library(rpact)
packageVersion("rpact") # version should be version 3.0 or laterHow 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.
Creating examples of selected rpact result objects
First, load the rpact package
[1] '3.3.4'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 1.762694designGroupSequential[["criticalValues"]][1] 3.069028 2.325888 1.977663 1.762694Print 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 kprint(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 | tolerance | alphaSpent | criticalValues | stageLevels |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | WT | 4 | 1 | 0.25 | 0.05 | 0.2 | FALSE | 0.1 | 1 | 0 | 0.0010738 | 3.069028 | 0.0010738 |
| 1 | WT | 4 | 2 | 0.50 | 0.05 | 0.2 | FALSE | 0.1 | 1 | 0 | 0.0105269 | 2.325889 | 0.0100123 |
| 1 | WT | 4 | 3 | 0.75 | 0.05 | 0.2 | FALSE | 0.1 | 1 | 0 | 0.0282060 | 1.977663 | 0.0239833 |
| 1 | WT | 4 | 4 | 1.00 | 0.05 | 0.2 | FALSE | 0.1 | 1 | 0 | 0.0500000 | 1.762694 | 0.0389761 |
| 2 | WT | 4 | 1 | 0.25 | 0.05 | 0.2 | FALSE | 0.3 | 1 | 0 | 0.0069159 | 2.461604 | 0.0069159 |
| 2 | WT | 4 | 2 | 0.50 | 0.05 | 0.2 | FALSE | 0.3 | 1 | 0 | 0.0201692 | 2.142951 | 0.0160585 |
| 2 | WT | 4 | 3 | 0.75 | 0.05 | 0.2 | FALSE | 0.3 | 1 | 0 | 0.0351084 | 1.976032 | 0.0240756 |
| 2 | WT | 4 | 4 | 1.00 | 0.05 | 0.2 | FALSE | 0.3 | 1 | 0 | 0.0500000 | 1.865547 | 0.0310524 |
| 3 | WT | 4 | 1 | 0.25 | 0.05 | 0.2 | FALSE | 0.4 | 1 | 0 | 0.0125050 | 2.241250 | 0.0125050 |
| 3 | WT | 4 | 2 | 0.50 | 0.05 | 0.2 | FALSE | 0.4 | 1 | 0 | 0.0262606 | 2.091160 | 0.0182569 |
| 3 | WT | 4 | 3 | 0.75 | 0.05 | 0.2 | FALSE | 0.4 | 1 | 0 | 0.0387925 | 2.008067 | 0.0223181 |
| 3 | WT | 4 | 4 | 1.00 | 0.05 | 0.2 | FALSE | 0.4 | 1 | 0 | 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 | 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 |
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
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 |
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 0.038976069as.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 1.738706Coerce 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 FALSEas.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 1.038026as.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 NACoerce 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 3.3.4, 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.