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Repeated Confidence Interval After Adaptation

Source: R/RcppExports.R
getADRCI.Rd

Obtains the repeated p-value, conservative point estimate, and repeated confidence interval for an adaptive group sequential trial.

Usage

getADRCI(
  L = NA_integer_,
  zL = NA_real_,
  IMax = NA_real_,
  kMax = NA_integer_,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  criticalValues = NA_real_,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  spendingTime = NA_real_,
  L2 = NA_integer_,
  zL2 = NA_real_,
  INew = NA_real_,
  MullerSchafer = 0L,
  informationRatesNew = NA_real_,
  efficacyStoppingNew = NA_integer_,
  typeAlphaSpendingNew = "sfOF",
  parameterAlphaSpendingNew = NA_real_,
  spendingTimeNew = NA_real_
)

Arguments

L

The interim adaptation look of the primary trial.

zL

The z-test statistic at the interim adaptation look of the primary trial.

IMax

The maximum information of the primary trial.

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.

criticalValues

The upper boundaries on the z-test statistic scale for efficacy stopping for the primary trial.

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, 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".

spendingTime

The error spending time of the primary trial. Defaults to missing, in which case, it is the same as informationRates.

L2

The look of interest in the secondary trial.

zL2

The z-test statistic at the look of the secondary trial.

INew

The maximum information of the secondary trial.

MullerSchafer

Whether to use the Muller and Schafer (2001) method for trial adaptation.

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 up to look L2. 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".

spendingTimeNew

The error spending time of the secondary trial. up to look L2. Defaults to missing, in which case, it is the same as informationRatesNew.

Value

A data frame with the following variables:

  • pvalue: Repeated p-value for rejecting the null hypothesis.

  • thetahat: Point estimate of the parameter.

  • cilevel: Confidence interval level.

  • lower: Lower bound of repeated confidence interval.

  • upper: Upper bound of repeated confidence interval.

References

Cyrus R. Mehta, Peter Bauer, Martin Posch and Werner Brannath. Repeated confidence intervals for adaptive group sequential trials. Stat Med. 2007;26:5422–5433.

See also

adaptDesign

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


# original group sequential design with 90% power to detect delta = 6
delta = 6
sigma = 17
n = 282
(des1 = getDesign(IMax = n/(4*sigma^2), theta = delta, kMax = 3,
                  alpha = 0.05, typeAlphaSpending = "sfHSD",
                  parameterAlphaSpending = -4))
#>                                                                          
#> Group-sequential design with 3 stages                                    
#> theta: 6, maximum information: 0.24                                      
#> Overall power: 0.9029, overall alpha (1-sided): 0.05                     
#> Drift parameter: 2.963, inflation factor: 1.014                          
#> Expected information under H1: 0.19, expected information under H0: 0.24 
#> Alpha spending: HSD(gamma = -4), beta spending: None                     
#>                                                                          
#>                           Stage 1 Stage 2 Stage 3
#> Information rate          0.333   0.667   1.000  
#> Efficacy boundary (Z)     2.794   2.289   1.680  
#> Cumulative rejection      0.1395  0.5588  0.9029 
#> Cumulative alpha spent    0.0026  0.0125  0.0500 
#> Efficacy boundary (theta) 9.797   5.676   3.401  
#> Efficacy boundary (p)     0.0026  0.0110  0.0465 
#> Information               0.08    0.16    0.24   

# interim look results
L = 1
n1 = n/3
delta1 = 4.5
sigma1 = 20
zL = delta1/sqrt(4/n1*sigma1^2)

t = des1$byStageResults$informationRates

# Muller & Schafer (2001) method to design the secondary trial:
des2 = adaptDesign(
  betaNew = 0.2, L = L, zL = zL, theta = 5,
  kMax = 3, informationRates = t,
  alpha = 0.05, typeAlphaSpending = "sfHSD",
  parameterAlphaSpending = -4,
  MullerSchafer = TRUE,
  kNew = 3, typeAlphaSpendingNew = "sfHSD",
  parameterAlphaSpendingNew = -2)

n2 = ceiling(des2$secondaryTrial$overallResults$information*4*20^2)
ns = round(n2*(1:3)/3)
(des2 = adaptDesign(
  INew = n2/(4*20^2), L = L, zL = zL, theta = 5,
  kMax = 3, informationRates = t,
  alpha = 0.05, typeAlphaSpending = "sfHSD",
  parameterAlphaSpending = -4,
  MullerSchafer = TRUE,
  kNew = 3, informationRatesNew = ns/n2,
  typeAlphaSpendingNew = "sfHSD",
  parameterAlphaSpendingNew = -2))
#>                                                      
#> Primary trial:                                       
#> Group-sequential design with 3 stages                
#> Interim adaptation look: 1, z-statistic value: 1.091 
#> Conditional type I error: 0.1033                     
#> Muller & Schafer method for secondary trial: TRUE    
#>                                                      
#>                       Stage 1 Stage 2 Stage 3
#> Information rate      0.333   0.667   1.000  
#> Efficacy boundary (Z) 2.794   2.289   1.680  
#>                                                                          
#> Secondary trial:                                                         
#> Group-sequential design with 3 stages                                    
#> theta: 5, maximum information: 0.18                                      
#> Overall power: 0.8004, overall significance level (1-sided): 0.1033      
#> Drift parameter: 2.151, inflation factor: 1.043                          
#> Expected information under H1: 0.14, Expected information under H0: 0.18 
#>                                                                          
#>                           Stage 1 Stage 2 Stage 3
#> Information rate          0.334   0.666   1.000  
#> Efficacy boundary (Z)     2.160   1.783   1.351  
#> Cumulative rejection      0.1798  0.5057  0.8004 
#> Cumulative alpha spent    0.0154  0.0450  0.1033 
#> Efficacy boundary (theta) 8.683   5.081   3.142  
#> Efficacy boundary (p)     0.0154  0.0373  0.0883 
#> Information               0.06    0.12    0.18   

# termination at the second look of the secondary trial
L2 = 2
delta2 = 6.86
sigma2 = 21.77
zL2 = delta2/sqrt(4/197*sigma2^2)

t2 = des2$secondaryTrial$byStageResults$informationRates[1:L2]

# repeated confidence interval
getADRCI(L = L, zL = zL,
         IMax = n/(4*sigma1^2), kMax = 3,
         informationRates = t,
         alpha = 0.05, typeAlphaSpending = "sfHSD",
         parameterAlphaSpending = -4,
         L2 = L2, zL2 = zL2,
         INew = n2/(4*sigma2^2),
         MullerSchafer = TRUE,
         informationRatesNew = t2,
         typeAlphaSpendingNew = "sfHSD",
         parameterAlphaSpendingNew = -2)
#>       pvalue thetahat cilevel     lower    upper
#> 1 0.02051599  4.28911     0.9 0.9048009 11.32133