How to use R Generics with rpact

Utilities

This document provides examples that illustrate the usage of R generic functions (short: R generics) with rpact, e.g., as.data.frame or summary.

Author

Friedrich Pahlke and Gernot Wassmer

Published

July 6, 2023

Creating examples of selected rpact result objects

First, load the rpact package

library(rpact)
packageVersion("rpact") # version should be version 3.0 or later

[1] '3.4.0'

In the following we define different (typical) examples of rpact applications. The results are rpact objects which refer to examples for design specifications, power and sample size calculations, simulation results and the results of a data analysis with defined design and datasets.

designGroupSequential <- getDesignGroupSequential(
    alpha = 0.05, kMax = 4,
    sided = 1, typeOfDesign = "WT", deltaWT = 0.1
)

designFisher <- getDesignFisher(
    kMax = 4, alpha = 0.025,
    informationRates = c(0.2, 0.5, 0.8, 1), alpha0Vec = rep(0.4, 3)
)

designCharacteristics <- getDesignCharacteristics(designGroupSequential)

powerAndASN <- getPowerAndAverageSampleNumber(designGroupSequential, theta = 0.5, nMax = 40)

sampleSizeResults <- getSampleSizeMeans(designGroupSequential)

powerResults <- getPowerMeans(designGroupSequential, maxNumberOfSubjects = 100)

designSet <- getDesignSet(design = designGroupSequential, deltaWT = c(0.3, 0.4))

dataset <- getDataset(
    n1 = c(22, 11, 22, 11),
    n2 = c(22, 13, 22, 13),
    means1 = c(1, 1.1, 1, 1),
    means2 = c(1.4, 1.5, 3, 2.5),
    stDevs1 = c(1, 2, 2, 1.3),
    stDevs2 = c(1, 2, 2, 1.3)
)

analysisResults <- getAnalysisResults(designGroupSequential, dataset)

How to use R generic functions with rpact objects

This section describes how the defined objects can be used and displayed. It is important to understand this is the way how typically R objects can be handled with. Particularly, we tried to make the summary() output (except for the technical developer summaries) “ready to use”, e.g., for a design report.

Get field names of the object

names(designGroupSequential)

 [1] "kMax"                   "alpha"                  "stages"                
 [4] "informationRates"       "userAlphaSpending"      "criticalValues"        
 [7] "stageLevels"            "alphaSpent"             "bindingFutility"       
[10] "tolerance"              "typeOfDesign"           "beta"                  
[13] "deltaWT"                "deltaPT1"               "deltaPT0"              
[16] "futilityBounds"         "gammaA"                 "gammaB"                
[19] "optimizationCriterion"  "sided"                  "betaSpent"             
[22] "typeBetaSpending"       "userBetaSpending"       "power"                 
[25] "twoSidedPower"          "constantBoundsHP"       "betaAdjustment"        
[28] "delayedInformation"     "decisionCriticalValues" "reversalProbabilities"

Access data of a field

designGroupSequential$criticalValues

[1] 3.069028 2.325888 1.977663 1.762694

designGroupSequential[["criticalValues"]]

[1] 3.069028 2.325888 1.977663 1.762694

Print object

print(designGroupSequential)

Design parameters and output of group sequential design:

User defined parameters:
  Type of design                               : Wang & Tsiatis Delta class 
  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                           : 0.2000 
  Two-sided power                              : FALSE 
  Test                                         : one-sided 
  Tolerance                                    : 0.00000001 

Output:
  Cumulative alpha spending                    : 0.001074, 0.010527, 0.028206, 0.050000 
  Critical values                              : 3.069, 2.326, 1.978, 1.763 
  Stage levels (one-sided)                     : 0.001074, 0.010012, 0.023983, 0.038976

print(designSet)

Trial design set with 3 designs

Design parameters and output of group sequential design:

User defined parameters:
  Type of design                               : Wang & Tsiatis Delta class 
  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                           : 0.2000 
  Two-sided power                              : FALSE 
  Test                                         : one-sided 
  Tolerance                                    : 0.00000001 

Output:
  Cumulative alpha spending                    : 0.001074, 0.010527, 0.028206, 0.050000 
  Critical values                              : 3.069, 2.326, 1.978, 1.763 
  Stage levels (one-sided)                     : 0.001074, 0.010012, 0.023983, 0.038976 

Design parameters and output of group sequential design:

