adaptDesign: Adaptive Design at an Interim Look

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

Adaptive Design at an Interim Look

Description

Calculates the conditional power for specified incremental information, given the interim results, parameter value, data-dependent changes in the error spending function, and the number and spacing of interim looks. Conversely, calculates the incremental information required to attain a specified conditional power, given the interim results, parameter value, data-dependent changes in the error spending function, and the number and spacing of interim looks.

Usage

adaptDesign(
  betaNew = NA_real_,
  INew = NA_real_,
  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,
  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_,
  userBetaSpendingNew = NA_real_,
  spendingTimeNew = NA_real_,
  varianceRatio = 1
)

Arguments

betaNew	The type II error for the secondary trial.
INew	The maximum information of the secondary trial. Either betaNew or INew should be provided, while the other must be missing.
L	The interim adaptation look of the primary trial.
zL	The z-test statistic at the interim adaptation look of the primary trial.
theta	The assumed parameter value.
IMax	The maximum information of 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. Defaults to TRUE if left unspecified.
criticalValues	The upper boundaries on the 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 lower boundaries on the z-test statistic scale for futility stopping 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.
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, "user" for user defined spending, 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".
userBetaSpendingNew	The user-defined cumulative beta spending. Represents the cumulative beta spent up to each stage of the secondary trial.
spendingTimeNew	The error spending time of the secondary trial. Defaults to missing, in which case it is assumed to be the same as informationRatesNew.
varianceRatio	The ratio of the variance under H0 to the variance under H1.

Value

An adaptDesign object with three list components:

• primaryTrial: A list of selected information for the primary trial, including L, zL, theta, maxInformation, kMax, informationRates, efficacyBounds, futilityBounds, information, alpha, conditionalAlpha, conditionalPower, predictivePower, and and MullerSchafer.

• secondaryTrial: A list of selected information for the secondary trial, including overallReject, alpha, kMax, maxInformation, informationRates, efficacyBounds, futilityBounds, cumulativeRejection, cumulativeFutility, cumulativeAlphaSpent, information, typeAlphaSpending, parameterAlphaSpending, typeBetaSpending, parameterBetaSpending, userBetaSpending, and spendingTime.

• integratedTrial: A list of selected information for the integrated trial, including L, zL, theta, maxInformation, kMax, informationRates, efficacyBounds, futilityBounds, and information.

Author(s)

Kaifeng Lu, [e-mail]

References

Lu Chi, H. M. James Hung, and Sue-Jane Wang. Modification of sample size in group sequential clinical trials. Biometrics 1999;55:853-857.

Hans-Helge Muller and Helmut Schafer. Adaptive group sequential designs for clinical trials: Combining the advantages of adaptive and of classical group sequential approaches. Biometrics 2001;57:886-891.

See Also

getDesign

Examples

# two-arm randomized clinical trial with a normally distributed endpoint
# 90% power to detect mean difference of 15 with a standard deviation of 50
# Design the Stage I Trial with 3 looks and Lan-DeMets O'Brien-Fleming type
# spending function
delta <- 15
sigma <- 50

(des1 <- getDesignMeanDiff(
  beta = 0.1, meanDiff = delta, stDev = sigma,
  kMax = 3, alpha = 0.025, typeAlphaSpending = "sfOF"
))

s1 <- des1$byStageResults$informationRates
b1 <- des1$byStageResults$efficacyBounds
n <- des1$overallResults$numberOfSubjects

# Monitoring the Stage I Trial
L <- 1
nL <- des1$byStageResults$numberOfSubjects[L]
deltahat <- 8
sigmahat <- 55
sedeltahat <- sigmahat * sqrt( 4 / nL)
zL <- deltahat / sedeltahat

# Making an Adaptive Change: Stage I to Stage II
# revised clinically meaningful difference downward to 10 power the study
# retain the standard deviation at the design stage
# Muller & Schafer (2001) method to design the secondary trial
# with 2 looks and Lan-DeMets Pocock type spending function
# re-estimate sample size to reach 90% conditional power
deltaNew <- 10

(des2 <- adaptDesign(
  betaNew = 0.1, L = L, zL = zL, theta = deltaNew,
  IMax = n / (4 * sigma^2), kMax = 3, informationRates = s1,
  alpha = 0.025, typeAlphaSpending = "sfOF",
  MullerSchafer = TRUE, kNew = 2, typeAlphaSpendingNew = "sfP"
))

INew <- des2$maxInformation
(nNew <- ceiling(INew * 4 * sigma^2))
(nTotal <- nL + nNew)

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