Compute subsequent stopping boundaries for a group sequential design

Given the boundary from the first analysis, determines the stopping boundary for the \(s\)-th analysis that controls the overall type I error rate. Uses an iterative search with the joint distribution of test statistics across analyses.

Usage

get_next_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,
  prev_bound = NULL,
  s = 2,
  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.

spend_fn

A character string specifying the alpha spending function. Either "OF" (O'Brien-Fleming) or "Pocock".

corr

A correlation matrix of Z-statistics across all analyses and regimes. Should have dimension \(SL \times SL\) by \(SL \times SL\).

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. Default is 1e-6.

prev_bound

A numeric vector of previously computed boundaries from analyses \(1, \ldots, s-1\), with dimension \((s-1) \times L\).

s

An integer indicating the current analysis number. Default is 2.

max_iter

A positive integer specifying the maximum number of iterations. Default is 1000.

Value

A list with the following components:

bound

The computed stopping boundary for analysis s.

typeI

The achieved cumulative type I error rate through analysis s.

convergence

A logical value indicating whether the algorithm converged.

iters

The number of iterations used.