Apply group sequential stopping rules to test statistics

Group sequential designs allow investigators to perform pre-planned interim assessments of futility or efficacy in an ongoing trial while preserving the Familywise Type I Error Rate (FWER). Differences between the observed information levels and those specified in the initial design require the boundaries to be updated in order to preserve FWER control. This function allows users to update the boundaries according to observed information levels, apply stopping rules, and return their resulting decisions.

Usage

apply_stopping_rule_z(
  test_statistics,
  trial_design,
  information_fraction,
  information_target
)

Arguments

test_statistics

A numeric vector of standardized test statistics

trial_design

A TrialDesignGroupSequential object created by rpact::getDesignGroupSequential()

information_fraction

A numeric vector containing the observed information fractions

information_target

A numeric scalar containing the target information level, created by required_information_single_stage()

Value

A list containing an updated TrialDesignGroupSequential object object, the resulting decision, and supporting data.

See also

required_information_single_stage() and required_information_mw_single_stage() for obtaining the target information level for a single stage design; rpact::getDesignGroupSequential() for obtaining trial_design, and required_information_sequential() for adjusting the information level to multi-stage designs.

Examples

# Two-sided design with O'Brien-Fleming efficacy stopping and non-binding
# O'Brien Fleming Beta Spending Futility with 2 interim analyses at 50% and
# 75%

# Create Initial `TrialDesignGroupSequential` Object:
two_sided_of_efficacy_nb_of_futility_0 <-
 rpact::getDesignGroupSequential(
   alpha = 0.05, # 5% Type I Error
   beta = 1 - 0.80, # 80% Power
   sided = 2, # Two-Sided Test
   # Interim analyses at 50%, 75%, 100% of Information Target
   informationRates = c(0.5, 0.75, 1),
   # Efficacy and Non-Binding Futility Stopping using O'Brien-Fleming
   # alpha- and beta- spending functions
   typeOfDesign = "asOF",
   typeBetaSpending = "bsOF",
   bindingFutility = FALSE
 )

 # Test Statistics at Interim Analysis 1
 test_statistics_1 <- c(1.0)

 # Observed information fraction at 1st analysis = 52.5% vs. 50% in design
 information_fraction_1 <- c(0.525)
 information_target <- 50

 analysis_decision_1 <-
   apply_stopping_rule_z(
     test_statistics = test_statistics_1,
     trial_design = two_sided_of_efficacy_nb_of_futility_0,
     information_fraction = information_fraction_1,
     information_target = information_target
   )

 # Test Statistics at Interim Analysis 2
 test_statistics_2 <- c(1.0, 2.2)

 # Observed information fraction at 2nd analysis = 74.5% vs. 75% in design
 information_fraction_2 <- c(0.525, 0.745)

 analysis_decision_2 <-
   apply_stopping_rule_z(
     test_statistics = test_statistics_2,
     trial_design =
     # Use updated design from analysis 1
     analysis_decision_1$trial_design_updated,
     information_fraction = information_fraction_2,
     information_target = information_target
 )

 # Test Statistics at Interim Analysis 3
 test_statistics_3 <- c(1.0, 2.2, 2.3)

 # Observed information fraction at 3rd analysis = 102% vs. 100% in design
 information_fraction_3 <- c(0.525, 0.745, 1.02)
 analysis_decision_3 <-
   apply_stopping_rule_z(
     test_statistics = test_statistics_3,
     trial_design =
     # Use updated design from analysis 1
     analysis_decision_2$trial_design_updated,
     information_fraction = information_fraction_3,
     information_target = information_target
 )