Lower and Upper Bound of Group Sequential Design

Usage

gs_bound(
  alpha,
  beta,
  theta,
  corr,
  analysis = 1:length(alpha),
  theta0 = rep(0, length(analysis)),
  binding_lower_bound = FALSE,
  algorithm = GenzBretz(maxpts = 1e+05, abseps = 1e-05),
  alpha_bound = FALSE,
  beta_bound = FALSE,
  ...
)

Arguments

alpha: a numeric vector of cumulative allocated alpha in each interim analysis
beta: a numeric vector of cumulative allocated beta in each interim analysis
theta: a numeric vector of effect size under alternative.
corr: a matrix of correlation matrix
analysis: a numeric vector of interim analysis indicator. Default is 1:length(alpha).
theta0: a numeric vector of effect size under null hypothesis. Default is 0.
binding_lower_bound: a logical value to indicate binding lower bound.
algorithm: an object of class GenzBretz, Miwa or TVPACK specifying both the algorithm to be used as well as the associated hyper parameters.
alpha_bound: logical value to indicate if alpha is Type I error or upper bound. Default is FALSE.
beta_bound: logical value to indicate if beta is Type II error or lower bound. Default is FALSE.
...: additional parameters transfer to mvtnorm::pmvnorm

Specification

The contents of this section are shown in PDF user manual only.

Examples

library(gsDesign)
#> Loading required package: ggplot2

x <- gsDesign::gsSurv( k = 3 , test.type = 4 , alpha = 0.025 ,
                       beta = 0.2 , astar = 0 , timing = c( 1 ) ,
                       sfu = sfLDOF , sfupar = c( 0 ) , sfl = sfLDOF ,
                       sflpar = c( 0 ) , lambdaC = c( 0.1 ) ,
                       hr = 0.6 , hr0 = 1 , eta = 0.01 ,
                       gamma = c( 10 ) ,
                       R = c( 12 ) , S = NULL ,
                       T = 36 , minfup = 24 , ratio = 1 )

cbind(x$lower$bound, x$upper$bound)
#>            [,1]     [,2]
#> [1,] -0.2361874 3.710303
#> [2,]  1.1703638 2.511407
#> [3,]  1.9929702 1.992970

gsdmvn:::gs_bound(alpha = sfLDOF(0.025, 1:3/3)$spend,
         beta = sfLDOF(0.2, 1:3/3)$spend,
         analysis = 1:3,
         theta = x$theta[2] * sqrt(x$n.I),
         corr = outer(1:3, 1:3, function(x,y) pmin(x,y) / pmax(x,y)))
#>      upper      lower
#> 1 3.710295 -0.2361879
#> 2 2.513755  1.1335603
#> 3 2.023170  2.0231696