Calibrate a fixed Z-statistic futility boundary

Finds the Z-statistic futility boundary at futility_IF such that the probability of stopping for futility under the "null" scenario equals target_null_futility_rate (the corresponding empirical quantile of the simulated null Z distribution), and reports the resulting futility-stopping rate under every supplied scenario. The result is used as GSD_model$futility_boundary_Z with GSD_model$futility_type = "MatchedZ" in calc_dte_assurance_adaptive.

Usage

calibrate_matched_futility_boundary(
  n_c,
  n_t,
  recruitment_model,
  futility_IF,
  total_events,
  analysis_model,
  target_null_futility_rate,
  scenarios,
  n_sims = 2000,
  n_cores = 1,
  seed = NULL
)

Arguments

n_c, n_t

Number of patients in the control / treatment group.

recruitment_model

Recruitment specification (see add_recruitment_time).

futility_IF

Information fraction of the futility look.

total_events

Maximum planned number of events.

analysis_model

Analysis specification (see survival_test).

target_null_futility_rate

Target probability of stopping for futility under the null scenario.

scenarios

Named list of data-generating scenarios (see single_matched_futility_rep); must include one named "null".

n_sims

Number of simulated trials per scenario (default 2000).

n_cores

Number of cores (uses parallel::mclapply when > 1).

seed

Optional integer seed.

Value

A list with boundary, scenario_futility_rates, raw_Z_by_scenario and settings.

Examples

scenarios <- list(
  null = list(lambda_c = log(2) / 12, delay_time = 0, post_delay_HR = 1),
  alt  = list(lambda_c = log(2) / 12, delay_time = 3, post_delay_HR = 0.6)
)
cal <- calibrate_matched_futility_boundary(
  n_c = 100, n_t = 100,
  recruitment_model = list(method = "power", period = 12, power = 1),
  futility_IF = 0.5, total_events = 120,
  analysis_model = list(method = "LRT", alpha = 0.025,
                        alternative_hypothesis = "one.sided"),
  target_null_futility_rate = 0.5,
  scenarios = scenarios, n_sims = 20, seed = 1)
cal$boundary
#> [1] 0.1815397
cal$scenario_futility_rates
#> null  alt 
#> 0.50 0.15