rpact: Confirmatory Adaptive Clinical Trial Design and Analysis
## [1] '2.0.1.9003'

1 Working with objects

1.1 Create an example of all available rpact objects

## [PROGRESS] Stage results calculated [0.016 secs] 
## [PROGRESS] Conditional power calculated [0.001 secs] 
## [PROGRESS] Conditional rejection probabilities (CRP) calculated [0.001 secs] 
## [PROGRESS] Repeated confidence interval of stage 1 calculated [0.2753 secs] 
## [PROGRESS] Repeated confidence interval of stage 2 calculated [0.3032 secs] 
## [PROGRESS] Repeated confidence interval of stage 3 calculated [0.3221 secs] 
## [PROGRESS] Repeated confidence interval of stage 4 calculated [0.3461 secs] 
## [PROGRESS] Repeated confidence interval calculated [1.2477 secs] 
## [PROGRESS] Overall repeated p-values of stage 1 calculated [0.4239 secs] 
## [PROGRESS] Overall repeated p-values of stage 2 calculated [0.373 secs] 
## [PROGRESS] Overall repeated p-values of stage 3 calculated [0.383 secs] 
## [PROGRESS] Overall repeated p-values of stage 4 calculated [0.38 secs] 
## [PROGRESS] Repeated p-values calculated [1.5608 secs] 
## [PROGRESS] Final p-value calculated [0.001 secs] 
## [PROGRESS] Final confidence interval calculated [0.0838 secs]

2 How to use R generic functions with rpact objects

2.1 Get field names of the object

##  [1] "kMax"                  "alpha"                
##  [3] "stages"                "informationRates"     
##  [5] "userAlphaSpending"     "criticalValues"       
##  [7] "stageLevels"           "alphaSpent"           
##  [9] "bindingFutility"       "tolerance"            
## [11] "typeOfDesign"          "beta"                 
## [13] "deltaWT"               "futilityBounds"       
## [15] "gammaA"                "gammaB"               
## [17] "optimizationCriterion" "sided"                
## [19] "betaSpent"             "typeBetaSpending"     
## [21] "userBetaSpending"      "power"                
## [23] "twoSidedPower"         "constantBoundsHP"
##  [1] "nFixed"                 "shift"                 
##  [3] "inflationFactor"        "stages"                
##  [5] "information"            "power"                 
##  [7] "rejectionProbabilities" "futilityProbabilities" 
##  [9] "averageSampleNumber1"   "averageSampleNumber01" 
## [11] "averageSampleNumber0"
##  [1] "nMax"                "theta"               "averageSampleNumber"
##  [4] "calculatedPower"     "overallEarlyStop"    "earlyStop"          
##  [7] "overallReject"       "rejectPerStage"      "overallFutility"    
## [10] "futilityPerStage"
## [1] "designs"          "variedParameters"
## [1] "stages"             "groups"             "sampleSizes"       
## [4] "means"              "stDevs"             "overallSampleSizes"
## [7] "overallMeans"       "overallStDevs"
##  [1] "stages"                "overallTestStatistics"
##  [3] "overallPValues"        "overallMeans1"        
##  [5] "overallMeans2"         "overallStDevs1"       
##  [7] "overallStDevs2"        "overallSampleSizes1"  
##  [9] "overallSampleSizes2"   "testStatistics"       
## [11] "pValues"               "effectSizes"          
## [13] "thetaH0"               "direction"            
## [15] "normalApproximation"   "equalVariances"
##  [1] "stages"                               
##  [2] "informationRates"                     
##  [3] "criticalValues"                       
##  [4] "futilityBounds"                       
##  [5] "alphaSpent"                           
##  [6] "stageLevels"                          
##  [7] "effectSizes"                          
##  [8] "testStatistics"                       
##  [9] "pValues"                              
## [10] "testActions"                          
## [11] "thetaH0"                              
## [12] "thetaH1"                              
## [13] "assumedStDev"                         
## [14] "conditionalRejectionProbabilities"    
## [15] "nPlanned"                             
## [16] "allocationRatioPlanned"               
## [17] "pi1"                                  
## [18] "pi2"                                  
## [19] "conditionalPower"                     
## [20] "repeatedConfidenceIntervalLowerBounds"
## [21] "repeatedConfidenceIntervalUpperBounds"
## [22] "repeatedPValues"                      
## [23] "finalStage"                           
## [24] "finalPValues"                         
## [25] "finalConfidenceIntervalLowerBounds"   
## [26] "finalConfidenceIntervalUpperBounds"   
## [27] "medianUnbiasedEstimates"              
## [28] "normalApproximation"                  
## [29] "equalVariances"                       
## [30] "directionUpper"                       
## [31] "overallTestStatistics"                
## [32] "overallPValues"
##  [1] "normalApproximation"            "meanRatio"                     
##  [3] "thetaH0"                        "alternative"                   
##  [5] "stDev"                          "groups"                        
##  [7] "allocationRatioPlanned"         "directionUpper"                
##  [9] "nFixed"                         "nFixed1"                       
## [11] "nFixed2"                        "informationRates"              
## [13] "maxNumberOfSubjects"            "maxNumberOfSubjects1"          
## [15] "maxNumberOfSubjects2"           "numberOfSubjects"              
## [17] "numberOfSubjects1"              "numberOfSubjects2"             
## [19] "expectedNumberOfSubjectsH0"     "expectedNumberOfSubjectsH01"   
## [21] "expectedNumberOfSubjectsH1"     "effect"                        
## [23] "expectedNumberOfSubjects"       "rejectPerStage"                
## [25] "overallReject"                  "futilityPerStage"              
## [27] "futilityStop"                   "earlyStop"                     
## [29] "criticalValuesEffectScale"      "criticalValuesEffectScaleLower"
## [31] "criticalValuesEffectScaleUpper" "criticalValuesPValueScale"     
## [33] "futilityBoundsEffectScale"      "futilityBoundsPValueScale"
##  [1] "maxNumberOfSubjects"       "accrualTime"              
##  [3] "accrualIntensity"          "plannedEvents"            
##  [5] "pi1"                       "pi2"                      
##  [7] "median1"                   "median2"                  
##  [9] "directionUpper"            "dropoutRate1"             
## [11] "dropoutRate2"              "dropoutTime"              
## [13] "eventTime"                 "thetaH0"                  
## [15] "allocation1"               "allocation2"              
## [17] "minNumberOfEventsPerStage" "maxNumberOfEventsPerStage"
## [19] "conditionalPower"          "thetaH1"                  
## [21] "maxNumberOfIterations"     "kappa"                    
## [23] "piecewiseSurvivalTime"     "lambda1"                  
## [25] "lambda2"                   "hazardRatio"              
## [27] "iterations"                "analysisTime"             
## [29] "studyDuration"             "eventsPerStage"           
## [31] "expectedNumberOfEvents"    "eventsNotAchieved"        
## [33] "numberOfSubjects"          "expectedNumberOfSubjects" 
## [35] "rejectPerStage"            "overallReject"            
## [37] "futilityPerStage"          "futilityStop"             
## [39] "earlyStop"                 "conditionalPowerAchieved" 
## [41] "seed"
##  [1] "piecewiseSurvivalTime"    "lambda1"                 
##  [3] "lambda2"                  "hazardRatio"             
##  [5] "pi1"                      "pi2"                     
##  [7] "median1"                  "median2"                 
##  [9] "eventTime"                "kappa"                   
## [11] "piecewiseSurvivalEnabled" "delayedResponseAllowed"  
## [13] "delayedResponseEnabled"
##  [1] "endOfAccrualIsUserDefined"                 
##  [2] "followUpTimeMustBeUserDefined"             
##  [3] "maxNumberOfSubjectsIsUserDefined"          
##  [4] "maxNumberOfSubjectsCanBeCalculatedDirectly"
##  [5] "absoluteAccrualIntensityEnabled"           
##  [6] "accrualTime"                               
##  [7] "accrualIntensity"                          
##  [8] "accrualIntensityRelative"                  
##  [9] "maxNumberOfSubjects"                       
## [10] "remainingTime"                             
## [11] "piecewiseAccrualEnabled"

