boundaries {RTSA}

Boundaries for group sequential designs

Description

Calculates alpha- and potentially beta-spending boundaries for group sequential designs for meta-analysis. Should be used for exploring how the different arguments affect the sequential design. The function is not intended to be used individually for Trial Sequential Analysis. For this purpose, we recommend RTSA().

Usage

boundaries(
  timing,
  alpha = 0.05,
  beta = 0.1,
  side = 2,
  futility = "none",
  es_alpha = "esOF",
  es_beta = NULL,
  type = "design",
  design_R = NULL,
  tol = 1e-09
)

Arguments

timing

Expected timings of interim analyses and final analysis as a vector consisting of values from 0 to 1.

alpha

The level of type I error as a percentage, the default is 0.05 corresponding to 5%.

beta

The level of type II error as a percentage, the default is 0.1 corresponding to 10%.

side

Whether a 1- or 2-sided hypothesis test is used. Defaults to 2. Options are 1 or 2.

futility

Futility boundaries added to design. Options are: none, non-binding and binding. Default is "none".

es_alpha

The error spending function for alpha-spending. Options are: "esOF" (Lan & DeMets version of O'Brien-Fleming boundaries), "esPoc" (Lan & DeMets version of Pocock boundaries), "HSDC" (Hwang Sihi and DeCani) and "rho" (rho family). Defaults to "esOF".

es_beta

The error spending function for beta-spending. For options see es_alpha. Defaults to NULL.

type

Whether the boundaries are used for design or analysis. We recommend only to use the boundaries() function with type equal to design. Defaults to design.

design_R

If type is analysis, a scalar for achieving the right amount of power is required. It is recommended not to use the boundaires() function with the setting type equal to analysis. Defaults to NULL.

tol

Tolerance level for numerical integration. Defaults to 1e-09.

Value

A boundaries object which includes:

inf_frac

Timing of interim analyses and final analysis. Potentially modified if type = "analysis".

org_inf_frac

Original timing. If type = "design".

alpha_ubound

Upper alpha-spending boundaries

alpha_lbound

Lower alpha-spending boundaries

alpha

As input

alpha_spend

List of cumulative and incremental spending

delta

Drift parameter

design_R

If type = "analysis" it is the scalar for correct power in the design. Else NULL.

info

List of the information as the squareroot of the information increments and the squareroot of the cumulative information

beta_ubound

Upper beta-spending boundaries

beta_lbound

Lower beta-spending boundaries

root

Scalar for achieving correct power

beta_spend

List of cumulative and incremental spending

pwr

List of probabilities for rejecting the null under the sample size settings being true at each analysis and the sum.

tIe

List of probabilities for type-I-error at each analysis and the sum

side

As input

beta

As input

es_alpha

As input

es_beta

As input

type

As input

futility

As input

Examples

boundaries(timing = c(0.25, 0.5, 0.75, 1), alpha = 0.05, beta = 0.1,
 side = 2, futility = "non-binding", es_alpha = "esOF", es_beta = "esOF")