getDesign_mams: Power and Sample Size for Multi-Arm Multi-Stage Design

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

Power and Sample Size for Multi-Arm Multi-Stage Design

Description

Computes either the maximum information and stopping boundaries for a multi-arm multi-stage design, or the achieved power when the maximum information and stopping boundaries are provided.

Usage

getDesign_mams(
  beta = NA_real_,
  IMax = NA_real_,
  theta = NA_real_,
  M = NA_integer_,
  r = 1,
  corr_known = TRUE,
  kMax = 1L,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  futilityStopping = NA_integer_,
  criticalValues = NULL,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  futilityBounds = NULL,
  futilityCP = NULL,
  futilityTheta = NULL,
  typeBetaSpending = "none",
  parameterBetaSpending = NA_real_,
  userBetaSpending = NA_real_,
  spendingTime = NA_real_
)

Arguments

beta	Type II error rate. Provide either beta or IMax; the other should be missing.
IMax	Maximum information for any active arm versus the common control. Provide either IMax or beta; the other should be missing.
theta	A vector of length M representing the true treatment effects for each active arm versus the common control. The global null is \theta_i = 0 for all i, and alternatives are one-sided: \theta_i > 0 for at least one i = 1, \ldots, M.
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 used.
kMax	Number of sequential looks.
informationRates	A numeric vector of information rates fixed before the trial. If unspecified, defaults to (1:kMax) / kMax.
efficacyStopping	Indicators of whether efficacy stopping is allowed at each stage. Defaults to TRUE if left unspecified.
futilityStopping	Indicators of whether futility stopping is allowed at each stage. Defaults to TRUE if left unspecified.
criticalValues	The matrix of by-level upper boundaries on the max z-test statistic scale for efficacy stopping. The first column is for level M, the second column is for level M - 1, and so on, with the last column for level 1. If left unspecified, the critical values will be computed based on the specified alpha spending function.
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.
futilityBounds	A numeric vector of length kMax - 1 specifying the futility boundaries on the max z-test statistic scale for futility stopping.
futilityCP	A numeric vector of length kMax - 1 specifying the futility boundaries on the conditional power scale for futility stopping.
futilityTheta	A numeric vector of length kMax - 1 specifying the futility boundaries on the parameter scale for futility stopping.
typeBetaSpending	The type of beta spending. One of the following: "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 futility stopping. Defaults to "none".
parameterBetaSpending	The parameter value for the beta spending. Corresponds to \rho for "sfKD", and \gamma for "sfHSD".
userBetaSpending	The user defined beta spending. Cumulative beta spent up to each stage.
spendingTime	A numeric vector of length kMax specifying the error spending time at each analysis. Values must be strictly increasing and ends at 1. If omitted, defaults to informationRates.

Details

If corr_known is FALSE, critical boundaries are computed assuming independence among the Wald statistics in each stage (a conservative assumption). Power calculations, however, use the correlation implied by the randomization ratio r.

Value

An S3 object of class mams with the following components:

• overallResults: A data frame containing:

  • overallReject: Overall probability of rejecting the global null hypothesis.

  • alpha: Overall significance level.

  • attainedAlpha: The attained significance level, which is different from the overall significance level in the presence of futility stopping.

  • M: Number of active arms.

  • r: Randomization ratio per active arm versus control.

  • corr_known: Whether the correlation among Wald statistics was assumed known.

  • kMax: Number of stages.

  • information: Maximum information for any active arm versus control.

  • expectedInformationH1: The expected information under H1.

  • expectedInformationH0: The expected information under H0.

• byStageResults: A data frame containing:

  • informationRates: Information rates at each analysis.

  • efficacyBounds: Efficacy boundaries on the max Z-scale.

  • futilityBounds: Futility boundaries on the max Z-scale.

  • rejectPerStage: Probability of efficacy stopping at each stage.

  • futilityPerStage: Probability of futility stopping at each stage.

  • cumulativeRejection: Cumulative probability of efficacy stopping.

  • cumulativeFutility: Cumulative probability of futility stopping.

  • cumulativeAlphaSpent: Cumulative alpha spent.

  • efficacyTheta: Efficacy boundaries on the parameter scale.

  • futilityTheta: Futility boundaries on the parameter scale.

  • efficacyP: Efficacy boundaries on the p-value scale.

  • futilityP: Futility boundaries on the p-value scale.

  • information: Cumulative information for any active arm versus control at each analysis.

  • efficacyStopping: Indicator of whether efficacy stopping is permitted at each stage.

  • futilityStopping: Indicator of whether futility stopping is permitted at each stage.

  • rejectPerStageH0: The probability for efficacy stopping under H0.

  • futilityPerStageH0: The probability for futility stopping under H0.

  • cumulativeRejectionH0: The cumulative probability for efficacy stopping under H0.

  • cumulativeFutilityH0: The cumulative probability for futility stopping under H0.

• settings: A list of input settings:

  • typeAlphaSpending: The type of alpha spending.

  • parameterAlphaSpending: The parameter value for the chosen alpha spending function.

  • userAlphaSpending: The user-specified alpha spending values.

  • typeBetaSpending: The type of beta spending.

  • parameterBetaSpending: The parameter value for the chosen beta spending function.

  • userBetaSpending: The user-specified beta spending values.

  • spendingTime: The error-spending time at each analysis.

• byLevelBounds: A data frame containing the efficacy boundaries for each level of testing (i.e., number of active arms remaining) and each stage. Columns include:

  • level: Number of active arms remaining (1 to M).

  • stage: Stage index (1 to kMax).

  • efficacyBounds: Efficacy boundaries on the max Z-scale for the given level and stage.

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

# Example 1: obtain the maximum information given power
(design1 <- getDesign_mams(
  beta = 0.1, theta = c(0.3, 0.5), M = 2, r = 1.0,
  kMax = 3, informationRates = seq(1, 3)/3,
  alpha = 0.025, typeAlphaSpending = "OF"))

# Example 2: obtain power given the maximum information
(design2 <- getDesign_mams(
  IMax = 110/(2*1^2), theta = c(0.3, 0.5), M = 2, r = 1.0,
  kMax = 3, informationRates = seq(1, 3)/3,
  alpha = 0.025, typeAlphaSpending = "OF"))

# Example 3: derive futility boundaries using beta spending
(design3 <- getDesign_mams(
  beta = 0.1, theta = c(-log(0.5), -log(0.75)),
  M = 2, r = 1.0, corr_known = FALSE,
  kMax = 3, informationRates = seq(1, 3)/3,
  alpha = 0.025, typeAlphaSpending = "sfOF",
  typeBetaSpending = "sfHSD", parameterBetaSpending = -2))

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