2.1.1 Access data of a field

## [1] 3.069028 2.325888 1.977663 1.762694
## [1] 3.069028 2.325888 1.977663 1.762694

2.3 Show a summary of the object

## This output summarizes the group sequential design specification.
## 
## Design parameters and output of group sequential design:
## 
## User defined parameters:
##   Type of design                               : WT 
##   Maximum number of stages                     : 4 
##   Stages                                       : 1, 2, 3, 4 
##   Information rates                            : 0.250, 0.500, 0.750, 1.000 
##   Significance level                           : 0.0500 
##   Delta for Wang & Tsiatis Delta class         : 0.1 
## 
## Derived from user defined parameters: not available
## 
## Default parameters:
##   Type II error rate                           : 0.2 
##   Two-sided power                              : FALSE 
##   Test                                         : one-sided 
##   Tolerance                                    : 1e-08 
## 
## Output:
##   Cumulative alpha spending                    : 0.001074, 0.010527, 0.028206, 0.050000 
##   Critical values                              : 3.069, 2.326, 1.978, 1.763 
##   Stage levels                                 : 0.001074, 0.010012, 0.023983, 0.038976 
## 
## 
## Technical summary of the trial design object of class "TrialDesignGroupSequential":
## 
##   [u] Type of design                           : WT 
##   [u] Maximum number of stages                 : 4 
##   [u] Stages                                   : 1, 2, 3, 4 
##   [u] Information rates                        : 0.250, 0.500, 0.750, 1.000 
##   [u] Significance level                       : 0.0500 
##   [d] Type II error rate                       : 0.2 
##   [.] Power                                    : NA, NA, NA, NA 
##   [d] Two-sided power                          : FALSE 
##   [u] Delta for Wang & Tsiatis Delta class     : 0.1 
##   [.] Futility bounds (non-binding)            : -Inf, -Inf, -Inf 
##   [.] Binding futility                         : FALSE 
##   [.] Haybittle Peto constants                 : NA 
##   [.] Parameter for alpha spending function    : 1 
##   [.] Parameter for beta spending function     : 1 
##   [.] Optimization criterion for optimum design within Wang & Tsiatis class : ASNH1 
##   [d] Test                                     : one-sided 
##   [d] Tolerance                                : 1e-08 
##   [g] Cumulative alpha spending                : 0.001074, 0.010527, 0.028206, 0.050000 
##   [.] User defined alpha spending              : NA 
##   [.] Cumulative beta spending                 : NA, NA, NA, NA 
##   [.] Type of beta spending                    : none 
##   [.] User defined beta spending               : NA 
##   [g] Critical values                          : 3.069, 2.326, 1.978, 1.763 
##   [g] Stage levels                             : 0.001074, 0.010012, 0.023983, 0.038976 
## 
## Legend:
##   u: user defined
##   >: derived value
##   d: default value
##   g: generated/calculated value
##   .: not applicable or hidden
## 
## Group sequential design table:
##           Information rate Power Futility bound (non-binding)
##   Stage 1 0.25                   -Inf                        
##   Stage 2 0.50                   -Inf                        
##   Stage 3 0.75                   -Inf                        
##   Stage 4 1.00                                               
##           Cumulative alpha spending Cumulative beta spending
##   Stage 1 0.001074                                          
##   Stage 2 0.010527                                          
##   Stage 3 0.028206                                          
##   Stage 4 0.050000                                          
##           Critical value Stage level
##   Stage 1 3.069          0.001074   
##   Stage 2 2.326          0.010012   
##   Stage 3 1.978          0.023983   
##   Stage 4 1.763          0.038976
## This output summarizes the group sequential design characteristics specification.
## 
## Group sequential design characteristics:
##   Number of subjects fixed                     : 6.2 
##   Shift                                        : 6.4822 
##   Inflation factor                             : 1.0485 
##   Informations                                 : 1.6205, 3.2411, 4.8616, 6.4822 
##   Power                                        : 0.03625, 0.30265, 0.60337, 0.80000 
##   Rejection probabilities                      : 0.03625, 0.26640, 0.30072, 0.19663 
##   Futility probabilities                       : 0, 0, 0 
##   Ratio expected vs fixed sample size under H1 : 0.8015 
##   Ratio expected vs fixed sample size under a value between H0 and H1 : 0.9724 
##   Ratio expected vs fixed sample size under H0 : 1.0380 
## 
## 
## Technical summary of the design characteristics object of class "TrialDesignCharacteristics":
##   [g] Number of subjects fixed                 : 6.2 
##   [g] Shift                                    : 6.4822 
##   [g] Inflation factor                         : 1.0485 
##   [u] Stages                                   : 1, 2, 3, 4 
##   [g] Informations                             : 1.6205, 3.2411, 4.8616, 6.4822 
##   [g] Power                                    : 0.03625, 0.30265, 0.60337, 0.80000 
##   [g] Rejection probabilities                  : 0.03625, 0.26640, 0.30072, 0.19663 
##   [g] Futility probabilities                   : 0, 0, 0 
##   [g] Ratio expected vs fixed sample size under H1 : 0.8015 
##   [g] Ratio expected vs fixed sample size under a value between H0 and H1 : 0.9724 
##   [g] Ratio expected vs fixed sample size under H0 : 1.0380 
## 
## Legend:
##   u: user defined
##   >: derived value
##   d: default value
##   g: generated/calculated value
##   .: not applicable or hidden
## 
## Group sequential design characteristics table:
##           Information Power   Rejection probability Futility probability
##   Stage 1 1.620541    0.03625 0.03625               0                   
##   Stage 2 3.241081    0.30265 0.26640               0                   
##   Stage 3 4.861622    0.60337 0.30072               0                   
##   Stage 4 6.482163    0.80000 0.19663
## This output summarizes the power and average sample size (ASN) specification.
## 
## Power and average sample size (ASN):
## 
## User defined parameters:
##   Effect                                       : 1 
## 
## Default parameters:
##   N_max                                        : 100 
## 
## Output:
##   Average sample sizes (ASN)                   : 25.7 
##   Power                                        : 1.0000 
##   Overall Early stop                           : 1 
##   Early stop [1]                               : 9.73e-01 
##   Early stop [2]                               : 2.67e-02 
##   Early stop [3]                               : 1.03e-06 
##   Early stop [4]                               : NA 
##   Overall reject                               : 1 
##   Reject per stage [1]                         : 9.73e-01 
##   Reject per stage [2]                         : 2.67e-02 
##   Reject per stage [3]                         : 1.02e-06 
##   Reject per stage [4]                         : 0.00e+00 
##   Overall futility                             : 0 
##   Futility stop per stage [1]                  : 0 
##   Futility stop per stage [2]                  : 0 
##   Futility stop per stage [3]                  : 0 
## 
## Legend:
##   [k]: values at stage k
## 
## 
## Technical summary of the power and average sample size (ASN) object:
##   [d] N_max                                    : 100 
##   [u] Effect                                   : 1 
##   [g] Average sample sizes (ASN)               : 25.7 
##   [g] Power                                    : 1.0000 
##   [g] Overall Early stop                       : 1 
##   [g] Early stop [1]                           : 9.73e-01 
##   [g] Early stop [2]                           : 2.67e-02 
##   [g] Early stop [3]                           : 1.03e-06 
##   [g] Early stop [4]                           : NA 
##   [g] Overall reject                           : 1 
##   [g] Reject per stage [1]                     : 9.73e-01 
##   [g] Reject per stage [2]                     : 2.67e-02 
##   [g] Reject per stage [3]                     : 1.02e-06 
##   [g] Reject per stage [4]                     : 0.00e+00 
##   [g] Overall futility                         : 0 
##   [g] Futility stop per stage [1]              : 0 
##   [g] Futility stop per stage [2]              : 0 
##   [g] Futility stop per stage [3]              : 0 
## 
## Legend:
##   u: user defined
##   >: derived value
##   d: default value
##   g: generated/calculated value
##   .: not applicable or hidden
## 
## Power and average sample size (ASN) table:
##           Early stop   Reject per stage Futility stop per stage
## stage = 1 9.732567e-01 9.73e-01         0                      
## stage = 2 2.674225e-02 2.67e-02         0                      
## stage = 3 1.025014e-06 1.02e-06         0                      
## stage = 4 <NA>         0.00e+00
##         Length          Class           Mode 
##              3 TrialDesignSet             S4
## This output summarizes the dataset of means specification.
## 
## Dataset of means:
##   Stages                                       : 1, 1, 2, 2, 3, 3, 4, 4 
##   Treatment groups                             : 1, 2, 1, 2, 1, 2, 1, 2 
##   Sample sizes                                 : 22, 22, 11, 13, 22, 22, 11, 13 
##   Means                                        : 1.0, 1.4, 1.1, 1.5, 1.0, 3.0, 1.0, 2.5 
##   Standard deviations                          : 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 1.3, 1.3 
## 
## Calculated data:
##   Overall sample sizes                         : 22, 22, 33, 35, 55, 57, 66, 70 
##   Overall means                                : 1.000, 1.400, 1.033, 1.437, 1.020, 2.040, 1.017, 2.126 
##   Overall standard deviations                  : 1.00, 1.00, 1.38, 1.43, 1.64, 1.82, 1.58, 1.74 
## 
## 
## Technical summary of the dataset object of class"DatasetMeans":
##   [u] Stages                                   : 1, 1, 2, 2, 3, 3, 4, 4 
##   [u] Treatment groups                         : 1, 2, 1, 2, 1, 2, 1, 2 
##   [u] Sample sizes                             : 22, 22, 11, 13, 22, 22, 11, 13 
##   [u] Means                                    : 1.0, 1.4, 1.1, 1.5, 1.0, 3.0, 1.0, 2.5 
##   [u] Standard deviations                      : 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 1.3, 1.3 
##   [g] Overall sample sizes                     : 22, 22, 33, 35, 55, 57, 66, 70 
##   [g] Overall means                            : 1.000, 1.400, 1.033, 1.437, 1.020, 2.040, 1.017, 2.126 
##   [g] Overall standard deviations              : 1.00, 1.00, 1.38, 1.43, 1.64, 1.82, 1.58, 1.74 
## 
## Legend:
##   u: user defined
##   >: derived value
##   d: default value
##   g: generated/calculated value
##   .: not applicable or hidden
## 
## Dataset of means table:
##           Treatment group Sample size Mean Standard deviation
##   Stage 1 1               22          1.0  1.0               
##   Stage 2 2               22          1.4  1.0               
##   Stage 3 1               11          1.1  2.0               
##   Stage 4 2               13          1.5  2.0               
##   Stage 5 1               22          1.0  2.0               
##   Stage 6 2               22          3.0  2.0               
##   Stage 7 1               11          1.0  1.3               
##   Stage 8 2               13          2.5  1.3               
##           Overall sample size Overall mean Overall standard deviation
##   Stage 1 22                  1.000        1.00                      
##   Stage 2 22                  1.400        1.00                      
##   Stage 3 33                  1.033        1.38                      
##   Stage 4 35                  1.437        1.43                      
##   Stage 5 55                  1.020        1.64                      
##   Stage 6 57                  2.040        1.82                      
##   Stage 7 66                  1.017        1.58                      
##   Stage 8 70                  2.126        1.74
## This output summarizes the stage results of means specification.
