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Adaptive Design at an Interim Look

Source: R/RcppExports.R
adaptDesign.Rd

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.

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

Author

Kaifeng Lu, kaifenglu@gmail.com

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"
))
#>                                                                                   
#> Group-sequential design with 3 stages for two-sample mean difference              
#> Mean difference under H0: 0, mean difference under H1: 15, standard deviation: 50 
#> Overall power: 0.9003, overall alpha (1-sided): 0.025                             
#> Drift parameter: 3.262, inflation factor: 1.012                                   
#> Maximum information: 0.05, expected under H1: 0.04, expected under H0: 0.05       
#> Maximum # subjects: 473, expected under H1: 379.2, expected under H0: 472         
#> Allocation ratio: 1                                                               
#> Alpha spending: Lan-DeMets O'Brien-Fleming, beta spending: None                   
#>                                                                                   
#>                               Stage 1 Stage 2 Stage 3
#> Information rate              0.334   0.666   1.000  
#> Efficacy boundary (Z)         3.706   2.513   1.993  
#> Cumulative rejection          0.0343  0.5596  0.9003 
#> Cumulative alpha spent        0.0001  0.0060  0.0250 
#> Number of subjects            158.0   315.0   473.0  
#> Efficacy boundary (mean diff) 29.484  14.159  9.163  
#> Efficacy boundary (p)         0.0001  0.0060  0.0231 
#> Information                   0.02    0.03    0.05   

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"
))
#>                                                      
#> Primary trial:                                       
#> Group-sequential design with 3 stages                
#> Max information: 0.05                                
#> Interim adaptation look: 1, z-statistic value: 0.914 
#> theta: 10                                            
#> Conditional type I error: 0.0378                     
#> Conditional power: 0.496, predictive power: 0.3877   
#> Muller & Schafer method for secondary trial: TRUE    
#>                                                      
#>                       Stage 1 Stage 2 Stage 3
#> Information rate      0.334   0.666   1.000  
#> Efficacy boundary (Z) 3.706   2.513   1.993  
#> Information           0.02    0.03    0.05   
#>                                                                  
#> Secondary trial:                                                 
#> Group-sequential design with 2 stages                            
#> Maximum information: 0.1                                         
#> Overall power: 0.9, overall significance level (1-sided): 0.0378 
#>                                                                  
#>                        Stage 1 Stage 2
#> Information rate       0.500   1.000  
#> Efficacy boundary (Z)  1.988   2.018  
#> Cumulative rejection   0.6157  0.9000 
#> Cumulative alpha spent 0.0234  0.0378 
#> Information            0.05    0.10   
#>                                                      
#> Integrated trial:                                    
#> Group-sequential design with 3 stages                
#> Maximum information: 0.12                            
#> Interim adaptation look: 1, z-statistic value: 0.914 
#>                                                      
#>                       Stage 1 Stage 2 Stage 3
#> Information rate      0.132   0.566   1.000  
#> Efficacy boundary (Z) 3.706   2.182   2.212  
#> Information           0.02    0.07    0.12   

INew <- des2$maxInformation
(nNew <- ceiling(INew * 4 * sigma^2))
#> numeric(0)
(nTotal <- nL + nNew)
#> numeric(0)