get_initial_design: Initial design

In adoptr: Adaptive Optimal Two-Stage Designs

Initial design

Description

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.

Usage

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	type of design
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 c_e=c_2 if c_2 is constant or c_e=c, where the null hypothesis is rejected if w_1 Z_1+w_2 Z_2>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.

Value

An object of class TwoStageDesign.

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)
)

adoptr documentation built on Oct. 3, 2024, 1:08 a.m.