).
ravnumeric: threshold when using convCrit='sas' that
applies absolute change (when \(<\)rav) or relative change (when
\(\ge\)rav) criterion; see Details. Default is
0.1, which is an order of magnitude higher than the SAS
implementation.
typecharacter: type of Monte Carlo integration method to use. Options are
type='montecarlo'Vanilla Monte Carlo sampling.
type='antithetic'Variance reduction method using antithetic simulation. This is the default option.
type='sobol'Quasi-Monte Carlo with a low deterministic Sobol sequence with Owen-type scrambling.
type='halton'Quasi-Monte Carlo with a low deterministic Halton sequence.
logical: should a progress bar be shown on the console to
indicate the percentage of bootstrap iterations completed? Default is
progress=TRUE.
integer: if more than one core is available, then the bootSE
function can run in parallel via the foreach
function. By default, ncores=1, which defaults to serial mode. Note
that if ncores>1, then progress is set to FALSE by
default, as it is not possible to display progress bars for parallel
processes at the current time.
logical: should each bootstrap replication be wrapped in a
tryCatch statement to catch errors (e.g. during the
optimisation progress)? When model fitting throws errors, a new bootstrap
sample is drawn for the current iteration and the model is re-fit; this
process continuex until a model fits successfully. Default is FALSE.
options passed to the control argument.
Graeme L. Hickey (graemeleehickey@gmail.com)
Standard errors and confidence intervals are obtained by repeated fitting of the requisite joint model to bootstrap samples of the original longitudinal and time-to-event data. Note that bootstrap is done by sampling subjects, not individual records.
Efron B, Tibshirani R. An Introduction to the Bootstrap. 2000; Boca Raton, FL: Chapman & Hall/CRC.
mjoint for approximate standard errors.
if (FALSE) {
# 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), ]
fit <- 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)
fit.boot <- bootSE(fit, 50, use.mle = TRUE, control = list(
burnin = 25, convCrit = "either",
tol0 = 6e-03, tol2 = 6e-03, mcmaxIter = 60))
}
Run the code above in your browser using DataLab