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
Value
An object of class TwoStageDesign.
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.