Conditional Power for Phase 2/3 Seamless Design

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

Usage

getCP_seamless(
  INew = NA_real_,
  M = NA_integer_,
  r = 1,
  corr_known = TRUE,
  L = NA_integer_,
  zL = NA_real_,
  theta = NA_real_,
  IMax = NA_real_,
  K = 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,
  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 the active arm versus the common control in the secondary trial.
M: Number of active treatment arms in Phase 2.
r: Randomization ratio of each active arm to the common control in Phase 2.
corr_known: Logical. If TRUE, the correlation between Wald statistics in Phase 2 is derived from the randomization ratio \(r\) as \(r / (r + 1)\). If FALSE, a conservative correlation of 0 is used.
L: The interim adaptation look in Phase 3.
zL: The z-test statistic at the interim adaptation look of Phase 3.
theta: The assumed treatment effect for the selected arm versus the common control.
IMax: Maximum information for the active arm versus the common control for the original trial. Must be provided.
K: Number of sequential looks in Phase 3.
informationRates: A numeric vector of information rates fixed before the trial. If unspecified, defaults to \((1:(K+1)) / (K+1)\).
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. Defaults to true if left unspecified.
criticalValues: The upper boundaries on the max z-test statistic scale for Phase 2 and the z-test statistics for the selected arm in Phase 3 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 lower boundaries on the max z-test statistic scale for Phase 2 and the z-test statistics for the selected arm in Phase 3 for the primary trial.
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.
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, "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, and "none" for no early efficacy stopping. Defaults to "sfOF".
parameterAlphaSpendingNew: The parameter value of alpha spending for the secondary trial. Corresponds to \(\Delta\) for "WT", \(\rho\) for "sfKD", and \(\gamma\) for "sfHSD".
futilityBoundsInt: The futility boundaries on the 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, and "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 two-stage seamless sequential design for clinical trials. Journal of Biopharmaceutical Statistics, 2025, 35(4), 565-587.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


getCP_seamless(
  INew = 198 / 4, M = 2, r = 1, corr_known = FALSE,
  L = 1, zL = -log(0.67) * sqrt(80 / 4), theta = -log(0.691),
  IMax = 120 / 4, K = 2, informationRates = c(1/3, 2/3, 1),
  alpha = 0.025, typeAlphaSpending = "OF", kNew = 1)
#> [1] 0.4402320 0.6983309