User defined parameters:
  Type of design                               : Wang & Tsiatis Delta class 
  Significance level                           : 0.0500 
  Delta for Wang & Tsiatis Delta class         : 0.3 

Derived from user defined parameters:
  Maximum number of stages                     : 4 
  Stages                                       : 1, 2, 3, 4 

Default parameters:
  Information rates                            : 0.250, 0.500, 0.750, 1.000 
  Type II error rate                           : 0.2000 
  Two-sided power                              : FALSE 
  Test                                         : one-sided 
  Tolerance                                    : 0.00000001 

Output:
  Cumulative alpha spending                    : 0.006916, 0.020169, 0.035108, 0.050000 
  Critical values                              : 2.462, 2.143, 1.976, 1.866 
  Stage levels (one-sided)                     : 0.006916, 0.016059, 0.024076, 0.031052 

Design parameters and output of group sequential design:

User defined parameters:
  Type of design                               : Wang & Tsiatis Delta class 
  Significance level                           : 0.0500 
  Delta for Wang & Tsiatis Delta class         : 0.4 

Derived from user defined parameters:
  Maximum number of stages                     : 4 
  Stages                                       : 1, 2, 3, 4 

Default parameters:
  Information rates                            : 0.250, 0.500, 0.750, 1.000 
  Type II error rate                           : 0.2000 
  Two-sided power                              : FALSE 
  Test                                         : one-sided 
  Tolerance                                    : 0.00000001 

Output:
  Cumulative alpha spending                    : 0.01250, 0.02626, 0.03879, 0.05000 
  Critical values                              : 2.241, 2.091, 2.008, 1.951 
  Stage levels (one-sided)                     : 0.01250, 0.01826, 0.02232, 0.02552

print(sampleSizeResults)

Design plan parameters and output for means:

Design parameters:
  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 
  Local one-sided significance levels          : 0.001074, 0.010012, 0.023983, 0.038976 
  Significance level                           : 0.0500 
  Type II error rate                           : 0.2000 
  Test                                         : one-sided 

User defined parameters: not available

Default parameters:
  Mean ratio                                   : FALSE 
  Theta H0                                     : 0 
  Normal approximation                         : FALSE 
  Alternatives                                 : 0.2, 0.4, 0.6, 0.8, 1.0 
  Standard deviation                           : 1 
  Treatment groups                             : 2 
  Planned allocation ratio                     : 1 

Sample size and output:
  Reject per stage [1]                         : 0.03625 
  Reject per stage [2]                         : 0.26640 
  Reject per stage [3]                         : 0.30072 
  Reject per stage [4]                         : 0.19663 
  Early stop                                   : 0.6034 
  Maximum number of subjects                   : 649.6, 163.5, 73.5, 42, 27.5 
  Maximum number of subjects (1)               : 324.8, 81.7, 36.7, 21, 13.7 
  Maximum number of subjects (2)               : 324.8, 81.7, 36.7, 21, 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, 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, 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, 25.5 
  Expected number of subjects under H1         : 496.6, 125, 56.2, 32.1, 21 
  Critical values (treatment effect scale) [1] : 0.490, 1.029, 1.697, 2.678, 4.519 
  Critical values (treatment effect scale) [2] : 0.259, 0.525, 0.804, 1.108, 1.452 
  Critical values (treatment effect scale) [3] : 0.180, 0.361, 0.545, 0.735, 0.933 
  Critical values (treatment effect scale) [4] : 0.139, 0.277, 0.417, 0.558, 0.701 

Legend:
  (i): values of treatment arm i
  [k]: values at stage k

print(dataset)

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:
  Cumulative sample sizes                      : 22, 22, 33, 35, 55, 57, 66, 70 
  Cumulative means                             : 1.000, 1.400, 1.033, 1.437, 1.020, 2.040, 1.017, 2.126 
  Cumulative standard deviations               : 1.000, 1.000, 1.381, 1.425, 1.639, 1.823, 1.579, 1.739

Print object (kable version)

kable(designGroupSequential)

Design parameters and output of group sequential design

User defined parameters

Type of design: Wang & Tsiatis Delta class
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

Default parameters

Type II error rate: 0.2000
Two-sided power: FALSE
Test: one-sided
Tolerance: 0.00000001

