Compute the first stopping boundary for a group sequential design

Determines the first analysis stopping boundary that controls the familywise type I error rate at a specified level, adjusting for the multiplicity of multiple treatment regimes. Uses an iterative search to find the boundary value. This function works only for superiority (one-sided) testing.

Usage

get_first_bound(
  alpha = 0.05,
  inf_frac = c(0.5, 1),
  spend_fn = "OF",
  corr = diag(x = 1, nrow = 1, ncol = 1),
  test_type = "one-sided",
  lambda = 0.1,
  tol = 1e-06,
  max_iter = 1000
)

Arguments

alpha: A numeric value specifying the overall type I error rate to control. Default is 0.05.
inf_frac: A numeric vector of information fractions indicating when analyses are conducted. Values should be between 0 and 1.
spend_fn: A character string specifying the alpha spending function. Either "OF" (O'Brien-Fleming) or "Pocock".
corr: A correlation matrix of Z-statistics at the first time point, accounting for multiple regimes. Default is a 1x1 identity matrix.
test_type: A character string specifying the type of test to be performed. Either "one-sided" or "two-sided". Default is "one-sided".
lambda: A numeric value for the initial step size used in the iterative boundary search. Default is 0.1.
tol: A numeric value specifying the convergence tolerance for the type I error boundary. Default is 1e-6.
max_iter: A positive integer specifying the maximum number of iterations for the boundary search. Default is 1000.

Value

A list with the following components:

bound: The computed stopping boundary for the first analysis.
typeI: The achieved type I error rate at the boundary.
convergence: A logical value indicating whether the algorithm converged.
iters: The number of iterations used.