## 
## Stage results of means:
##   Stages                                       : 1, 2, 3, 4 
##   Overall test statistics                      : -1.327, -1.185, -3.111, -3.887 
##   Overall p-values                             : 0.9041, 0.8799, 0.9988, 0.9999 
##   Overall means (1)                            : 1.000, 1.033, 1.020, 1.017 
##   Overall means (2)                            : 1.400, 1.437, 2.040, 2.126 
##   Overall standard deviations (1)              : 1.00, 1.38, 1.64, 1.58 
##   Overall standard deviations (2)              : 1.00, 1.43, 1.82, 1.74 
##   Overall sample sizes (1)                     : 22, 33, 55, 66 
##   Overall sample sizes (2)                     : 22, 35, 57, 70 
##   Test statistics                              : -1.327, -0.488, -3.317, -2.817 
##   p-values                                     : 0.9041, 0.6849, 0.9991, 0.9950 
##   Effect sizes                                 : -0.4000, -0.4038, -1.0204, -1.1090 
##   Theta H0                                     : 0 
##   Direction                                    : upper 
##   Normal approximation                         : FALSE 
##   Equal variances                              : TRUE 
## 
## 
## Technical summary of the stage results object of class "StageResultsMeans":
## 
##   [u] Stages                                   : 1, 2, 3, 4 
##   [?] Overall test statistics                  : -1.327, -1.185, -3.111, -3.887 
##   [?] Overall p-values                         : 0.9041, 0.8799, 0.9988, 0.9999 
##   [?] Overall means (1)                        : 1.000, 1.033, 1.020, 1.017 
##   [?] Overall means (2)                        : 1.400, 1.437, 2.040, 2.126 
##   [?] Overall standard deviations (1)          : 1.00, 1.38, 1.64, 1.58 
##   [?] Overall standard deviations (2)          : 1.00, 1.43, 1.82, 1.74 
##   [?] Overall sample sizes (1)                 : 22, 33, 55, 66 
##   [?] Overall sample sizes (2)                 : 22, 35, 57, 70 
##   [?] Test statistics                          : -1.327, -0.488, -3.317, -2.817 
##   [?] p-values                                 : 0.9041, 0.6849, 0.9991, 0.9950 
##   [?] Effect sizes                             : -0.4000, -0.4038, -1.0204, -1.1090 
##   [?] Theta H0                                 : 0 
##   [?] Direction                                : upper 
##   [?] Normal approximation                     : FALSE 
##   [?] Equal variances                          : TRUE 
##   [?] Inverse normal combination               : -1.305, -1.263, -2.826, -3.734 
##   [?] Fisher combination                       : 0.9041, 0.6192, 0.6186, 0.6155 
##   [?] Weights Fisher                           : 1.000, 1.000, 1.000, 1.000 
##   [?] Weights inverse normal                   : 0.500, 0.500, 0.500, 0.500 
##   [?] Overall means                            :  
##   [?] Overall standard deviations              : 1.00, 1.40, 1.74, 1.66 
##   [?] Overall sample sizes                     :  
## 
## Legend:
##   u: user defined
##   >: derived value
##   d: default value
##   g: generated/calculated value
##   .: not applicable or hidden
## 
## Stage results of means table:
##           Overall test statistic Overall p-value Overall mean (1)
##   Stage 1 -1.326650              0.9041          1.000           
##   Stage 2 -1.185099              0.8799          1.033           
##   Stage 3 -3.111238              0.9988          1.020           
##   Stage 4 -3.886959              0.9999          1.017           
##           Overall mean (2) Overall standard deviation (1)
##   Stage 1 1.400            1.00                          
##   Stage 2 1.437            1.38                          
##   Stage 3 2.040            1.64                          
##   Stage 4 2.126            1.58                          
##           Overall standard deviation (2) Overall sample size (1)
##   Stage 1 1.00                           22                     
##   Stage 2 1.43                           33                     
##   Stage 3 1.82                           55                     
##   Stage 4 1.74                           66                     
##           Overall sample size (2) Test statistic p-value Effect size
##   Stage 1 22                      -1.327         0.9041  -0.4000    
##   Stage 2 35                      -0.488         0.6849  -0.4038    
##   Stage 3 57                      -3.317         0.9991  -1.0204    
##   Stage 4 70                      -2.817         0.9950  -1.1090
## This output summarizes the analysis results (group sequential design) specification.
## 
## Analysis results (group sequential design):
##   Stages                                       : 1, 2, 3, 4 
##   Information rates                            : 0.250, 0.500, 0.750, 1.000 
##   Critical values                              : 3.069, 2.326, 1.978, 1.763 
##   Futility bounds (non-binding)                : -Inf, -Inf, -Inf 
##   Cumulative alpha spending                    : 0.001074, 0.010527, 0.028206, 0.050000 
##   Stage levels                                 : 0.001074, 0.010012, 0.023983, 0.038976 
##   Effect sizes                                 : -0.4000, -0.4038, -1.0204, -1.1090 
##   Test statistics                              : -1.327, -0.488, -3.317, -2.817 
##   p-values                                     : 0.9041, 0.6849, 0.9991, 0.9950 
##   Overall test statistics                      : -1.327, -1.185, -3.111, -3.887 
##   Overall p-values                             : 0.9041, 0.8799, 0.9988, 0.9999 
##   Actions                                      : continue, continue, continue, accept 
##   Theta H0                                     : 0 
##   CRP                                          : 2.810e-03, 1.227e-04, 6.661e-16, NA 
##   Planned sample size                          : NA, NA, NA, NA 
##   Planned allocation ratio                     : 1 
##   Assumed effect                               : NA 
##   Assumed standard deviation                   : 1.66 
##   Conditional power                            : NA, NA, NA, NA 
##   RCIs (lower)                                 : -1.39, -1.22, -1.68, -1.62 
##   RCIs (upper)                                 : 0.586, 0.408, -0.364, -0.602 
##   Repeated p-values                            : >0.5, >0.5, >0.5, >0.5 
##   Final stage                                  : 4 
##   Final p-value                                : NA, NA, NA, 0.9999 
##   Final CIs (lower)                            : NA, NA, NA, -1.55 
##   Final CIs (upper)                            : NA, NA, NA, -0.608 
##   Median unbiased estimate                     : NA, NA, NA, -1.08 
## 
## 
## Technical summary of the analysis results object of class "AnalysisResultsGroupSequential":
##   [u] Stages                                   : 1, 2, 3, 4 
##   [?] Information rates                        : 0.250, 0.500, 0.750, 1.000 
##   [?] Critical values                          : 3.069, 2.326, 1.978, 1.763 
##   [?] Futility bounds (non-binding)            : -Inf, -Inf, -Inf 
##   [?] Cumulative alpha spending                : 0.001074, 0.010527, 0.028206, 0.050000 
##   [?] Stage levels                             : 0.001074, 0.010012, 0.023983, 0.038976 
##   [?] Effect sizes                             : -0.4000, -0.4038, -1.0204, -1.1090 
##   [?] Test statistics                          : -1.327, -0.488, -3.317, -2.817 
##   [?] p-values                                 : 0.9041, 0.6849, 0.9991, 0.9950 
##   [?] Overall test statistics                  : -1.327, -1.185, -3.111, -3.887 
##   [?] Overall p-values                         : 0.9041, 0.8799, 0.9988, 0.9999 
##   [?] Actions                                  : continue, continue, continue, accept 
##   [?] Theta H0                                 : 0 
##   [?] CRP                                      : 2.810e-03, 1.227e-04, 6.661e-16, NA 
##   [?] Planned sample size                      : NA, NA, NA, NA 
##   [?] Planned allocation ratio                 : 1 
##   [?] Assumed effect                           : NA 
##   [?] Assumed standard deviation               : 1.66 
##   [?] Conditional power                        : NA, NA, NA, NA 
##   [?] RCIs (lower)                             : -1.39, -1.22, -1.68, -1.62 
##   [?] RCIs (upper)                             : 0.586, 0.408, -0.364, -0.602 
##   [?] Repeated p-values                        : >0.5, >0.5, >0.5, >0.5 
##   [?] Final stage                              : 4 
##   [?] Final p-value                            : NA, NA, NA, 0.9999 
##   [?] Final CIs (lower)                        : NA, NA, NA, -1.55 
##   [?] Final CIs (upper)                        : NA, NA, NA, -0.608 
##   [?] Median unbiased estimate                 : NA, NA, NA, -1.08 
##   [?] pi (1)                                   :  
##   [?] pi (2)                                   :  
##   [?] Normal approximation                     : FALSE 
##   [?] Equal variances                          : TRUE 
##   [?] Direction upper                          : TRUE 
## 
## Legend:
##   u: user defined
##   >: derived value
##   d: default value
##   g: generated/calculated value
##   .: not applicable or hidden
## 
## Analysis results (group sequential design) table:
##           Information rate Critical value Futility bound (binding)
##   Stage 1 0.25             3.069          -Inf                    
##   Stage 2 0.50             2.326          -Inf                    
##   Stage 3 0.75             1.978          -Inf                    
##   Stage 4 1.00             1.763                                  
##           Cumulative alpha spending Stage level Effect size Test statistic
##   Stage 1 0.001074                  0.001074    -0.4000     -1.327        
##   Stage 2 0.010527                  0.010012    -0.4038     -0.488        
##   Stage 3 0.028206                  0.023983    -1.0204     -3.317        
##   Stage 4 0.050000                  0.038976    -1.1090     -2.817        
##           p-value Overall test statistic Overall p-value Action  
##   Stage 1 0.9041  -1.327                 0.9041          continue
##   Stage 2 0.6849  -1.185                 0.8799          continue
##   Stage 3 0.9991  -3.111                 0.9988          continue
##   Stage 4 0.9950  -3.887                 0.9999          accept  
##           CRP       Planned sample size Conditional power RCI (lower)
##   Stage 1 2.810e-03                                       -1.39      
##   Stage 2 1.227e-04                                       -1.22      
##   Stage 3 6.661e-16                                       -1.68      
##   Stage 4                                                 -1.62      
##           RCI (upper) Repeated p-value Final p-value Final CI (lower)
##   Stage 1 0.586       >0.5                                           
##   Stage 2 0.408       >0.5                                           
##   Stage 3 -0.364      >0.5                                           
##   Stage 4 -0.602      >0.5             0.9999        -1.55           
##           Final CI (upper) Median unbiased estimate
##   Stage 1                                          
##   Stage 2                                          
##   Stage 3                                          
##   Stage 4 -0.608           -1.08
## This output summarizes the means specification.
## 
## Design plan parameters and output for means:
## 
## Design parameters:
##   Significance level                           : 0.0500 
##   Type II error rate                           : 0.2 
##   Test                                         : one-sided 
## 
## User defined parameters: not available
## 
## Default parameters:
##   Normal approximation                         : FALSE 
##   Mean ratio                                   : FALSE 
##   Theta H0                                     : 0 
##   Alternatives                                 : 0.2, 0.4, 0.6, 0.8, 1 
##   Standard deviation                           : 1 
##   Treatment groups                             : 2 
##   Planned allocation ratio                     : 1 
## 
## Sample size and output:
##   Information rates [1]                        : 0.250 
##   Information rates [2]                        : 0.500 
##   Information rates [3]                        : 0.750 
##   Information rates [4]                        : 1.000 
##   Maximum number of subjects                   : 649.6, 163.5, 73.5, 42.0, 27.5 
##   Maximum number of subjects (1)               : 324.8, 81.7, 36.7, 21.0, 13.7 
##   Maximum number of subjects (2)               : 324.8, 81.7, 36.7, 21.0, 13.7 
##   Number of subjects [1]                       : 162.4, 40.9, 18.4, 10.5, 6.9 
##   Number of subjects [2]                       : 324.8, 81.7, 36.7, 21.0, 13.7 
##   Number of subjects [3]                       : 487.2, 122.6, 55.1, 31.5, 20.6 
##   Number of subjects [4]                       : 649.6, 163.5, 73.5, 42.0, 27.5 
##   Expected number of subjects under H0         : 643.2, 161.9, 72.8, 41.6, 27.2 
##   Expected number of subjects under H0/H1      : 602.5, 151.6, 68.2, 39.0, 25.5 
##   Expected number of subjects under H1         : 496.6, 125.0, 56.2, 32.1, 21.0 
##   Reject per stage [1]                         : 0.0362 
##   Reject per stage [2]                         : 0.2664 
##   Reject per stage [3]                         : 0.3007 
##   Reject per stage [4]                         : 0.1966 
##   Early stop                                   : 0.603 
##   Critical values (effect scale) [1]           : 0.482, 0.960, 1.432, 1.894, 2.342 
##   Critical values (effect scale) [2]           : 0.258, 0.515, 0.767, 1.015, 1.255 
##   Critical values (effect scale) [3]           : 0.179, 0.357, 0.533, 0.705, 0.871 
##   Critical values (effect scale) [4]           : 0.138, 0.276, 0.411, 0.544, 0.673 
##   Local one-sided significance levels [1]      : 0.001074 
##   Local one-sided significance levels [2]      : 0.010012 
##   Local one-sided significance levels [3]      : 0.023983 
##   Local one-sided significance levels [4]      : 0.038976 
## 
## Legend:
##   (i): values of treatment arm i
##   [k]: values at stage k
## 
## 
## Technical summary of the design plan object of class "TrialDesignPlanMeans":
## 
##   [d] Normal approximation                     : FALSE 
##   [d] Mean ratio                               : FALSE 
##   [d] Theta H0                                 : 0 
##   [d] Alternatives                             : 0.2, 0.4, 0.6, 0.8, 1 
##   [d] Standard deviation                       : 1 
##   [d] Treatment groups                         : 2 
##   [d] Planned allocation ratio                 : 1 
##   [.] Direction upper                          :  
##   [.] Number of subjects fixed                 : 619.6, 155.9, 70.1, 40.1, 26.2 
##   [.] Number of subjects fixed (1)             : 309.8, 78.0, 35.0, 20.0, 13.1 
##   [.] Number of subjects fixed (2)             : 309.8, 78.0, 35.0, 20.0, 13.1 
##   [g] Information rates [1]                    : 0.250 
##   [g] Information rates [2]                    : 0.500 
##   [g] Information rates [3]                    : 0.750 
##   [g] Information rates [4]                    : 1.000 
##   [g] Maximum number of subjects               : 649.6, 163.5, 73.5, 42.0, 27.5 
##   [g] Maximum number of subjects (1)           : 324.8, 81.7, 36.7, 21.0, 13.7 
##   [g] Maximum number of subjects (2)           : 324.8, 81.7, 36.7, 21.0, 13.7 
##   [g] Number of subjects [1]                   : 162.4, 40.9, 18.4, 10.5, 6.9 
##   [g] Number of subjects [2]                   : 324.8, 81.7, 36.7, 21.0, 13.7 
##   [g] Number of subjects [3]                   : 487.2, 122.6, 55.1, 31.5, 20.6 
##   [g] Number of subjects [4]                   : 649.6, 163.5, 73.5, 42.0, 27.5 
##   [.] Number of subjects (1) [1]               : 81.2, 20.4, 9.2, 5.3, 3.4 
##   [.] Number of subjects (1) [2]               : 162.4, 40.9, 18.4, 10.5, 6.9 
##   [.] Number of subjects (1) [3]               : 243.6, 61.3, 27.6, 15.8, 10.3 
##   [.] Number of subjects (1) [4]               : 324.8, 81.7, 36.7, 21.0, 13.7 
##   [.] Number of subjects (2) [1]               : 81.2, 20.4, 9.2, 5.3, 3.4 
##   [.] Number of subjects (2) [2]               : 162.4, 40.9, 18.4, 10.5, 6.9 
##   [.] Number of subjects (2) [3]               : 243.6, 61.3, 27.6, 15.8, 10.3 
##   [.] Number of subjects (2) [4]               : 324.8, 81.7, 36.7, 21.0, 13.7 
##   [g] Expected number of subjects under H0     : 643.2, 161.9, 72.8, 41.6, 27.2 
##   [g] Expected number of subjects under H0/H1  : 602.5, 151.6, 68.2, 39.0, 25.5 
##   [g] Expected number of subjects under H1     : 496.6, 125.0, 56.2, 32.1, 21.0 
##   [.] Effect                                   :  
##   [.] Expected number of subjects              :  
##   [g] Reject per stage [1]                     : 0.0362 
##   [g] Reject per stage [2]                     : 0.2664 
##   [g] Reject per stage [3]                     : 0.3007 
##   [g] Reject per stage [4]                     : 0.1966 
##   [.] Overall reject                           :  
##   [.] Futility stop                            :  
##   [g] Early stop                               : 0.603 
##   [g] Critical values (effect scale) [1]       : 0.482, 0.960, 1.432, 1.894, 2.342 
##   [g] Critical values (effect scale) [2]       : 0.258, 0.515, 0.767, 1.015, 1.255 
##   [g] Critical values (effect scale) [3]       : 0.179, 0.357, 0.533, 0.705, 0.871 
##   [g] Critical values (effect scale) [4]       : 0.138, 0.276, 0.411, 0.544, 0.673 
##   [g] Local one-sided significance levels [1]  : 0.001074 
##   [g] Local one-sided significance levels [2]  : 0.010012 
##   [g] Local one-sided significance levels [3]  : 0.023983 
##   [g] Local one-sided significance levels [4]  : 0.038976 
##   [.] Futility bounds (effect scale) [1]       : NA 
##   [.] Futility bounds (effect scale) [2]       : NA 
##   [.] Futility bounds (effect scale) [3]       : NA 
## 
## Legend:
##   u: user defined
##   >: derived value
##   d: default value
##   g: generated/calculated value
##   .: not applicable or hidden
## 
## Means table:
##      Normal approximation Mean ratio Theta H0 Alternative
##    1 FALSE                FALSE      0        0.2        
##    2 <NA>                                     0.4        
##    3 <NA>                                     0.6        
##    4 <NA>                                     0.8        
##    5 <NA>                                     1          
##      Standard deviation Treatment group Planned allocation ratio
##    1 1                  2               1                       
##    2                                                            
##    3                                                            
##    4                                                            
##    5                                                            
##      Direction upper # subjects fixed # subjects fixed (1)
##    1                 619.6            309.8               
##    2                 155.9            78.0                
##    3                 70.1             35.0                
##    4                 40.1             20.0                
##    5                 26.2             13.1                
##      # subjects fixed (2) Information rate Max # subjects
##    1 309.8                0.250            649.6         
##    2 78.0                 0.500            163.5         
##    3 35.0                 0.750            73.5          
##    4 20.0                 1.000            42.0          
##    5 13.1                                  27.5          
##      Max # subjects (1) Max # subjects (2) Expected # subjects under H0
##    1 324.8              324.8              643.2                       
##    2 81.7               81.7               161.9                       
##    3 36.7               36.7               72.8                        
##    4 21.0               21.0               41.6                        
##    5 13.7               13.7               27.2                        
##      Expected # subjects under H0/H1 Expected # subjects under H1 Effect
##    1 602.5                           496.6                              
##    2 151.6                           125.0                              
##    3 68.2                            56.2                               
##    4 39.0                            32.1                               
##    5 25.5                            21.0                               
##      Expected # subjects Reject per stage Overall reject Futility stop
##    1                     0.0362                                       
##    2                     0.2664                                       
##    3                     0.3007                                       
##    4                     0.1966                                       
##    5                                                                  
##      Early stop Local one-sided significance level
##    1 0.603      0.001074                          
##    2            0.010012                          
##    3            0.023983                          
##    4            0.038976                          
##    5                                              
##      Futility bound (effect scale)
##    1                              
##    2                              
##    3                              
##    4                              
##    5
## This output summarizes the simulation of survival data (group sequential design) specification.
## 
## Simulation of survival data (group sequential design):
## 
## User defined parameters:
##   Maximum number of subjects                   : 100.0 
##   Planned events                               : 50, 100, 150, 200 
## 
## Default parameters:
##   Accrual time                                 : 12 
##   pi (1)                                       : 0.200, 0.300, 0.400, 0.500 
##   pi (2)                                       : 0.200 
##   Direction upper                              : TRUE 
##   Drop-out rate (1)                            : 0.000 
##   Drop-out rate (2)                            : 0.000 
##   Drop-out time                                : 12 
##   Event time                                   : 12 
##   Theta H0                                     : 1 
##   Allocation 1                                 : 1 
##   Allocation 2                                 : 1 
##   Conditional power                            : NA 
##   Maximum number of iterations                 : 1000 
##   Kappa                                        : 1 
##   Seed                                         : -125184577 
## 
## Results:
##   Accrual intensity                            : 8.3 
##   Median (1)                                   : 37.3, 23.3, 16.3, 12.0 
##   Median (2)                                   : 37.3 
##   Lambda (1)                                   : 0.0186, 0.0297, 0.0426, 0.0578 
##   Lambda (2)                                   : 0.0186 
##   Hazard ratio                                 : 1.000, 1.598, 2.289, 3.106 
##   Iterations [1]                               : 1000, 1000, 1000, 1000 
##   Iterations [2]                               : 0, 0, 0, 0 
##   Iterations [3]                               : 0, 0, 0, 0 
##   Iterations [4]                               : 0, 0, 0, 0 
##   Analysis times [1]                           : 43.20, 35.15, 30.09, 26.16 
##   Analysis times [2]                           : NA, NA, NA, NA 
##   Analysis times [3]                           : NA, NA, NA, NA 
##   Analysis times [4]                           : NA, NA, NA, NA 
##   Expected study duration                      : 0.00, 2.54, 13.01, 20.56 
##   Number of events by stage [1]                : 50.0, 50.0, 50.0, 50.0 
##   Number of events by stage [2]                : NA, NA, NA, NA 
##   Number of events by stage [3]                : NA, NA, NA, NA 
##   Number of events by stage [4]                : NA, NA, NA, NA 
##   Expected number of events                    : 0.0, 3.5, 21.1, 38.9 
##   Events not achieved [1]                      : 0.000, 0.000, 0.000, 0.000 
##   Events not achieved [2]                      : 1.000, 0.929, 0.577, 0.222 
##   Events not achieved [3]                      : 0.000, 0.000, 0.000, 0.000 
##   Events not achieved [4]                      : 0.000, 0.000, 0.000, 0.000 
##   Number of subjects [1]                       : 100.0, 100.0, 100.0, 100.0 
##   Number of subjects [2]                       : NA, NA, NA, NA 
##   Number of subjects [3]                       : NA, NA, NA, NA 
##   Number of subjects [4]                       : NA, NA, NA, NA 
##   Expected number of subjects                  : 0.0, 7.1, 42.3, 77.8 
##   Reject per stage [1]                         : 0.000, 0.071, 0.423, 0.778 
##   Reject per stage [2]                         : 0.000, 0.000, 0.000, 0.000 
##   Reject per stage [3]                         : 0.000, 0.000, 0.000, 0.000 
##   Reject per stage [4]                         : 0.000, 0.000, 0.000, 0.000 
##   Overall reject                               : 0.000, 0.071, 0.423, 0.778 
##   Futility stop per stage [1]                  : 0, 0, 0, 0 
##   Futility stop per stage [2]                  : 0, 0, 0, 0 
##   Futility stop per stage [3]                  : 0, 0, 0, 0 
##   Futility stop                                : 0, 0, 0, 0 
##   Early stop                                   : 0.000, 0.071, 0.423, 0.778 
## 
## Simulated data:
##   Analysis times [1], pi1 = 0.2                : median [range]: 42.95 [30.162 - 62.511]; mean +/-sd: 43.205 +/-5.215 
##   Analysis times [1], pi1 = 0.3                : median [range]: 35.062 [22.928 - 53.555]; mean +/-sd: 35.146 +/-4.309 
##   Analysis times [1], pi1 = 0.4                : median [range]: 29.841 [21.077 - 47.083]; mean +/-sd: 30.089 +/-3.609 
##   Analysis times [1], pi1 = 0.5                : median [range]: 26.1 [18.164 - 38.468]; mean +/-sd: 26.164 +/-2.9 
##   Number of subjects [1], pi1 = 0.2            : median [range]: 100 [100 - 100]; mean +/-sd: 100 +/-0 
##   Number of subjects [1], pi1 = 0.3            : median [range]: 100 [100 - 100]; mean +/-sd: 100 +/-0 
##   Number of subjects [1], pi1 = 0.4            : median [range]: 100 [100 - 100]; mean +/-sd: 100 +/-0 
##   Number of subjects [1], pi1 = 0.5            : median [range]: 100 [100 - 100]; mean +/-sd: 100 +/-0 
##   Observed # events by stage (1) [1], pi1 = 0.2 : median [range]: 25 [17 - 33]; mean +/-sd: 25.086 +/-2.544 
##   Observed # events by stage (1) [1], pi1 = 0.3 : median [range]: 29 [22 - 37]; mean +/-sd: 29.02 +/-2.463 
##   Observed # events by stage (1) [1], pi1 = 0.4 : median [range]: 32 [23 - 39]; mean +/-sd: 32.011 +/-2.322 
##   Observed # events by stage (1) [1], pi1 = 0.5 : median [range]: 34 [26 - 42]; mean +/-sd: 34.271 +/-2.437 
##   Observed # events by stage (2) [1], pi1 = 0.2 : median [range]: 25 [17 - 33]; mean +/-sd: 24.914 +/-2.544 
##   Observed # events by stage (2) [1], pi1 = 0.3 : median [range]: 21 [13 - 28]; mean +/-sd: 20.98 +/-2.463 
##   Observed # events by stage (2) [1], pi1 = 0.4 : median [range]: 18 [11 - 27]; mean +/-sd: 17.989 +/-2.322 
##   Observed # events by stage (2) [1], pi1 = 0.5 : median [range]: 16 [8 - 24]; mean +/-sd: 15.729 +/-2.437 
##   Number of events by stage [1], pi1 = 0.2     : median [range]: 50 [50 - 50]; mean +/-sd: 50 +/-0 
##   Number of events by stage [1], pi1 = 0.3     : median [range]: 50 [50 - 50]; mean +/-sd: 50 +/-0 
##   Number of events by stage [1], pi1 = 0.4     : median [range]: 50 [50 - 50]; mean +/-sd: 50 +/-0 
##   Number of events by stage [1], pi1 = 0.5     : median [range]: 50 [50 - 50]; mean +/-sd: 50 +/-0 
##   Test statistic [1], pi1 = 0.2                : median [range]: 0.029 [-3.193 - 3.067]; mean +/-sd: 0.015 +/-1.008 
##   Test statistic [1], pi1 = 0.3                : median [range]: 1.667 [-1.216 - 5.076]; mean +/-sd: 1.632 +/-0.991 
##   Test statistic [1], pi1 = 0.4                : median [range]: 2.898 [-0.87 - 5.95]; mean +/-sd: 2.895 +/-0.96 
##   Test statistic [1], pi1 = 0.5                : median [range]: 3.854 [-0.076 - 6.646]; mean +/-sd: 3.838 +/-1.035 
##   Log-rank statistic [1], pi1 = 0.2            : median [range]: 0.029 [-3.193 - 3.067]; mean +/-sd: 0.015 +/-1.008 
##   Log-rank statistic [1], pi1 = 0.3            : median [range]: 1.667 [-1.216 - 5.076]; mean +/-sd: 1.632 +/-0.991 
##   Log-rank statistic [1], pi1 = 0.4            : median [range]: 2.898 [-0.87 - 5.95]; mean +/-sd: 2.895 +/-0.96 
##   Log-rank statistic [1], pi1 = 0.5            : median [range]: 3.854 [-0.076 - 6.646]; mean +/-sd: 3.838 +/-1.035 
##   Hazard ratio estimate LR [1], pi1 = 0.2      : median [range]: 1.008 [0.405 - 2.381]; mean +/-sd: 1.046 +/-0.3 
##   Hazard ratio estimate LR [1], pi1 = 0.3      : median [range]: 1.602 [0.709 - 4.203]; mean +/-sd: 1.65 +/-0.471 
##   Hazard ratio estimate LR [1], pi1 = 0.4      : median [range]: 2.27 [0.782 - 5.381]; mean +/-sd: 2.353 +/-0.654 
##   Hazard ratio estimate LR [1], pi1 = 0.5      : median [range]: 2.975 [0.979 - 6.552]; mean +/-sd: 3.089 +/-0.906 
## 
## Legend:
##   (i): values of treatment arm i
##   [k]: values at stage k
## 
## 
## Technical summary of the simulation results object of class "SimulationResultsSurvival":
##   [u] Maximum number of subjects               : 100.0 
##   [d] Accrual time                             : 12 
##   [g] Accrual intensity                        : 8.3 
##   [u] Planned events                           : 50, 100, 150, 200 
##   [d] pi (1)                                   : 0.200, 0.300, 0.400, 0.500 
##   [d] pi (2)                                   : 0.200 
##   [g] Median (1)                               : 37.3, 23.3, 16.3, 12.0 
##   [g] Median (2)                               : 37.3 
##   [d] Direction upper                          : TRUE 
##   [d] Drop-out rate (1)                        : 0.000 
##   [d] Drop-out rate (2)                        : 0.000 
##   [d] Drop-out time                            : 12 
##   [d] Event time                               : 12 
##   [d] Theta H0                                 : 1 
##   [d] Allocation 1                             : 1 
##   [d] Allocation 2                             : 1 
##   [.] Minimum number of events per stage       :  
##   [.] Maximum number of events per stage       :  
##   [d] Conditional power                        : NA 
##   [.] Assumed effect                           : NA 
##   [d] Maximum number of iterations             : 1000 
##   [d] Kappa                                    : 1 
##   [.] Piecewise survival times                 : NA 
##   [g] Lambda (1)                               : 0.0186, 0.0297, 0.0426, 0.0578 
##   [g] Lambda (2)                               : 0.0186 
##   [g] Hazard ratio                             : 1.000, 1.598, 2.289, 3.106 
##   [g] Iterations [1]                           : 1000, 1000, 1000, 1000 
##   [g] Iterations [2]                           : 0, 0, 0, 0 
##   [g] Iterations [3]                           : 0, 0, 0, 0 
##   [g] Iterations [4]                           : 0, 0, 0, 0 
##   [g] Analysis times [1]                       : 43.20, 35.15, 30.09, 26.16 
##   [g] Analysis times [2]                       : NA, NA, NA, NA 
##   [g] Analysis times [3]                       : NA, NA, NA, NA 
##   [g] Analysis times [4]                       : NA, NA, NA, NA 
##   [g] Expected study duration                  : 0.00, 2.54, 13.01, 20.56 
##   [g] Number of events by stage [1]            : 50.0, 50.0, 50.0, 50.0 
##   [g] Number of events by stage [2]            : NA, NA, NA, NA 
##   [g] Number of events by stage [3]            : NA, NA, NA, NA 
##   [g] Number of events by stage [4]            : NA, NA, NA, NA 
##   [g] Expected number of events                : 0.0, 3.5, 21.1, 38.9 
##   [g] Events not achieved [1]                  : 0.000, 0.000, 0.000, 0.000 
##   [g] Events not achieved [2]                  : 1.000, 0.929, 0.577, 0.222 
##   [g] Events not achieved [3]                  : 0.000, 0.000, 0.000, 0.000 
##   [g] Events not achieved [4]                  : 0.000, 0.000, 0.000, 0.000 
##   [g] Number of subjects [1]                   : 100.0, 100.0, 100.0, 100.0 
##   [g] Number of subjects [2]                   : NA, NA, NA, NA 
##   [g] Number of subjects [3]                   : NA, NA, NA, NA 
##   [g] Number of subjects [4]                   : NA, NA, NA, NA 
##   [g] Expected number of subjects              : 0.0, 7.1, 42.3, 77.8 
##   [g] Reject per stage [1]                     : 0.000, 0.071, 0.423, 0.778 
##   [g] Reject per stage [2]                     : 0.000, 0.000, 0.000, 0.000 
##   [g] Reject per stage [3]                     : 0.000, 0.000, 0.000, 0.000 
##   [g] Reject per stage [4]                     : 0.000, 0.000, 0.000, 0.000 
##   [g] Overall reject                           : 0.000, 0.071, 0.423, 0.778 
##   [g] Futility stop per stage [1]              : 0, 0, 0, 0 
##   [g] Futility stop per stage [2]              : 0, 0, 0, 0 
##   [g] Futility stop per stage [3]              : 0, 0, 0, 0 
##   [g] Futility stop                            : 0, 0, 0, 0 
##   [g] Early stop                               : 0.000, 0.071, 0.423, 0.778 
##   [d] Seed                                     : -125184577 
## 
## Legend:
##   u: user defined
##   >: derived value
##   d: default value
##   g: generated/calculated value
##   .: not applicable or hidden
## 
## Simulation of survival data (group sequential design) table:
##      Required planned events pi (1) Median (1)
## [1,]  50                     0.200  37.3      
## [2,] 100                     0.300  23.3      
## [3,] 150                     0.400  16.3      
## [4,] 200                     0.500  12.0      
##      Minimum # additional events per stage
## [1,]                                      
## [2,]                                      
## [3,]                                      
## [4,]                                      
##      Maximum # additional events per stage Lambda (1) Hazard ratio
## [1,]                                       0.0186     1.000       
## [2,]                                       0.0297     1.598       
## [3,]                                       0.0426     2.289       
## [4,]                                       0.0578     3.106       
##      Expected study duration Expected # events Expected # subjects
## [1,] 0.00                    0.0               0.0                
## [2,] 2.54                    3.5               7.1                
## [3,] 13.01                   21.1              42.3               
## [4,] 20.56                   38.9              77.8               
##      Overall reject Futility stop Early stop
## [1,] 0.000          0             0.000     
## [2,] 0.071          0             0.071     
## [3,] 0.423          0             0.423     
## [4,] 0.778          0             0.778
## This output summarizes the piecewise survival time specification.
## 
## Piecewise exponential survival times:
##    0 - < 6: 0.025
##    6 - < 9: 0.040
##    9 - <15: 0.015
##   15 - <21: 0.010
##       >=21: 0.007
## 
## Details:
## 
## User defined parameters:
##   Piecewise survival times                     : 0.00, 6.00, 9.00, 15.00, 21.00 
##   Lambda (2)                                   : 0.025, 0.040, 0.015, 0.010, 0.007 
##   Hazard ratio                                 : 0.800 
## 
## Default parameters:
##   Event time                                   : 12 
##   Kappa                                        : 1 
##   Delayed response allowed                     : FALSE 
## 
## Generated parameters:
##   Lambda (1)                                   : 0.0200, 0.0320, 0.0120, 0.0080, 0.0056 
##   Piecewise exponential survival enabled       : TRUE 
## 
## 
## Technical summary of the piecewise survival time object of class"PiecewiseSurvivalTime":
## 
##   [u] Piecewise survival times                 : 0.00, 6.00, 9.00, 15.00, 21.00 
##   [g] Lambda (1)                               : 0.0200, 0.0320, 0.0120, 0.0080, 0.0056 
##   [u] Lambda (2)                               : 0.025, 0.040, 0.015, 0.010, 0.007 
##   [u] Hazard ratio                             : 0.800 
##   [.] pi (1)                                   : NA 
##   [.] pi (2)                                   : NA 
##   [.] Median (1)                               : NA 
##   [.] Median (2)                               : NA 
##   [d] Event time                               : 12 
##   [d] Kappa                                    : 1 
##   [g] Piecewise exponential survival enabled   : TRUE 
##   [d] Delayed response allowed                 : FALSE 
##   [.] Delayed response enabled                 : FALSE 
## 
## Legend:
##   u: user defined
##   >: derived value
##   d: default value
##   g: generated/calculated value
##   .: not applicable or hidden
## 
## Piecewise survival time table:
##      Piecewise survival times Lambda (1) Lambda (2)
## [1,]  0                       0.0200     0.025     
## [2,]  6                       0.0320     0.040     
## [3,]  9                       0.0120     0.015     
## [4,] 15                       0.0080     0.010     
## [5,] 21                       0.0056     0.007
## This output summarizes the accrual time specification.
## 
## Accrual time and intensity:
##    0.00000 -  <12.00000: 15
##   12.00000 -  <13.00000: 21
##   13.00000 -  <14.00000: 27
##   14.00000 -  <15.00000: 33
##   15.00000 -  <16.00000: 39
##   16.00000 - <=40.44444: 45
## 
## Formula:
##   maxNumberOfSubjects = 1400 = 12 * 15 + 1 * 21 + 1 * 27 + 1 * 33 + 1 * 39 + 24.4444 * 45
## 
## Case (#5):
##   'maxNumberOfSubjects' and absolute accrual intensity are given, end of accrual* and 'followUpTime'** shall be calculated
##   Example: getAccrualTime(accrualTime = c(0, 6), accrualIntensity = c(22, 33), maxNumberOfSubjects = 1000)
## 
##   (*) Can be calculated directly.
##   (**) Cannot be calculated directly but with 'getSampleSizeSurvival' or 'getPowerSurvival'.
## 
## Details:
## 
## User defined parameters:
##   Accrual intensity                            : 15.0, 21.0, 27.0, 33.0, 39.0, 45.0 
##   Maximum number of subjects                   : 1400.0 
## 
## Default parameters: not available
## 
## Generated parameters:
##   End of accrual is user defined               : FALSE 
##   Follow-up time must be user defined          : FALSE 
##   Max number of subjects is user defined       : TRUE 
##   Max number of subjects can be calculated directly : TRUE 
##   Absolute accrual intensity is enabled        : TRUE 
##   Accrual time                                 : 0.00, 12.00, 13.00, 14.00, 15.00, 16.00, 40.44 
##   Remaining time                               : 24.44 
## 
## 
## Technical summary of the accrual time object of class"AccrualTime":
## 
##   [g] End of accrual is user defined           : FALSE 
##   [g] Follow-up time must be user defined      : FALSE 
##   [g] Max number of subjects is user defined   : TRUE 
##   [g] Max number of subjects can be calculated directly : TRUE 
##   [g] Absolute accrual intensity is enabled    : TRUE 
##   [g] Accrual time                             : 0.00, 12.00, 13.00, 14.00, 15.00, 16.00, 40.44 
##   [u] Accrual intensity                        : 15.0, 21.0, 27.0, 33.0, 39.0, 45.0 
##   [.] Accrual intensity (relative)             : NA 
##   [u] Maximum number of subjects               : 1400.0 
##   [g] Remaining time                           : 24.44 
##   [?] %piecewiseAccrualEnabled%                : TRUE 
## 
## Legend:
##   u: user defined
##   >: derived value
##   d: default value
##   g: generated/calculated value
##   .: not applicable or hidden
## 
## Accrual time table:
##      Accrual time Accrual intensity
## [1,]  0.00000     15.0             
## [2,] 12.00000     21.0             
## [3,] 13.00000     27.0             
## [4,] 14.00000     33.0             
## [5,] 15.00000     39.0             
## [6,] 16.00000     45.0             
## [7,] 40.44444