Output

Cumulative alpha spending: 0.001074, 0.010527, 0.028206, 0.050000
Critical values: 3.069, 2.326, 1.978, 1.763
Stage levels (one-sided): 0.001074, 0.010012, 0.023983, 0.038976

kable(designSet)

designNumber	typeOfDesign	kMax	stages	informationRates	alpha	beta	twoSidedPower	deltaWT	sided	alphaSpent	criticalValues	stageLevels
1	WT	4	1	0.25	0.05	0.2	FALSE	0.1	1	0.0010738	3.069028	0.0010738
1	WT	4	2	0.50	0.05	0.2	FALSE	0.1	1	0.0105269	2.325889	0.0100123
1	WT	4	3	0.75	0.05	0.2	FALSE	0.1	1	0.0282060	1.977663	0.0239833
1	WT	4	4	1.00	0.05	0.2	FALSE	0.1	1	0.0500000	1.762694	0.0389761
2	WT	4	1	0.25	0.05	0.2	FALSE	0.3	1	0.0069159	2.461604	0.0069159
2	WT	4	2	0.50	0.05	0.2	FALSE	0.3	1	0.0201692	2.142951	0.0160585
2	WT	4	3	0.75	0.05	0.2	FALSE	0.3	1	0.0351084	1.976032	0.0240756
2	WT	4	4	1.00	0.05	0.2	FALSE	0.3	1	0.0500000	1.865547	0.0310524
3	WT	4	1	0.25	0.05	0.2	FALSE	0.4	1	0.0125050	2.241250	0.0125050
3	WT	4	2	0.50	0.05	0.2	FALSE	0.4	1	0.0262606	2.091160	0.0182569
3	WT	4	3	0.75	0.05	0.2	FALSE	0.4	1	0.0387925	2.008067	0.0223181
3	WT	4	4	1.00	0.05	0.2	FALSE	0.4	1	0.0500000	1.951121	0.0255213

kable(sampleSizeResults)

Design plan parameters and output for means

Design parameters

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
Local one-sided significance levels: 0.001074, 0.010012, 0.023983, 0.038976
Significance level: 0.0500
Type II error rate: 0.2000
Test: one-sided

Default parameters

Mean ratio: FALSE
Theta H0: 0
Normal approximation: FALSE
Alternatives: 0.2, 0.4, 0.6, 0.8, 1.0
Standard deviation: 1
Treatment groups: 2
Planned allocation ratio: 1

Sample size and output

Reject per stage [1]: 0.03625
Reject per stage [2]: 0.26640
Reject per stage [3]: 0.30072
Reject per stage [4]: 0.19663
Early stop: 0.6034
Maximum number of subjects: 649.6, 163.5, 73.5, 42, 27.5
Maximum number of subjects (1): 324.8, 81.7, 36.7, 21, 13.7
Maximum number of subjects (2): 324.8, 81.7, 36.7, 21, 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, 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, 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, 25.5
Expected number of subjects under H1: 496.6, 125, 56.2, 32.1, 21
Critical values (treatment effect scale) [1]: 0.490, 1.029, 1.697, 2.678, 4.519
Critical values (treatment effect scale) [2]: 0.259, 0.525, 0.804, 1.108, 1.452
Critical values (treatment effect scale) [3]: 0.180, 0.361, 0.545, 0.735, 0.933
Critical values (treatment effect scale) [4]: 0.139, 0.277, 0.417, 0.558, 0.701

Legend

(i): values of treatment arm i
[k]: values at stage k

kable(dataset)

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

Cumulative sample sizes: 22, 22, 33, 35, 55, 57, 66, 70
Cumulative means: 1.000, 1.400, 1.033, 1.437, 1.020, 2.040, 1.017, 2.126
Cumulative standard deviations: 1.000, 1.000, 1.381, 1.425, 1.639, 1.823, 1.579, 1.739

Show a summary of the object

kable(summary(designFisher))

Sequential analysis with a maximum of 4 looks (Fisher’s combination test design)

Fisher’s combination test design, binding futility, one-sided overall significance level 2.5%, undefined endpoint.

