lrstat (version 0.3.3)

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

Description

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

Usage

getBound_multiarm(
  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_,
  nthreads = 0
)

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.

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.

nthreads

The number of threads to use (0 leaves the RcppParallel setting unchanged).

Author

Kaifeng Lu,

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.

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_multiarm(M = 2, k = 3, informationRates = seq(1, 3)/3,
                  alpha = 0.025, typeAlphaSpending = "OF",
                  nthreads = 1)