getBound_mams: Efficacy Boundaries for Multi-Arm Multi-Stage Design

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Efficacy Boundaries for Multi-Arm Multi-Stage Design

Description

Calculates the efficacy stopping boundaries for a multi-arm multi-stage design.

Usage

getBound_mams(
  M = NA_integer_,
  r = 1,
  corr_known = TRUE,
  k = NA_integer_,
  informationRates = NA_real_,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  spendingTime = NA_real_,
  efficacyStopping = NA_integer_
)

Arguments

M	Number of active treatment arms.
r	Randomization ratio of each active arm to the common control.
corr_known	Logical. If TRUE, the correlation between Wald statistics is derived from the randomization ratio r as r / (r + 1). If FALSE, a conservative correlation of 0 is assumed.
k	The index of the current look.
informationRates	A numeric vector of information rates up to the current look. Values must be strictly increasing and \le 1.
alpha	The significance level. Defaults to 0.025.
typeAlphaSpending	The type of alpha spending. One of the following: "OF" for O'Brien-Fleming boundaries, "P" for Pocock boundaries, "WT" for Wang & Tsiatis boundaries, "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early efficacy stopping. Defaults to "sfOF".
parameterAlphaSpending	The parameter value for the alpha spending. Corresponds to \Delta for "WT", \rho for "sfKD", and \gamma for "sfHSD".
userAlphaSpending	The user defined alpha spending. Cumulative alpha spent up to each stage.
spendingTime	A numeric vector of length k specifying the error spending time at each analysis. Values must be strictly increasing and \le 1. If omitted, defaults to informationRates.
efficacyStopping	Indicators of whether efficacy stopping is allowed at each stage. Defaults to TRUE if left unspecified.

Details

The function determines critical values by solving for the boundary that satisfies the alpha-spending requirement.

If typeAlphaSpending is "OF", "P", "WT", or "none", then informationRates, efficacyStopping, and spendingTime must be of full length kMax, and informationRates and spendingTime must end with 1.

Value

A numeric vector of length k containing the critical values (on the standard normal Z-scale) for each analysis up to the current look.

Author(s)

Kaifeng Lu, [e-mail]

References

Ping Gao, Yingqiu Li. Adaptive multiple comparison sequential design (AMCSD) for clinical trials. Journal of Biopharmaceutical Statistics, 2024, 34(3), 424-440.

Examples

# Determine O'Brien-Fleming boundaries for a TSSSD with
# 2 active arms and 3 looks.
getBound_mams(M = 2, k = 3, informationRates = seq(1, 3)/3,
              alpha = 0.025, typeAlphaSpending = "OF")

lrstat documentation built on May 13, 2026, 9:06 a.m.