2.4 Coerce object to data.frame: as.data.frame

##   Type of design Maximum # stages Stage Information rate
## 1             WT                4     1             0.25
## 2           <NA>               NA     2             0.50
## 3           <NA>               NA     3             0.75
## 4           <NA>               NA     4             1.00
##   Significance level Type II error rate Two-sided power
## 1               0.05                0.2           FALSE
## 2                 NA                 NA              NA
## 3                 NA                 NA              NA
## 4                 NA                 NA              NA
##   Delta (Wang & Tsiatis) Futility bound (non-binding) Binding futility
## 1                    0.1                         -Inf            FALSE
## 2                     NA                         -Inf               NA
## 3                     NA                         -Inf               NA
## 4                     NA                           NA               NA
##   Parameter for alpha spending function
## 1                                     1
## 2                                    NA
## 3                                    NA
## 4                                    NA
##   Parameter for beta spending function
## 1                                    1
## 2                                   NA
## 3                                   NA
## 4                                   NA
##   Optimization criterion (Wang & Tsiatis) Test Tolerance
## 1                                   ASNH1    1     1e-08
## 2                                    <NA>   NA        NA
## 3                                    <NA>   NA        NA
## 4                                    <NA>   NA        NA
##   Cumulative alpha spending Type of beta spending Critical value
## 1               0.001073781                  none       3.069028
## 2               0.010526914                  <NA>       2.325888
## 3               0.028205994                  <NA>       1.977663
## 4               0.050000000                  <NA>       1.762694
##   Stage level
## 1 0.001073781
## 2 0.010012250
## 3 0.023983344
## 4 0.038976069
##   Inflation factor Stage Information      Power Rejection probability
## 1          1.04846     1    1.620541 0.03624538            0.03624538
## 2               NA     2    3.241081 0.30264612            0.26640074
## 3               NA     3    4.861622 0.60337036            0.30072424
## 4               NA     4    6.482163 0.80000000            0.19662964
##   Futility probability Ratio expected vs fixed sample size under H1
## 1         9.865876e-10                                    0.8014789
## 2         9.758407e-10                                           NA
## 3         9.359906e-10                                           NA
## 4                   NA                                           NA
##   Ratio expected vs fixed sample size under a value between H0 and H1
## 1                                                           0.9724133
## 2                                                                  NA
## 3                                                                  NA
## 4                                                                  NA
##   Ratio expected vs fixed sample size under H0
## 1                                     1.038026
## 2                                           NA
## 3                                           NA
## 4                                           NA
##   Stage Effect Average sample size (ASN) Power Overall Early stop
## 1     1      1                  25.66861     1                  1
## 2     2     NA                        NA    NA                 NA
## 3     3     NA                        NA    NA                 NA
## 4     4     NA                        NA    NA                 NA
##     Early stop Overall reject Reject per stage Overall futility
## 1 9.732567e-01              1     9.732567e-01     2.580925e-09
## 2 2.674225e-02             NA     2.674225e-02               NA
## 3 1.025014e-06             NA     1.024395e-06               NA
## 4           NA             NA     0.000000e+00               NA
##   Futility stop per stage
## 1            9.865876e-10
## 2            9.755040e-10
## 3            6.188329e-10
## 4                      NA
##    Design number Type of design Maximum # stages Stage Information rate
## 1              1             WT                4     1             0.25
## 2              1           <NA>               NA     2             0.50
## 3              1           <NA>               NA     3             0.75
## 4              1           <NA>               NA     4             1.00
## 5              2             WT                4     1             0.25
## 6              2           <NA>               NA     2             0.50
## 7              2           <NA>               NA     3             0.75
## 8              2           <NA>               NA     4             1.00
## 9              3             WT                4     1             0.25
## 10             3           <NA>               NA     2             0.50
## 11             3           <NA>               NA     3             0.75
## 12             3           <NA>               NA     4             1.00
##    Significance level Type II error rate Two-sided power
## 1                0.05                0.2           FALSE
## 2                  NA                 NA              NA
## 3                  NA                 NA              NA
## 4                  NA                 NA              NA
## 5                0.05                0.2           FALSE
## 6                  NA                 NA              NA
## 7                  NA                 NA              NA
## 8                  NA                 NA              NA
## 9                0.05                0.2           FALSE
## 10                 NA                 NA              NA
## 11                 NA                 NA              NA
## 12                 NA                 NA              NA
##    Delta (Wang & Tsiatis) Futility bound (non-binding) Binding futility
## 1                     0.1                         -Inf            FALSE
## 2                      NA                         -Inf               NA
## 3                      NA                         -Inf               NA
## 4                      NA                           NA               NA
## 5                     0.3                         -Inf            FALSE
## 6                      NA                         -Inf               NA
## 7                      NA                         -Inf               NA
## 8                      NA                           NA               NA
## 9                     0.4                         -Inf            FALSE
## 10                     NA                         -Inf               NA
## 11                     NA                         -Inf               NA
## 12                     NA                           NA               NA
##    Parameter for alpha spending function
## 1                                      1
## 2                                     NA
## 3                                     NA
## 4                                     NA
## 5                                      1
## 6                                     NA
## 7                                     NA
## 8                                     NA
## 9                                      1
## 10                                    NA
## 11                                    NA
## 12                                    NA
##    Parameter for beta spending function
## 1                                     1
## 2                                    NA
## 3                                    NA
## 4                                    NA
## 5                                     1
## 6                                    NA
## 7                                    NA
## 8                                    NA
## 9                                     1
## 10                                   NA
## 11                                   NA
## 12                                   NA
##    Optimization criterion (Wang & Tsiatis) Test Tolerance
## 1                                    ASNH1    1     1e-08
## 2                                     <NA>   NA        NA
## 3                                     <NA>   NA        NA
## 4                                     <NA>   NA        NA
## 5                                    ASNH1    1     1e-08
## 6                                     <NA>   NA        NA
## 7                                     <NA>   NA        NA
## 8                                     <NA>   NA        NA
## 9                                    ASNH1    1     1e-08
## 10                                    <NA>   NA        NA
## 11                                    <NA>   NA        NA
## 12                                    <NA>   NA        NA
##    Cumulative alpha spending Type of beta spending Critical value
## 1                0.001073781                  none       3.069028
## 2                0.010526914                  <NA>       2.325888
## 3                0.028205994                  <NA>       1.977663
## 4                0.050000000                  <NA>       1.762694
## 5                0.006915859                  none       2.461604
## 6                0.020169238                  <NA>       2.142951
## 7                0.035108439                  <NA>       1.976032
## 8                0.050000000                  <NA>       1.865547
## 9                0.012504953                  none       2.241250
## 10               0.026260600                  <NA>       2.091160
## 11               0.038792487                  <NA>       2.008067
## 12               0.050000000                  <NA>       1.951121
##    Stage level
## 1  0.001073781
## 2  0.010012250
## 3  0.023983344
## 4  0.038976069
## 5  0.006915859
## 6  0.016058517
## 7  0.024075572
## 8  0.031052371
## 9  0.012504953
## 10 0.018256866
## 11 0.022318106
## 12 0.025521316
##   Stage Treatment group Sample size Mean Standard deviation
## 1     1               1          22  1.0                1.0
## 2     1               2          22  1.4                1.0
## 3     2               1          11  1.1                2.0
## 4     2               2          13  1.5                2.0
## 5     3               1          22  1.0                2.0
## 6     3               2          22  3.0                2.0
## 7     4               1          11  1.0                1.3
## 8     4               2          13  2.5                1.3
##   Overall sample size Overall mean Overall standard deviation
## 1                  22     1.000000                   1.000000
## 2                  22     1.400000                   1.000000
## 3                  33     1.033333                   1.381500
## 4                  35     1.437143                   1.425418
## 5                  55     1.020000                   1.639151
## 6                  57     2.040351                   1.822857
## 7                  66     1.016667                   1.578664
## 8                  70     2.125714                   1.738706
##   Stage Overall test statistic Overall p-value Overall mean (1)
## 1     1              -1.326650       0.9041035         1.000000
## 2     2              -1.185099       0.8798860         1.033333
## 3     3              -3.111238       0.9988132         1.020000
## 4     4              -3.886959       0.9999205         1.016667
##   Overall mean (2) Overall standard deviation (1)
## 1         1.400000                       1.000000
## 2         1.437143                       1.381500
## 3         2.040351                       1.639151
## 4         2.125714                       1.578664
##   Overall standard deviation (2) Overall sample size (1)
## 1                       1.000000                      22
## 2                       1.425418                      33
## 3                       1.822857                      55
## 4                       1.738706                      66
##   Overall sample size (2) Test statistic   p-value Effect size Theta H0
## 1                      22      -1.326650 0.9041035  -0.4000000        0
## 2                      35      -0.488194 0.6848785  -0.4038095       NA
## 3                      57      -3.316625 0.9990567  -1.0203509       NA
## 4                      70      -2.816504 0.9949743  -1.1090476       NA
##   Direction Normal approximation Equal variance
## 1     upper                FALSE           TRUE
## 2      <NA>                   NA             NA
## 3      <NA>                   NA             NA
## 4      <NA>                   NA             NA
##   Stage Information rate Critical value Futility bound (non-binding)
## 1     1             0.25       3.069028                         -Inf
## 2     2             0.50       2.325888                         -Inf
## 3     3             0.75       1.977663                         -Inf
## 4     4             1.00       1.762694                           NA
##   Cumulative alpha spending Stage level Effect size Test statistic
## 1               0.001073781 0.001073781  -0.4000000      -1.326650
## 2               0.010526914 0.010012250  -0.4038095      -0.488194
## 3               0.028205994 0.023983344  -1.0203509      -3.316625
## 4               0.050000000 0.038976069  -1.1090476      -2.816504
##     p-value Overall test statistic Overall p-value   Action          CRP
## 1 0.9041035              -1.326650       0.9041035 continue 2.810091e-03
## 2 0.6848785              -1.185099       0.8798860 continue 1.226756e-04
## 3 0.9990567              -3.111238       0.9988132 continue 6.661338e-16
## 4 0.9949743              -3.886959       0.9999205   accept           NA
##   Assumed standard deviation RCI (lower) RCI (upper) Repeated p-value
## 1                   1.662998   -1.386144   0.5861439         0.499999
## 2                         NA   -1.216028   0.4084087         0.499999
## 3                         NA   -1.676258  -0.3644440         0.499999
## 4                         NA   -1.615872  -0.6022231         0.499999
##   Final p-value Final CI (lower) Final CI (upper) Median unbiased estimate
## 1            NA               NA               NA                       NA
## 2            NA               NA               NA                       NA
## 3            NA               NA               NA                       NA
## 4     0.9999205        -1.546886        -0.608249                -1.077568
##   Normal approximation Mean ratio Theta H0 Alternative Standard deviation
## 1                FALSE      FALSE        0         0.2                  1
## 2                   NA         NA       NA         0.4                 NA
## 3                   NA         NA       NA         0.6                 NA
## 4                   NA         NA       NA         0.8                 NA
## 5                   NA         NA       NA         1.0                 NA
##   Treatment group Planned allocation ratio # subjects fixed
## 1               2                        1        619.61294
## 2              NA                       NA        155.93452
## 3              NA                       NA         70.08807
## 4              NA                       NA         40.06552
## 5              NA                       NA         26.19553
##   # subjects fixed (1) # subjects fixed (2) Information rate
## 1            309.80647            309.80647             0.25
## 2             77.96726             77.96726             0.50
## 3             35.04403             35.04403             0.75
## 4             20.03276             20.03276             1.00
## 5             13.09776             13.09776               NA
##   Max # subjects Max # subjects (1) Max # subjects (2)
## 1      649.63926          324.81963          324.81963
## 2      163.49107           81.74554           81.74554
## 3       73.48452           36.74226           36.74226
## 4       42.00708           21.00354           21.00354
## 5       27.46496           13.73248           13.73248
##   Expected # subjects under H0 Expected # subjects under H0/H1
## 1                    643.17426                       602.51988
## 2                    161.86406                       151.63280
## 3                     72.75323                        68.15457
## 4                     41.58904                        38.96024
## 5                     27.19163                        25.47288
##   Expected # subjects under H1 Reject per stage Early stop
## 1                    496.60668       0.03624538  0.6033704
## 2                    124.97822       0.26640074         NA
## 3                     56.17411       0.30072424         NA
## 4                     32.11166       0.19662964         NA
## 5                     20.99516               NA         NA
##   Local one-sided significance level
## 1                        0.001073781
## 2                        0.010012250
## 3                        0.023983344
## 4                        0.038976069
## 5                                 NA
##   Max # subjects Accrual time Accrual intensity Required planned events
## 1            100           12          8.333333                      50
## 2             NA           NA                NA                     100
## 3             NA           NA                NA                     150
## 4             NA           NA                NA                     200
##   pi (1) pi (2) Median (1) Median (2) Direction upper Drop-out rate (1)
## 1    0.2    0.2   37.27540    37.2754            TRUE                 0
## 2    0.3     NA   23.32030         NA              NA                NA
## 3    0.4     NA   16.28299         NA              NA                NA
## 4    0.5     NA   12.00000         NA              NA                NA
##   Drop-out rate (2) Drop-out time Event time Theta H0 Allocation 1
## 1                 0            12         12        1            1
## 2                NA            NA         NA       NA           NA
## 3                NA            NA         NA       NA           NA
## 4                NA            NA         NA       NA           NA
##   Allocation 2 Maximum # iterations Kappa Lambda (1) Lambda (2)
## 1            1                 1000     1 0.01859530  0.0185953
## 2           NA                   NA    NA 0.02972291         NA
## 3           NA                   NA    NA 0.04256880         NA
## 4           NA                   NA    NA 0.05776227         NA
##   Hazard ratio Expected study duration Expected # events
## 1     1.000000                0.000000              0.00
## 2     1.598410                2.542747              3.55
## 3     2.289224               13.007195             21.15
## 4     3.106284               20.559835             38.90
##   Expected # subjects Overall reject Futility stop Early stop       Seed
## 1                 0.0          0.000             0      0.000 -125184577
## 2                 7.1          0.071             0      0.071         NA
## 3                42.3          0.423             0      0.423         NA
## 4                77.8          0.778             0      0.778         NA
##   Piecewise survival times Lambda (1) Lambda (2) Hazard ratio Event time
## 1                        0     0.0200      0.025          0.8         12
## 2                        6     0.0320      0.040           NA         NA
## 3                        9     0.0120      0.015           NA         NA
## 4                       15     0.0080      0.010           NA         NA
## 5                       21     0.0056      0.007           NA         NA
##   Kappa Piecewise exponential survival enabled Delayed response allowed
## 1     1                                   TRUE                    FALSE
## 2    NA                                     NA                       NA
## 3    NA                                     NA                       NA
## 4    NA                                     NA                       NA
## 5    NA                                     NA                       NA
##   Delayed response enabled
## 1                    FALSE
## 2                       NA
## 3                       NA
## 4                       NA
## 5                       NA
##   End of accrual is user defined Follow-up time must be user defined
## 1                          FALSE                               FALSE
## 2                             NA                                  NA
## 3                             NA                                  NA
## 4                             NA                                  NA
## 5                             NA                                  NA
## 6                             NA                                  NA
## 7                             NA                                  NA
##   Max number of subjects is user defined
## 1                                   TRUE
## 2                                     NA
## 3                                     NA
## 4                                     NA
## 5                                     NA
## 6                                     NA
## 7                                     NA
##   Max number of subjects can be calculated directly
## 1                                              TRUE
## 2                                                NA
## 3                                                NA
## 4                                                NA
## 5                                                NA
## 6                                                NA
## 7                                                NA
##   Absolute accrual intensity is enabled Accrual time Accrual intensity
## 1                                  TRUE      0.00000                15
## 2                                    NA     12.00000                21
## 3                                    NA     13.00000                27
## 4                                    NA     14.00000                33
## 5                                    NA     15.00000                39
## 6                                    NA     16.00000                45
## 7                                    NA     40.44444                NA
##   Max # subjects Remaining time piecewiseAccrualEnabled
## 1           1400       24.44444                    TRUE
## 2             NA             NA                      NA
## 3             NA             NA                      NA
## 4             NA             NA                      NA
## 5             NA             NA                      NA
## 6             NA             NA                      NA
## 7             NA             NA                      NA