Stage	1	2	3	4
Information rate	20%	50%	80%	100%
Efficacy boundary (p product scale)	0.01366638	0.00089215	0.00009643	0.00002151
Stage levels (one-sided)	0.0137	0.0137	0.0137	0.0137
Futility boundary (separate p-value scale)	0.400	0.400	0.400
Cumulative alpha spent	0.0137	0.0206	0.0237	0.0250

Design parameters and output of Fisher’s combination test design

User defined parameters

Maximum number of stages: 4
Stages: 1, 2, 3, 4
Information rates: 0.200, 0.500, 0.800, 1.000
Alpha_0: 0.4000, 0.4000, 0.4000

Default parameters

Method: equalAlpha
Significance level: 0.0250
Binding futility: TRUE
Test: one-sided
Tolerance: 0.00000000000001

Output

Cumulative alpha spending: 0.01367, 0.02055, 0.02372, 0.02500
Critical values: 0.01366638, 0.00089215, 0.00009643, 0.00002151
Stage levels (one-sided): 0.01367, 0.01367, 0.01367, 0.01367
Non stochastic curtailment: FALSE

kable(summary(powerResults))

Power calculation for a continuous endpoint

Sequential analysis with a maximum of 4 looks (group sequential design), overall significance level 5% (one-sided). The results were calculated for a two-sample t-test, H0: mu(1) - mu(2) = 0, power directed towards larger values, H1: effect as specified, standard deviation = 1, maximum number of subjects = 100.

Stage	1	2	3	4
Information rate	25%	50%	75%	100%
Efficacy boundary (z-value scale)	3.069	2.326	1.978	1.763
Overall power, alt. = 0	0.0011	0.0105	0.0282	0.0500
Overall power, alt. = 0.2	0.0050	0.0537	0.1431	0.2471
Overall power, alt. = 0.4	0.0189	0.1810	0.4137	0.6140
Overall power, alt. = 0.6	0.0571	0.4163	0.7370	0.8979
Overall power, alt. = 0.8	0.1394	0.6877	0.9317	0.9879
Overall power, alt. = 1	0.2788	0.8831	0.9905	0.9994
Expected number of subjects, alt. = 0	99.0
Expected number of subjects, alt. = 0.2	95.0
Expected number of subjects, alt. = 0.4	84.7
Expected number of subjects, alt. = 0.6	69.7
Expected number of subjects, alt. = 0.8	56.0
Expected number of subjects, alt. = 1	46.2
Number of subjects	25.0	50.0	75.0	100.0
Cumulative alpha spent	0.0011	0.0105	0.0282	0.0500
One-sided local significance level	0.0011	0.0100	0.0240	0.0390
Efficacy boundary (t)	1.382	0.681	0.465	0.356
Exit probability for efficacy (under H0)	0.0011	0.0095	0.0177
Exit probability for efficacy (under H1), alt. = 0	0.0011	0.0095	0.0177
Exit probability for efficacy (under H1), alt. = 0.2	0.0050	0.0486	0.0894
Exit probability for efficacy (under H1), alt. = 0.4	0.0189	0.1621	0.2326
Exit probability for efficacy (under H1), alt. = 0.6	0.0571	0.3592	0.3207
Exit probability for efficacy (under H1), alt. = 0.8	0.1394	0.5483	0.2440
Exit probability for efficacy (under H1), alt. = 1	0.2788	0.6043	0.1074

Legend:

alt.: alternative
(t): treatment effect scale

Design plan parameters and output for means

Design parameters

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
Local one-sided significance levels: 0.001074, 0.010012, 0.023983, 0.038976
Significance level: 0.0500
Test: one-sided

User defined parameters

Direction upper: NA
Maximum number of subjects: 100

Default parameters

Mean ratio: FALSE
Theta H0: 0
Normal approximation: FALSE
Alternatives: 0.0, 0.2, 0.4, 0.6, 0.8, 1.0
Standard deviation: 1
Treatment groups: 2
Planned allocation ratio: 1

Sample size and output

Effect: 0.0, 0.2, 0.4, 0.6, 0.8, 1.0
Overall reject: 0.0500, 0.2471, 0.6140, 0.8979, 0.9879, 0.9994
Reject per stage [1]: 0.001074, 0.005049, 0.018949, 0.057118, 0.139417, 0.278781
Reject per stage [2]: 0.009453, 0.048618, 0.162098, 0.359202, 0.548302, 0.604293
Reject per stage [3]: 0.017679, 0.089440, 0.232641, 0.320713, 0.244012, 0.107409
Reject per stage [4]: 0.021794, 0.103953, 0.200271, 0.160885, 0.056164, 0.008921
Early stop: 0.02821, 0.14311, 0.41369, 0.73703, 0.93173, 0.99048
Expected number of subjects: 99, 95, 84.7, 69.7, 56, 46.2
Number of subjects [1]: 25
Number of subjects [2]: 50
Number of subjects [3]: 75
Number of subjects [4]: 100
Critical values (treatment effect scale) [1]: 1.382
Critical values (treatment effect scale) [2]: 0.681
Critical values (treatment effect scale) [3]: 0.465
Critical values (treatment effect scale) [4]: 0.356

Legend

(i): values of treatment arm i
[k]: values at stage k

kable(summary(analysisResults))

Analysis results for a continuous endpoint

Sequential analysis with 4 looks (group sequential design). The results were calculated using a two-sample t-test (one-sided, alpha = 0.05), equal variances option. H0: mu(1) - mu(2) = 0 against H1: mu(1) - mu(2) > 0.

