getCP_mams: Conditional Power for Multi-Arm Multi-Stage Design

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

Conditional Power for Multi-Arm Multi-Stage Design

Description

Obtains the conditional power for specified incremental information given the interim results, parameter values, and data-dependent changes in the selected treatment(s), the error spending function, as well as the number and spacing of interim looks.

Usage

getCP_mams(
  INew = NA_real_,
  M = NA_integer_,
  r = 1,
  corr_known = TRUE,
  L = NA_integer_,
  zL = NA_real_,
  theta = NA_real_,
  IMax = NA_real_,
  kMax = NA_integer_,
  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,
  spendingTime = NA_real_,
  MullerSchafer = FALSE,
  MNew = NA_integer_,
  selected = NA_integer_,
  rNew = 1,
  kNew = NA_integer_,
  informationRatesNew = NA_real_,
  efficacyStoppingNew = NA_integer_,
  futilityStoppingNew = NA_integer_,
  typeAlphaSpendingNew = "sfOF",
  parameterAlphaSpendingNew = NA_real_,
  futilityBoundsInt = NULL,
  futilityCPInt = NULL,
  futilityThetaInt = NULL,
  typeBetaSpendingNew = "none",
  parameterBetaSpendingNew = NA_real_,
  spendingTimeNew = NA_real_
)

Arguments

INew	The maximum information for any active arm versus the common control in the secondary trial.
M	Number of active treatment arms in the primary trial.
r	Randomization ratio of each active arm to the common control in the primary trial.
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.
L	The interim adaptation look of the primary trial.
zL	The z-test statistics at the interim adaptation look of the primary trial.
theta	A vector of length M representing the assumed 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.
IMax	Maximum information for any active arm versus the common control for the primary trial. Must be provided.
kMax	The maximum number of stages of the primary trial.
informationRates	The information rates of the primary trial.
efficacyStopping	Indicators of whether efficacy stopping is allowed at each stage of the primary trial. Defaults to TRUE if left unspecified.
futilityStopping	Indicators of whether futility stopping is allowed at each stage of the primary trial.
criticalValues	The upper boundaries on the max z-test statistic scale for efficacy stopping for the primary trial. If missing, boundaries will be computed based on the specified alpha spending function.
alpha	The significance level of the primary trial. Defaults to 0.025.
typeAlphaSpending	The type of alpha spending for the primary trial. 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 of alpha spending for the primary trial. Corresponds to \Delta for "WT", \rho for "sfKD", and \gamma for "sfHSD".
userAlphaSpending	The user-defined alpha spending for the primary trial. Represents the cumulative alpha spent up to each stage.
futilityBounds	The futility boundaries on the max-z statistic scale for the primary trial. Defaults to rep(-8, kMax-1) if left unspecified.
futilityCP	The conditional power-based futility bounds for the primary trial.
futilityTheta	The parameter value-based futility bounds for the primary trial.
spendingTime	The error spending time of the primary trial. Defaults to missing, in which case it is assumed to be the same as informationRates.
MullerSchafer	Whether to use the Muller and Schafer (2001) method for trial adaptation.
MNew	Number of active treatment arms in the secondary trial.
selected	The indices of the selected active treatment arms for the secondary trial.
rNew	Randomization ratio of each active arm to the common control in the secondary trial.
kNew	The number of looks of the secondary trial.
informationRatesNew	The spacing of looks of the secondary trial.
efficacyStoppingNew	The indicators of whether efficacy stopping is allowed at each look of the secondary trial. Defaults to TRUE if left unspecified.
futilityStoppingNew	The indicators of whether futility stopping is allowed at each look of the secondary trial. Defaults to TRUE if left unspecified.
typeAlphaSpendingNew	The type of alpha spending for the secondary trial. One of the following: "OF" for O'Brien-Fleming 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, and "none" for no early efficacy stopping. Defaults to "sfOF".
parameterAlphaSpendingNew	The parameter value of alpha spending for the secondary trial. Corresponds to \rho for "sfKD", and \gamma for "sfHSD".
futilityBoundsInt	The futility boundaries on the max-z statistic scale for new stages of the integrated trial.
futilityCPInt	The conditional power-based futility bounds for new stages of the integrated trial.
futilityThetaInt	The parameter value-based futility bounds for the new stages of the integrated trial.
typeBetaSpendingNew	The type of beta spending for the secondary trial. 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, "none" for no early futility stopping. Defaults to "none".
parameterBetaSpendingNew	The parameter value of beta spending for the secondary trial. Corresponds to \rho for "sfKD", and \gamma for "sfHSD".
spendingTimeNew	The error spending time of the secondary trial. Defaults to missing, in which case it is assumed to be the same as informationRatesNew.

Value

A vector of two conditional powers given the interim results and parameter values, one without design change and the other with data-dependent design changes.

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.

See Also

adaptDesign_mams

Examples

getCP_mams(
  INew = 373 / 4, M = 2, r = 1, corr_known = FALSE,
  L = 1, zL = c(-log(0.91), -log(0.78)) * sqrt(324 / 4 / 2),
  theta = c(-log(0.91), -log(0.78)),
  IMax = 324 / 4, kMax = 2, informationRates = c(1/2, 1),
  alpha = 0.025, typeAlphaSpending = "OF",
  MNew = 1, selected = 2, rNew = 1)

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