2.5 Coerce object to matrix: as.matrix

##           Type of design Maximum # stages Stage Information rate
##   Stage 1 "WT"           " 4"             "1"   "0.25"          
##   Stage 2 NA             NA               "2"   "0.50"          
##   Stage 3 NA             NA               "3"   "0.75"          
##   Stage 4 NA             NA               "4"   "1.00"          
##           Significance level Type II error rate Two-sided power
##   Stage 1 "0.05"             "0.2"              "FALSE"        
##   Stage 2 NA                 NA                 NA             
##   Stage 3 NA                 NA                 NA             
##   Stage 4 NA                 NA                 NA             
##           Delta (Wang & Tsiatis) Futility bound (non-binding)
##   Stage 1 "0.1"                  "-Inf"                      
##   Stage 2 NA                     "-Inf"                      
##   Stage 3 NA                     "-Inf"                      
##   Stage 4 NA                     NA                          
##           Binding futility Parameter for alpha spending function
##   Stage 1 "FALSE"          " 1"                                 
##   Stage 2 NA               NA                                   
##   Stage 3 NA               NA                                   
##   Stage 4 NA               NA                                   
##           Parameter for beta spending function
##   Stage 1 " 1"                                
##   Stage 2 NA                                  
##   Stage 3 NA                                  
##   Stage 4 NA                                  
##           Optimization criterion (Wang & Tsiatis) Test Tolerance
##   Stage 1 "ASNH1"                                 " 1" "1e-08"  
##   Stage 2 NA                                      NA   NA       
##   Stage 3 NA                                      NA   NA       
##   Stage 4 NA                                      NA   NA       
##           Cumulative alpha spending Type of beta spending Critical value
##   Stage 1 "0.001073781"             "none"                "3.069028"    
##   Stage 2 "0.010526914"             NA                    "2.325888"    
##   Stage 3 "0.028205994"             NA                    "1.977663"    
##   Stage 4 "0.050000000"             NA                    "1.762694"    
##           Stage level  
##   Stage 1 "0.001073781"
##   Stage 2 "0.010012250"
##   Stage 3 "0.023983344"
##   Stage 4 "0.038976069"
##           Inflation factor Stage Information      Power
##   Stage 1          1.04846     1    1.620541 0.03624538
##   Stage 2               NA     2    3.241081 0.30264612
##   Stage 3               NA     3    4.861622 0.60337036
##   Stage 4               NA     4    6.482163 0.80000000
##           Rejection probability Futility probability
##   Stage 1            0.03624538         9.865876e-10
##   Stage 2            0.26640074         9.758407e-10
##   Stage 3            0.30072424         9.359906e-10
##   Stage 4            0.19662964                   NA
##           Ratio expected vs fixed sample size under H1
##   Stage 1                                    0.8014789
##   Stage 2                                           NA
##   Stage 3                                           NA
##   Stage 4                                           NA
##           Ratio expected vs fixed sample size under a value between H0 and H1
##   Stage 1                                                           0.9724133
##   Stage 2                                                                  NA
##   Stage 3                                                                  NA
##   Stage 4                                                                  NA
##           Ratio expected vs fixed sample size under H0
##   Stage 1                                     1.038026
##   Stage 2                                           NA
##   Stage 3                                           NA
##   Stage 4                                           NA
##           Stage Effect Average sample size (ASN) Power Overall Early stop
##   Stage 1     1      1                  25.66861     1                  1
##   Stage 2     2     NA                        NA    NA                 NA
##   Stage 3     3     NA                        NA    NA                 NA
##   Stage 4     4     NA                        NA    NA                 NA
##             Early stop Overall reject Reject per stage Overall futility
##   Stage 1 9.732567e-01              1     9.732567e-01     2.580925e-09
##   Stage 2 2.674225e-02             NA     2.674225e-02               NA
##   Stage 3 1.025014e-06             NA     1.024395e-06               NA
##   Stage 4           NA             NA     0.000000e+00               NA
##           Futility stop per stage
##   Stage 1            9.865876e-10
##   Stage 2            9.755040e-10
##   Stage 3            6.188329e-10
##   Stage 4                      NA
##       Design number Type of design Maximum # stages Stage Information rate
##  [1,] "1"           "WT"           " 4"             "1"   "0.25"          
##  [2,] "1"           NA             NA               "2"   "0.50"          
##  [3,] "1"           NA             NA               "3"   "0.75"          
##  [4,] "1"           NA             NA               "4"   "1.00"          
##  [5,] "2"           "WT"           " 4"             "1"   "0.25"          
##  [6,] "2"           NA             NA               "2"   "0.50"          
##  [7,] "2"           NA             NA               "3"   "0.75"          
##  [8,] "2"           NA             NA               "4"   "1.00"          
##  [9,] "3"           "WT"           " 4"             "1"   "0.25"          
## [10,] "3"           NA             NA               "2"   "0.50"          
## [11,] "3"           NA             NA               "3"   "0.75"          
## [12,] "3"           NA             NA               "4"   "1.00"          
##       Significance level Type II error rate Two-sided power
##  [1,] "0.05"             "0.2"              "FALSE"        
##  [2,] NA                 NA                 NA             
##  [3,] NA                 NA                 NA             
##  [4,] NA                 NA                 NA             
##  [5,] "0.05"             "0.2"              "FALSE"        
##  [6,] NA                 NA                 NA             
##  [7,] NA                 NA                 NA             
##  [8,] NA                 NA                 NA             
##  [9,] "0.05"             "0.2"              "FALSE"        
## [10,] NA                 NA                 NA             
## [11,] NA                 NA                 NA             
## [12,] NA                 NA                 NA             
##       Delta (Wang & Tsiatis) Futility bound (non-binding) Binding futility
##  [1,] "0.1"                  "-Inf"                       "FALSE"         
##  [2,] NA                     "-Inf"                       NA              
##  [3,] NA                     "-Inf"                       NA              
##  [4,] NA                     NA                           NA              
##  [5,] "0.3"                  "-Inf"                       "FALSE"         
##  [6,] NA                     "-Inf"                       NA              
##  [7,] NA                     "-Inf"                       NA              
##  [8,] NA                     NA                           NA              
##  [9,] "0.4"                  "-Inf"                       "FALSE"         
## [10,] NA                     "-Inf"                       NA              
## [11,] NA                     "-Inf"                       NA              
## [12,] NA                     NA                           NA              
##       Parameter for alpha spending function
##  [1,] " 1"                                 
##  [2,] NA                                   
##  [3,] NA                                   
##  [4,] NA                                   
##  [5,] " 1"                                 
##  [6,] NA                                   
##  [7,] NA                                   
##  [8,] NA                                   
##  [9,] " 1"                                 
## [10,] NA                                   
## [11,] NA                                   
## [12,] NA                                   
##       Parameter for beta spending function
##  [1,] " 1"                                
##  [2,] NA                                  
##  [3,] NA                                  
##  [4,] NA                                  
##  [5,] " 1"                                
##  [6,] NA                                  
##  [7,] NA                                  
##  [8,] NA                                  
##  [9,] " 1"                                
## [10,] NA                                  
## [11,] NA                                  
## [12,] NA                                  
##       Optimization criterion (Wang & Tsiatis) Test Tolerance
##  [1,] "ASNH1"                                 " 1" "1e-08"  
##  [2,] NA                                      NA   NA       
##  [3,] NA                                      NA   NA       
##  [4,] NA                                      NA   NA       
##  [5,] "ASNH1"                                 " 1" "1e-08"  
##  [6,] NA                                      NA   NA       
##  [7,] NA                                      NA   NA       
##  [8,] NA                                      NA   NA       
##  [9,] "ASNH1"                                 " 1" "1e-08"  
## [10,] NA                                      NA   NA       
## [11,] NA                                      NA   NA       
## [12,] NA                                      NA   NA       
##       Cumulative alpha spending Type of beta spending Critical value
##  [1,] "0.001073781"             "none"                "3.069028"    
##  [2,] "0.010526914"             NA                    "2.325888"    
##  [3,] "0.028205994"             NA                    "1.977663"    
##  [4,] "0.050000000"             NA                    "1.762694"    
##  [5,] "0.006915859"             "none"                "2.461604"    
##  [6,] "0.020169238"             NA                    "2.142951"    
##  [7,] "0.035108439"             NA                    "1.976032"    
##  [8,] "0.050000000"             NA                    "1.865547"    
##  [9,] "0.012504953"             "none"                "2.241250"    
## [10,] "0.026260600"             NA                    "2.091160"    
## [11,] "0.038792487"             NA                    "2.008067"    
## [12,] "0.050000000"             NA                    "1.951121"    
##       Stage level  
##  [1,] "0.001073781"
##  [2,] "0.010012250"
##  [3,] "0.023983344"
##  [4,] "0.038976069"
##  [5,] "0.006915859"
##  [6,] "0.016058517"
##  [7,] "0.024075572"
##  [8,] "0.031052371"
##  [9,] "0.012504953"
## [10,] "0.018256866"
## [11,] "0.022318106"
## [12,] "0.025521316"
##           Stage Treatment group Sample size Mean Standard deviation
##   Stage 1     1               1          22  1.0                1.0
##   Stage 2     1               2          22  1.4                1.0
##   Stage 3     2               1          11  1.1                2.0
##   Stage 4     2               2          13  1.5                2.0
##   Stage 5     3               1          22  1.0                2.0
##   Stage 6     3               2          22  3.0                2.0
##   Stage 7     4               1          11  1.0                1.3
##   Stage 8     4               2          13  2.5                1.3
##           Overall sample size Overall mean Overall standard deviation
##   Stage 1                  22     1.000000                   1.000000
##   Stage 2                  22     1.400000                   1.000000
##   Stage 3                  33     1.033333                   1.381500
##   Stage 4                  35     1.437143                   1.425418
##   Stage 5                  55     1.020000                   1.639151
##   Stage 6                  57     2.040351                   1.822857
##   Stage 7                  66     1.016667                   1.578664
##   Stage 8                  70     2.125714                   1.738706
##           Stage Overall test statistic Overall p-value Overall mean (1)
##   Stage 1 "1"   "-1.326650"            "0.9041035"     "1.000000"      
##   Stage 2 "2"   "-1.185099"            "0.8798860"     "1.033333"      
##   Stage 3 "3"   "-3.111238"            "0.9988132"     "1.020000"      
##   