Conditional Power for Multi-Arm Multi-Stage Design

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.

References

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

Author

Kaifeng Lu, kaifenglu@gmail.com

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)
#> [1] 0.4955179 0.8000917