Stage	1	2	3	4
Fixed weight	0.25	0.5	0.75	1
Efficacy boundary (z-value scale)	3.069	2.326	1.978	1.763
Cumulative alpha spent	0.0011	0.0105	0.0282	0.0500
Stage level	0.0011	0.0100	0.0240	0.0390
Cumulative effect size	-0.400	-0.404	-1.020	-1.109
Cumulative (pooled) standard deviation	1.000	1.404	1.735	1.663
Overall test statistic	-1.327	-1.185	-3.111	-3.887
Overall p-value	0.9041	0.8799	0.9988	0.9999
Test action	continue	continue	continue	accept
Conditional rejection probability	0.0028	0.0001	0
90% repeated confidence interval	[-1.386; 0.586 ]	[-1.216; 0.408 ]	[-1.676; -0.364]	[-1.616; -0.602]
Repeated p-value	>0.5	>0.5	>0.5	>0.5
Final p-value				0.9999
Final confidence interval				[-1.547; -0.608]
Median unbiased estimate				-1.078

Analysis results (means of 2 groups, group sequential design)

Design parameters

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
Local one-sided significance levels: 0.001074, 0.010012, 0.023983, 0.038976
Significance level: 0.0500
Test: one-sided

Default parameters

Normal approximation: FALSE
Direction upper: TRUE
Theta H0: 0
Equal variances: TRUE

Stage results

Cumulative effect sizes: -0.4000, -0.4038, -1.0204, -1.1090
Cumulative (pooled) standard deviations: 1.000, 1.404, 1.735, 1.663
Stage-wise test statistics: -1.327, -0.488, -3.317, -2.817
Stage-wise 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

Analysis results

Assumed standard deviation: 1.663
Actions: continue, continue, continue, accept
Conditional rejection probability: 0.0028101, 0.0001227, 0.0000000, NA
Conditional power: NA, NA, NA, NA
Repeated confidence intervals (lower): -1.386, -1.216, -1.676, -1.616
Repeated confidence intervals (upper): 0.5861, 0.4084, -0.3644, -0.6022
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, -1.547
Final CIs (upper): NA, NA, NA, -0.6082
Median unbiased estimate: NA, NA, NA, -1.078

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

as.data.frame(designGroupSequential)

  typeOfDesign kMax stages informationRates alpha beta twoSidedPower deltaWT
1           WT    4      1             0.25  0.05  0.2         FALSE     0.1
2           WT    4      2             0.50  0.05  0.2         FALSE     0.1
3           WT    4      3             0.75  0.05  0.2         FALSE     0.1
4           WT    4      4             1.00  0.05  0.2         FALSE     0.1
  sided  tolerance  alphaSpent criticalValues stageLevels
1     1 0.00000001 0.001073781       3.069028 0.001073781
2     1 0.00000001 0.010526914       2.325888 0.010012250
3     1 0.00000001 0.028205994       1.977663 0.023983344
4     1 0.00000001 0.050000000       1.762694 0.038976069

as.data.frame(dataset)

  stages groups sampleSizes means stDevs overallSampleSizes overallMeans
1      1      1          22   1.0    1.0                 22     1.000000
2      1      2          22   1.4    1.0                 22     1.400000
3      2      1          11   1.1    2.0                 33     1.033333
4      2      2          13   1.5    2.0                 35     1.437143
5      3      1          22   1.0    2.0                 55     1.020000
6      3      2          22   3.0    2.0                 57     2.040351
7      4      1          11   1.0    1.3                 66     1.016667
8      4      2          13   2.5    1.3                 70     2.125714
  overallStDevs
1      1.000000
2      1.000000
3      1.381500
4      1.425418
5      1.639151
6      1.822857
7      1.578664
8      1.738706