Stage 4 "4"   "-3.886959"            "0.9999205"     "1.016667"      
##           Overall mean (2) Overall standard deviation (1)
##   Stage 1 "1.400000"       "1.000000"                    
##   Stage 2 "1.437143"       "1.381500"                    
##   Stage 3 "2.040351"       "1.639151"                    
##   Stage 4 "2.125714"       "1.578664"                    
##           Overall standard deviation (2) Overall sample size (1)
##   Stage 1 "1.000000"                     "22"                   
##   Stage 2 "1.425418"                     "33"                   
##   Stage 3 "1.822857"                     "55"                   
##   Stage 4 "1.738706"                     "66"                   
##           Overall sample size (2) Test statistic p-value     Effect size 
##   Stage 1 "22"                    "-1.326650"    "0.9041035" "-0.4000000"
##   Stage 2 "35"                    "-0.488194"    "0.6848785" "-0.4038095"
##   Stage 3 "57"                    "-3.316625"    "0.9990567" "-1.0203509"
##   Stage 4 "70"                    "-2.816504"    "0.9949743" "-1.1090476"
##           Theta H0 Direction Normal approximation Equal variance
##   Stage 1 " 0"     "upper"   "FALSE"              "TRUE"        
##   Stage 2 NA       NA        NA                   NA            
##   Stage 3 NA       NA        NA                   NA            
##   Stage 4 NA       NA        NA                   NA
##           Stage Information rate Critical value
##   Stage 1 "1"   "0.25"           "3.069028"    
##   Stage 2 "2"   "0.50"           "2.325888"    
##   Stage 3 "3"   "0.75"           "1.977663"    
##   Stage 4 "4"   "1.00"           "1.762694"    
##           Futility bound (non-binding) Cumulative alpha spending
##   Stage 1 "-Inf"                       "0.001073781"            
##   Stage 2 "-Inf"                       "0.010526914"            
##   Stage 3 "-Inf"                       "0.028205994"            
##   Stage 4 NA                           "0.050000000"            
##           Stage level   Effect size  Test statistic p-value    
##   Stage 1 "0.001073781" "-0.4000000" "-1.326650"    "0.9041035"
##   Stage 2 "0.010012250" "-0.4038095" "-0.488194"    "0.6848785"
##   Stage 3 "0.023983344" "-1.0203509" "-3.316625"    "0.9990567"
##   Stage 4 "0.038976069" "-1.1090476" "-2.816504"    "0.9949743"
##           Overall test statistic Overall p-value Action     CRP           
##   Stage 1 "-1.326650"            "0.9041035"     "continue" "2.810091e-03"
##   Stage 2 "-1.185099"            "0.8798860"     "continue" "1.226756e-04"
##   Stage 3 "-3.111238"            "0.9988132"     "continue" "6.661338e-16"
##   Stage 4 "-3.886959"            "0.9999205"     "accept"   NA            
##           Assumed standard deviation RCI (lower) RCI (upper) 
##   Stage 1 "1.662998"                 "-1.386144" " 0.5861439"
##   Stage 2 NA                         "-1.216028" " 0.4084087"
##   Stage 3 NA                         "-1.676258" "-0.3644440"
##   Stage 4 NA                         "-1.615872" "-0.6022231"
##           Repeated p-value Final p-value Final CI (lower) Final CI (upper)
##   Stage 1 "0.499999"       NA            NA               NA              
##   Stage 2 "0.499999"       NA            NA               NA              
##   Stage 3 "0.499999"       NA            NA               NA              
##   Stage 4 "0.499999"       "0.9999205"   "-1.546886"      "-0.608249"     
##           Median unbiased estimate
##   Stage 1 NA                      
##   Stage 2 NA                      
##   Stage 3 NA                      
##   Stage 4 "-1.077568"
##      Normal approximation Mean ratio Theta H0 Alternative
##    1                    0          0        0         0.2
##    2                   NA         NA       NA         0.4
##    3                   NA         NA       NA         0.6
##    4                   NA         NA       NA         0.8
##    5                   NA         NA       NA         1.0
##      Standard deviation Treatment group Planned allocation ratio
##    1                  1               2                        1
##    2                 NA              NA                       NA
##    3                 NA              NA                       NA
##    4                 NA              NA                       NA
##    5                 NA              NA                       NA
##      # subjects fixed # subjects fixed (1) # subjects fixed (2)
##    1        619.61294            309.80647            309.80647
##    2        155.93452             77.96726             77.96726
##    3         70.08807             35.04403             35.04403
##    4         40.06552             20.03276             20.03276
##    5         26.19553             13.09776             13.09776
##      Information rate Max # subjects Max # subjects (1) Max # subjects (2)
##    1             0.25      649.63926          324.81963          324.81963
##    2             0.50      163.49107           81.74554           81.74554
##    3             0.75       73.48452           36.74226           36.74226
##    4             1.00       42.00708           21.00354           21.00354
##    5               NA       27.46496           13.73248           13.73248
##      Expected # subjects under H0 Expected # subjects under H0/H1
##    1                    643.17426                       602.51988
##    2                    161.86406                       151.63280
##    3                     72.75323                        68.15457
##    4                     41.58904                        38.96024
##    5                     27.19163                        25.47288
##      Expected # subjects under H1 Reject per stage Early stop
##    1                    496.60668       0.03624538  0.6033704
##    2                    124.97822       0.26640074         NA
##    3                     56.17411       0.30072424         NA
##    4                     32.11166       0.19662964         NA
##    5                     20.99516               NA         NA
##      Local one-sided significance level
##    1                        0.001073781
##    2                        0.010012250
##    3                        0.023983344
##    4                        0.038976069
##    5                                 NA
##      Max # subjects Accrual time Accrual intensity Required planned events
## [1,]            100           12          8.333333                      50
## [2,]             NA           NA                NA                     100
## [3,]             NA           NA                NA                     150
## [4,]             NA           NA                NA                     200
##      pi (1) pi (2) Median (1) Median (2) Direction upper Drop-out rate (1)
## [1,]    0.2    0.2   37.27540    37.2754               1                 0
## [2,]    0.3     NA   23.32030         NA              NA                NA
## [3,]    0.4     NA   16.28299         NA              NA                NA
## [4,]    0.5     NA   12.00000         NA              NA                NA
##      Drop-out rate (2) Drop-out time Event time Theta H0 Allocation 1
## [1,]                 0            12         12        1            1
## [2,]                NA            NA         NA       NA           NA
## [3,]                NA            NA         NA       NA           NA
## [4,]                NA            NA         NA       NA           NA
##      Allocation 2 Maximum # iterations Kappa Lambda (1) Lambda (2)
## [1,]            1                 1000     1 0.01859530  0.0185953
## [2,]           NA                   NA    NA 0.02972291         NA
## [3,]           NA                   NA    NA 0.04256880         NA
## [4,]           NA                   NA    NA 0.05776227         NA
##      Hazard ratio Expected study duration Expected # events
## [1,]     1.000000                0.000000              0.00
## [2,]     1.598410                2.542747              3.55
## [3,]     2.289224               13.007195             21.15
## [4,]     3.106284               20.559835             38.90
##      Expected # subjects Overall reject Futility stop Early stop
## [1,]                 0.0          0.000             0      0.000
## [2,]                 7.1          0.071             0      0.071
## [3,]                42.3          0.423             0      0.423
## [4,]                77.8          0.778             0      0.778
##            Seed
## [1,] -125184577
## [2,]         NA
## [3,]         NA
## [4,]         NA
##      Piecewise survival times Lambda (1) Lambda (2) Hazard ratio
## [1,]                        0     0.0200      0.025          0.8
## [2,]                        6     0.0320      0.040           NA
## [3,]                        9     0.0120      0.015           NA
## [4,]                       15     0.0080      0.010           NA
## [5,]                       21     0.0056      0.007           NA
##      Event time Kappa Piecewise exponential survival enabled
## [1,]         12     1                                      1
## [2,]         NA    NA                                     NA
## [3,]         NA    NA                                     NA
## [4,]         NA    NA                                     NA
## [5,]         NA    NA                                     NA
##      Delayed response allowed Delayed response enabled
## [1,]                        0                        0
## [2,]                       NA                       NA
## [3,]                       NA                       NA
## [4,]                       NA                       NA
## [5,]                       NA                       NA
##      End of accrual is user defined Follow-up time must be user defined
## [1,]                              0                                   0
## [2,]                             NA                                  NA
## [3,]                             NA                                  NA
## [4,]                             NA                                  NA
## [5,]                             NA                                  NA
## [6,]                             NA                                  NA
## [7,]                             NA                                  NA
##      Max number of subjects is user defined
## [1,]                                      1
## [2,]                                     NA
## [3,]                                     NA
## [4,]                                     NA
## [5,]                                     NA
## [6,]                                     NA
## [7,]                                     NA
##      Max number of subjects can be calculated directly
## [1,]                                                 1
## [2,]                                                NA
## [3,]                                                NA
## [4,]                                                NA
## [5,]                                                NA
## [6,]                                                NA
## [7,]                                                NA
##      Absolute accrual intensity is enabled Accrual time Accrual intensity
## [1,]                                     1      0.00000                15
## [2,]                                    NA     12.00000                21
## [3,]                                    NA     13.00000                27
## [4,]                                    NA     14.00000                33
## [5,]                                    NA     15.00000                39
## [6,]                                    NA     16.00000                45
## [7,]                                    NA     40.44444                NA
##      Max # subjects Remaining time piecewiseAccrualEnabled
## [1,]           1400       24.44444                       1
## [2,]             NA             NA                      NA
## [3,]             NA             NA                      NA
## [4,]             NA             NA                      NA
## [5,]             NA             NA                      NA
## [6,]             NA             NA                      NA
## [7,]             NA             NA                      NA

System: rpact 2.0.1.9003, R version 3.5.3 (2019-03-11), platform: x86_64-w64-mingw32

To cite package ‘rpact’ in publications use:

Gernot Wassmer and Friedrich Pahlke (2019). rpact: Confirmatory Adaptive Clinical Trial Design and Analysis. R package version 2.0.1.9003. https://www.rpact.org

 

Creative Commons License
This work by Gernot Wassmer and Friedrich Pahlke is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.