summary_level_bootstrap_ICA() performs a parametric type of bootstrap based
on the estimated multivariate normal sampling distribution of the maximum
likelihood estimator for the (observable) D-vine copula model parameters.
summary_level_bootstrap_ICA(
fitted_model,
copula_par_unid,
copula_family2,
rotation_par_unid,
n_prec,
B,
measure = "ICA",
mutinfo_estimator = NULL,
ICA_estimator = NULL,
composite = FALSE,
seed,
restr_time = +Inf,
ncores = 1
)(numeric) Vector of bootstrap replications for the estimated ICA.
Returned value from fit_copula_OrdOrd(),
fit_copula_OrdCont(), or fit_copula_ContCont(). This object
contains the estimated identifiable part of the joint distribution for the
potential outcomes.
Parameter vector for the sequence of unidentifiable
bivariate copulas that define the D-vine copula. The elements of
copula_par correspond to \((c_{23}, c_{13;2}, c_{24;3}, c_{14;23})\).
Copula family of the other bivariate copulas. For the
possible options, see loglik_copula_scale(). The elements of
copula_family2 correspond to \((c_{23}, c_{13;2}, c_{24;3}, c_{14;23})\).
Vector of rotation parameters for the sequence of
unidentifiable bivariate copulas that define the D-vine copula. The elements of
rotation_par correspond to \((c_{23}, c_{13;2},
c_{24;3}, c_{14;23})\).
Number of Monte Carlo samples for the computation of the mutual information.
Number of bootstrap replications
Compute intervals for which measure of surrogacy? Defaults to
"ICA". See first column names of sens_results for other possibilities.
Function that estimates the mutual information
between the first two arguments which are numeric vectors. Defaults to
FNN::mutinfo() with default arguments in the survival-survival setting. This
argument is not used for non-survival-survival settings.
Function that estimates the ICA between the first two
arguments which are numeric vectors. Defaults to NULL which corresponds
to using estimate_ICA_ContCont(), estimate_ICA_OrdCont(), or
estimate_ICA_OrdOrd() (depending on the endpoint types). This argument is
not used in the survival-survival setting.
(boolean) If composite is TRUE, then the surrogate
endpoint is a composite of both a "pure" surrogate endpoint and the true
endpoint, e.g., progression-free survival is the minimum of time-to-progression
and time-to-death.
Seed for Monte Carlo sampling. This seed does not affect the global environment.
Restriction time for the potential outcomes. Defaults to
+Inf which means no restriction. Otherwise, the sampled potential outcomes
are replace by pmin(S0, restr_time) (and similarly for the other potential
outcomes).
Number of cores used in the sensitivity analysis. The computations are computationally heavy, and this option can speed things up considerably.
Let \(\hat{\boldsymbol{\beta}}\) be the estimated identifiable parameter vector, \(\hat{\Sigma}\) the corresponding estimated covariance matrix, and \(\boldsymbol{\nu}\) a fixed value for the sensitivity parameter. The bootstrap is then performed in the following steps
Resample the identifiable parameters from the estimated sampling distribution, $$\hat{\boldsymbol{\beta}}^{(b)} \sim N(\hat{\boldsymbol{\beta}}, \hat{\Sigma}).$$
For each resampled parameter vector and the fixed sensitivty parameter, compute the ICA as \(ICA(\hat{\boldsymbol{\beta}}^{(b)}, \boldsymbol{\nu})\).