Coerce object to data.frame: as.data.frame with argument ‘niceColumnNamesEnabled = TRUE’

as.data.frame(designFisher, niceColumnNamesEnabled = TRUE)

      Method Maximum # stages Stage Information rate Significance level Alpha_0
1 equalAlpha                4     1              0.2              0.025     0.4
2 equalAlpha                4     2              0.5              0.025     0.4
3 equalAlpha                4     3              0.8              0.025     0.4
4 equalAlpha                4     4              1.0              0.025      NA
  Binding futility Test        Tolerance Cumulative alpha spending
1             TRUE    1 0.00000000000001                0.01366638
2             TRUE    1 0.00000000000001                0.02055086
3             TRUE    1 0.00000000000001                0.02372061
4             TRUE    1 0.00000000000001                0.02500000
  Critical value Stage level Non stochastic curtailment
1  0.01366637982  0.01366638                      FALSE
2  0.00089215382  0.01366638                      FALSE
3  0.00009643023  0.01366638                      FALSE
4  0.00002151406  0.01366638                      FALSE

as.data.frame(designCharacteristics, niceColumnNamesEnabled = TRUE)

  Inflation factor Stage Information      Power Rejection probability under H1
1          1.04846     1    1.620541 0.03624538                     0.03624538
2          1.04846     2    3.241081 0.30264612                     0.26640074
3          1.04846     3    4.861622 0.60337036                     0.30072424
4          1.04846     4    6.482163 0.80000000                     0.19662964
  Futility probability under H1 Ratio expected vs fixed sample size under H1
1                             0                                    0.8014789
2                             0                                    0.8014789
3                             0                                    0.8014789
4                            NA                                    0.8014789
  Ratio expected vs fixed sample size under a value between H0 and H1
1                                                           0.9724133
2                                                           0.9724133
3                                                           0.9724133
4                                                           0.9724133
  Ratio expected vs fixed sample size under H0
1                                     1.038026
2                                     1.038026
3                                     1.038026
4                                     1.038026

as.data.frame(powerAndASN, niceColumnNamesEnabled = TRUE)

  Stage Effect Average sample size (ASN)     Power Early stop Overall reject
1     1    0.5                   26.7863 0.9266075 0.06839003      0.9266075
2     2    0.5                   26.7863 0.9266075 0.39887080      0.9266075
3     3    0.5                   26.7863 0.9266075 0.31845861      0.9266075
4     4    0.5                   26.7863 0.9266075         NA      0.9266075
  Reject per stage  Overall futility Futility stop per stage
1       0.06839003 0.000000002898419      0.0000000009865876
2       0.39887080 0.000000002898419      0.0000000009758407
3       0.31845861 0.000000002898419      0.0000000009359906
4       0.14088808 0.000000002898419                      NA

Coerce object to matrix: as.matrix

as.matrix(designGroupSequential)

 Stage Type of design Maximum # stages Information rate Significance level
 "1"   "WT"           "4"              "0.25"           "0.05"            
 "2"   "WT"           "4"              "0.50"           "0.05"            
 "3"   "WT"           "4"              "0.75"           "0.05"            
 "4"   "WT"           "4"              "1.00"           "0.05"            
 Type II error rate Two-sided power Delta (Wang & Tsiatis) Test Tolerance   
 "0.2"              "FALSE"         "0.1"                  "1"  "0.00000001"
 "0.2"              "FALSE"         "0.1"                  "1"  "0.00000001"
 "0.2"              "FALSE"         "0.1"                  "1"  "0.00000001"
 "0.2"              "FALSE"         "0.1"                  "1"  "0.00000001"
 Cumulative alpha spending Critical value Stage level  
 "0.001073781"             "3.069028"     "0.001073781"
 "0.010526914"             "2.325888"     "0.010012250"
 "0.028205994"             "1.977663"     "0.023983344"
 "0.050000000"             "1.762694"     "0.038976069"

System: rpact 3.4.0, R version 4.2.2 (2022-10-31 ucrt), platform: x86_64-w64-mingw32

To cite R in publications use:

R Core Team (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

To cite package ‘rpact’ in publications use:

Wassmer G, Pahlke F (2023). rpact: Confirmatory Adaptive Clinical Trial Design and Analysis. https://www.rpact.org, https://www.rpact.com, https://github.com/rpact-com/rpact, https://rpact-com.github.io/rpact/.

Reuse

https://creativecommons.org/licenses/by-sa/4.0/