Initial design

The optimization method minimize requires an initial design for optimization. This function provides a variety of possibilities to hand-craft designs that fulfill type I error and type II error constraints which may be used as initial designs.

get_initial_design(
  theta,
  alpha,
  beta,
  type_design = c("two-stage", "group-sequential", "one-stage"),
  type_c2 = c("linear_decreasing", "constant"),
  type_n2 = c("optimal", "constant", "linear_decreasing", "linear_increasing"),
  dist = Normal(),
  cf,
  ce,
  info_ratio = 0.5,
  slope,
  weight = sqrt(info_ratio),
  order = 7L,
  ...
)

Arguments

theta

the alternative effect size in the normal case, the rate difference under the alternative in the binomial case

alpha

maximal type I error rate

beta

maximal type II error rate

type_design

is a two-stage, group-sequential, or one-stage design required?

type_c2

either linear-decreasing c2-function according to inverse normal combination test or constant c2

type_n2

design of n2-function

dist

distribution of the test statistic

cf

first-stage futility boundary

ce

first-stage efficacy boundary. Note that specifying this boundary implies that the type I error constraint might not be fulfilled anymore

info_ratio

the ratio between first and second stage sample size

slope

slope of n2 function

weight

weight of first stage test statistics in inverse normal combination test

order

desired integration order

...

further optional arguments

Details

The distribution of the test statistic is specified by dist. The default assumes a two-armed z-test. The first stage efficacy boundary and the c2 boundary are chosen as Pocock-boundaries, so either ce=c2 if c2 is constant or ce=c, where the null hypothesis is rejected if w1 Z1+w2 Z2>c. By specifying ce, it's clear that the boundaries are not Pocock-boundaries anymore, so the type I error constraint may not be fulfilled. IMPORTANT: When using the t-distribution or ANOVA, the design does probably not keep the type I and type II error, only approximate designs are returned.

Examples

init <- get_initial_design(
   theta = 0.3,
   alpha = 0.025,
   beta  = 0.2,
   type_design="two-stage",
   type_c2="linear_decreasing",
   type_n2="linear_increasing",
   dist=Normal(),
   cf=0.7,
   info_ratio=0.5,
   slope=23,
   weight = 1/sqrt(3)
)