summary_level_bootstrap_ICA {Surrogate}

Bootstrap based on the multivariate normal sampling distribution

Description

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.

Usage

summary_level_bootstrap_ICA(
  fitted_model,
  copula_par_unid,
  copula_family2,
  rotation_par_unid,
  n_prec,
  B,
  measure = "ICA",
  mutinfo_estimator = NULL,
  composite,
  seed,
  restr_time = +Inf,
  ncores = 1
)

Arguments

fitted_model

Returned value from fit_model_SurvSurv(). This object contains the estimated identifiable part of the joint distribution for the potential outcomes.

copula_par_unid

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_family2

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}).

rotation_par_unid

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}).

n_prec

Number of Monte Carlo samples for the computation of the mutual information.

B

Number of bootstrap replications

measure

Compute intervals for which measure of surrogacy? Defaults to "ICA". See first column names of sens_results for other possibilities.

mutinfo_estimator

Function that estimates the mutual information between the first two arguments which are numeric vectors. Defaults to FNN::mutinfo() with default arguments. @param plot_deltas (logical) Plot the sampled individual treatment effects?

composite

(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

Seed for Monte Carlo sampling. This seed does not affect the global environment.

restr_time

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).

ncores

Number of cores used in the sensitivity analysis. The computations are computationally heavy, and this option can speed things up considerably.

Details

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

1. Resample the identifiable parameters from the estimated sampling distribution,

   \hat{\boldsymbol{\beta}}^{(b)} \sim N(\hat{\boldsymbol{\beta}}, \hat{\Sigma}).

2. For each resampled parameter vector and the fixed sensitivty parameter, compute the ICA as ICA(\hat{\boldsymbol{\beta}}^{(b)}, \boldsymbol{\nu}).

Value

(numeric) Vector of bootstrap replications for the estimated ICA.