bdr.gs.mc.fut: Calculates the boundaries for the group sequential tests with...

In SurrogateSeq: Group Sequential Testing of a Treatment Effect Using a Surrogate Marker

Calculates the boundaries for the group sequential tests with futility stopping

Description

Returns the boundaries for any group sequential test of the null vs. 2-sided alternative whose boundaries take the form of a single constant times a known weight vector, which is w.vec; allows for futility stopping. These include Pocock (w.vec=(1,1,..)), O'Brien-Fleming (w.vec=(sqrt(n.stg/1), sqrt(n.stg/2), ..., 1)), etc. It does this by returning quantiles of the sample paths of the (null) test statistic paths in mc.paths.

Usage

bdr.gs.mc.fut(c1 = NULL, c2 = NULL, pp = 0.4, n.stg, j.star = 1, alpha = 0.05, 
alpha0 = (j.star/n.stg) * alpha, mc.paths, inf.fraction = (1:n.stg)/n.stg, 
N.iter.max = 100, alpha.tol = 0.02 * alpha)

Arguments

c1	c1 and c2 are the constants determining the outer boundary b[j] = c1 * (j/J)^{pp-1/2} and futility boundaries a[j] = (c1+c2) * (j/J)^{1/2} - c2 * (j/J)^{pp-1/2} for j >= j.star, where J is the max no of stages (AKA n.stg). If c1 is null, it is found as the upper alpha0 quantile of the max over the first j.star stages.
c2	see description in c1
pp	power parameter for Wang-Tsiatis boundaries; default is 0.4
n.stg	maximum number of analyses
j.star	earliest stage at which futility stopping is allowed. Should be <= n.stg-1 (there is already "futility stopping" at the n.stg-th stage anyway). Default is 1.
alpha	desired rejection probability of the test; default is 0.05
alpha0	the part of alpha that c1 is chosen to spend in first j.star stages; default is (j.star/n.stg) * alpha
mc.paths	matrix of sample paths, each row being a sample path, no. of columns is number of stages
inf.fraction	information fraction vector of the same length as n.stg which reflects the fraction of information at each analysis, should be positive, non-decreasing, and the last entry should be 1; default is (1:n.stg)/n.stg, user may want to specify a different vector for unequal time points
N.iter.max	max no. of iterations for finding c2
alpha.tol	the tolerance for stopping search for c2

Value

Returns a list:

a	the futility boundary vectors
b	the null-rejection boundary vectors
prej	prob. of rejecting the null (at any stage)
EM	expected stopping stage number
se.M	standard error of stopping time
c1	constants used in boundaries a, b
c2	constants used in boundaries a, b

Author(s)

Jay Bartroff

SurrogateSeq documentation built on April 4, 2025, 12:27 a.m.